PY 121 Passaic County Community College Physics II The Faraday Pail Lab Report

User Generated

Nyfnu123

Science

PY 121

Passaic County Community College

PY

Description

please help with labs 5 and 6 due monday please thank you please work on it carefully thoroughly

Unformatted Attachment Preview

Laboratory Manual PY-121 Physics II Wayne Warrick Passaic County Community College Laboratory Manual PY-121 Physics II Laboratory Passaic County Community College Instructor: Wayne Warrick Introduction As part of the Passaic County Community College physics course sequence, the laboratory is a required and integral component to all offered physics courses within the Biological and Physical Sciences Department. This manual will act as a comprehensive reference guide for students to follow during each laboratory experiment. The following pages will detail the laboratory grading criteria, expected report format, laboratory safety and etiquette protocol, and detailed instructions for each experiment. Each laboratory section of this manual includes the necessary theoretical background, pertaining to physics, in order for students to perform each experiment. The laboratory aspect of physics, as with any physical or life science course, represents a necessary part to gather not only an adequate understanding of physics but to obtain a solid foundation which will benefit students of all STEM majors. This is why it is highly recommended to read through this manual, ahead of time, so that you are prepared to not only follow along in the lab, but to actively engage with each of your colleagues and understand each experiment. Additional references, links, and helpful websites are listed within each experiment section. Laboratory Manual Authored by: Wayne Warrick May 22nd, 2019 Rev: August 27th, 2019, January 7th, 2020, June 2020 Table of Contents Laboratory Requirements___________________________________________________________ 1 Laboratory Grading Criteria________________________________________________________ 2 Sample Laboratory Report__________________________________________________________ 3 Laboratory 1: Simple Harmonic Motion________________________________________________ 4 Laboratory 1: Prelab________________________________________________________________ 6 Laboratory 2: The Simple Pendulum___________________________________________________ 9 Laboratory 2: Prelab_______________________________________________________________ 11 Laboratory 3: Standing Waves and Resonance__________________________________________ 13 Laboratory 3: Prelab_______________________________________________________________ 16 Laboratory 4: Demonstrations of Static Electricity and The Electroscope______________________ 18 Laboratory 4: Prelab_______________________________________________________________ 20 Laboratory 5: The Faraday Pail______________________________________________________ 22 Laboratory 5: Prelab_______________________________________________________________ 23 Laboratory 6: Equipotential Mapping_________________________________________________ 25 Laboratory 6: Prelab_______________________________________________________________ 27 Laboratory 7: DC Circuits__________________________________________________________ 29 Laboratory 7: Prelab_______________________________________________________________ 31 Laboratory 8: RC Circuits___________________________________________________________34 Laboratory 8: Prelab_______________________________________________________________ 37 Laboratory 9: Magnetic Fields and Ampere’s Law_______________________________________ 39 Laboratory 9: Prelab_______________________________________________________________ 41 Laboratory 10: Faraday’s Law of Induction and Lenz’s Law________________________________44 Laboratory 10: Prelab______________________________________________________________ 46 References_______________________________________________________________________ 49 Laboratory Requirements PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick The laboratory portion of the course counts towards 25% of the final course grade. In total, throughout the semester, there will be eleven (11) laboratory experiments. Each lab report will be graded out of a total of 10 (ten) points. Unless otherwise stated, each experiment will require a written report. The required format of this report is detailed in the Sample Lab Report section of this manual. The laboratory assessment for each report is divided into the following categories: Prelab, Participation, Experimental Data Collection, and the submitted Lab Report. Each of these categories and grading criteria is explained below. 1) Prelab The prelab is intended to prepare students for the laboratory experiment. Before handling sensitive apparatus, complicated equipment, computer-controlled data collection, or virtual lab simulations, etc., it is necessary to have an adequate understanding of the experimental requirements prior to beginning the lab. The prelab will test your knowledge and comprehension of the necessary theory of physics required to perform the experiment as well as a training preview to demonstrate each student’s level of preparedness for the experiment. The prelab questions do not have to be submitted, rather these questions will be asked by the instructor at the beginning of each lab session. Students who do not successfully answer the prelab questions are not permitted to perform the experiment for that week. The prelab for each experiment can be found in the lab manual. Read Ahead! It is imperative to read the lab manual prior to performing each experiment. 2) Participation Laboratory attendance is mandatory. For the beginning of each lab session students are required to participate, e.g. answer questions posed by the instructor. The experiments are to be performed individually by each student on their own time. Additional details regarding the attendance portion of the lab can be found on the course syllabus. Lab Safety The instructor will discuss the safety aspects of each experiment at the beginning of the laboratory as if the experiments were conducted in a non-virtual environment. 3) Experimental Data During each lab experiment, students will collect data, often a lot of data. Sometimes this is manual data, read from protractors, meter sticks, and scales, other times it is data from electronic instrumentation, micro-controlled devices, or as in the case of this semester, virtual simulation data. Each student will be graded on the quality and completeness of their collected data. It is recommended that each student record their data from each experiment in a lab notebook. 4) Report Each student will submit one lab report corresponding to each lab. The format for the report can be found in the Sample Lab Report section of this lab manual. 1 Lab Report Grading Criteria Each lab report is graded out of ten (10) points. The grading is based on the following criteria: • • • • • • • Did the student include the abstract? Does the abstract include a brief summary of the critical results, values and findings from the experiment? Does the lab report contain and present all of the required experimental data? Does the lab report contain data analysis, calculations, tables, graphs with each axis labeled? Are the correct units included? etc. Does the lab report contain plagiarized content? Were all of the questions answered correctly? Was the lab report submitted by the due date? Refer to the syllabus. Careful! If a lab report contains data, pictures, answers, etc. obtained from external sources, for example, internet, other lab groups, etc., this will count as plagiarism, and the student will receive a zero for that report. Lab Report Submission The lab reports must be typed up. This includes data, tables, answers to questions, etc. The graphs and plots must be electronically created. The calculations may either be typed up or hand-written. The completed lab reports must be submitted electronically as one file. The completed lab report is to be submitted to Blackboard. Each lab report is due the Monday of the following week. Lab Final Exam There will be a lab final exam at the end of the semester, usually the last lab session. This exam will be based on the laboratory experiments from the semester. The lab exam will be a cumulative assessment based on prelab questions, virtual experiments, and the introductions as found in the lab manual. The lab final exam will count towards 10% of the lab portion of the course. If a student fails the lab portion of the course, the student will receive a failing grade for the course. Please review the course syllabus for additional details regarding the lab portion of the course. 2 Sample Lab Report-Summer III Only PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Lab # Lab Title Student First and Last name Date of Experiment: mm/dd/year Instructor’s Name: Abstract An abstract is a brief overall summary of the experiment. The abstract should be written as though you were explaining this to a colleague as a summary of the experiment. A reader should be able to grasp a basic understanding of what happened during the experiment simply by reading the abstract. It is preferred to use the active voice. This means that you write as though the event was recently performed in the lab, not in the past. For example: instead of writing “we studied,” you should write “in this experiment we study the effects of...” Here, you will also summarize the conclusions from the experiment. The abstract only needs to be one paragraph. Include a brief summary of the critical results, values and findings in the abstract. Results and Analysis In this section, you will present your experimental results. This is where you report your data, equations, calculations, tables, graphs, etc. Be sure to show all pertinent calculations. Number the tables, graphs, pictures, etc. Label each axis of a graph and include units. Do not copy material from the instructor’s lab manual. Questions In the lab report, include the complete answers to all questions in the lab manual pertaining to the specific experiment. Lab Report Submission The lab reports must be typed up. This includes data, tables, answers to questions, etc. The graphs and plots must be electronically created. The calculations may either be typed up or hand-written. The completed lab reports must be submitted electronically as one file. The completed lab report is to be submitted to Blackboard. Each report is due the Monday of the following week. 3 Laboratory 1 Simple Harmonic Oscillation PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The objective of this lab is to determine the spring constant of a real (non-ideal) spring by utilizing the theory of simple harmonic motion as covered in the course. Two methods will be used to determine the spring constant. In Part 1, by application of Hooke’s Law with the aid of graphical analysis the spring constant can be determined. In Part 2, the spring constant can be found by observing oscillations of the spring when a known mass is placed on it and timing the period of oscillation. For Part 1 of this lab, the spring constant will be determined using Hooke’s Law, which states that when a spring is displaced some amount Δr, the spring exerts a restoring force in the opposite direction towards its equilibrium position, as given by, 𝑭# = −𝑘Δ𝒓 (1) The Δ𝒓 is used instead of x because the displacement could be either along the x or the y-axis. k is the spring constant. The magnitude of the restoring force is directly proportional to the displacement 𝒓. The direction of the restoring force is opposite to the displacement. A plot of force as a function of displacement will yield the force constant. From Newton’s second law, the acceleration of the mass as it oscillates can be written as, + 𝒂* = − , 𝒙 (2) + The subscript indicates the acceleration is in the x-direction. The constant, , can be replaced with the square of the angular frequency so that the acceleration can be expressed as, 𝒂* = −𝜔/ 𝒙 (3) The acceleration of the mass can be expressed in terms of the displacement by taking the second derivative of the displacement as a function of time as shown in Eq. 4. 01 𝒙 02 1 = −𝜔/ 𝒙 (4) The solution to this second order ordinary differential equation is, 𝑥(𝑡) = 𝐴𝑐𝑜𝑠(𝜔𝑡 + 𝜙) (5) Where, A is the amplitude of the motion of the mass as it oscillates, 𝜔 is the angular frequency of the oscillations, and 𝜙 is the phase constant representing the displacement of the motion at t = 0. The velocity of the mass can be determined by taking the derivative of the displacement Eq. (5). 4 𝑣 (𝑡 ) = 0* = −𝜔𝐴𝑠𝑖𝑛(𝜔𝑡 + 𝜙) 02 (6) The acceleration of the mass can be determined by taking the derivative of the velocity Eq. (6). 𝑎 (𝑡 ) = 01 * 02 1 = −𝜔/ 𝐴𝑐𝑜𝑠(𝜔𝑡 + 𝜙) (7) In Part 2 of this lab, the spring constant will be determined by observing simple harmonic oscillations (SHM). From the theory of SHM, we know the period of oscillation is given by, 𝑇= /B C = 2𝜋F ,GHGIJ (8) + The period of oscillation, T can be directly measured by observing the oscillations of the spring and timing the duration of the period. However, the spring cannot be treated as an ideal spring. This means that we must take the mass of the spring into account. Add onethird of the mass of the spring to the value of the suspended mass. Also, include the mass of the mass hanger. The total mass is the combined mass of the mass hanger, added mass and one-third of the mass of the spring. Fig. 1 illustrates the conceptual setup of this experiment. Notice that unlike the examples in class, where the spring is on a horizontal surface, the spring is now hanging vertically. This is actually an easier experiment since attempting to create a nearly frictionless horizontal surface would be very difficult. This also means that your expressions should include the subscript y and not x. Figure 1. Vertical spring with mass attached [1]. The kinetic energy of the mass can be found using, M 𝐾𝐸 = / 𝑚𝑣 / (9) The potential energy of the spring can be found using, M 𝑈# = / 𝑘𝑥 / (10) Substituting in Eq. (5), the total energy of the mass-spring system is given by, M 𝐸 = / 𝑘𝐴/ 5 (11) Laboratory 1-Prelab Simple Harmonic Motion PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What does the negative sign in Hooke’s law represent? Question 2 If the mass of the spring is not neglected, can we still treat the mass as a particle and analyze the massspring system? Question 3 How do we take the mass of a non-ideal spring into account? Question 4 During simple harmonic motion, where does the oscillating object have its maximum velocity? Question 5 At what points does a spring oscillating with simple harmonic motion have its maximum elastic potential energy? 6 Lab Procedure Part 1 Step 1) The spring is vertically supported from a workbench and allowed to reach equilibrium. Step 2) Visit the site: https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html Step 3) Select the Lab icon. Step 4) Set the Damping scale to 1/6th and slide the Spring Constant scale to small. Step 5) Place the ruler next to the spring. Step 6) Slide the mass scale to a value between 50g and 100 g. Step 7) Attach the mass to the spring. Assume that the added mass includes the mass hanger. Step 8) Allow the mass-spring system to reach equilibrium. Click the Mass Equilibrium box. Step 9) Use the ruler to measure the displacement of the spring and calculate the spring constant. Step 10) Repeat Steps 6 through 9 using consistent increments of masses. Do not add too much mass. Step 11) Calculate the value for the spring constant for each trial. Fill in Table 1. Show all calculations. Step 12) Use graphical analysis software, plot the force as a function of displacement. • If you do not have access to Excel, Vernier Graph Analysis can be downloaded online for free. Step 13) Perform a linear regression fit of the data. Include this plot in your lab report. m(added) (kg) m(spring) (kg) 0.030 0.030 0.030 0.030 0.030 m(total) (kg) Table 1 Force (N) Displacement (m) k (N/m) Calculate the kinetic energy of the hanging mass as it oscillates, the potential energy of the spring, and the total mechanical energy of the mass-spring oscillating system. For the value of mass, use the data from Trial 1. Use x = A as the total displacement. KEmass = ________ (J), Us = ___________ (J), ETotal = ____________ (J) Part 2 Step 1) Use the same simulation as Part 1. Step 2) Set the damping scale to 1/6th and slide the Spring Constant scale to small. Step 3) Place the ruler next to the spring. Step 4) A photogate timer is aligned so that the mass completely passes through the sensor when the spring is displaced. Select the Period Trace box. 7 Step 5) The time it takes for the spring-mass system to oscillate one (1) period is measured and recorded. Click and drag the stop watch and place it next to the ruler. By clicking on the Slow button, it will be easier to measure the period. Step 6) Attach a mass to the spring and record the period. Step 7) Use the value obtained from Step 6) to calculate the spring constant. Step 8) Steps 6 and 7 were repeated for a total of five (5) trials using the same value of mass. Step 9) When performing this experiment in the lab there is human reaction time error present. This will also be the case for the simulation. There will be delay between the beginning of oscillation and the start of the stop watch. Step 10) Fill in Table 2. Show all calculations. Trial T (s) k (N/m) Tavg = _________ (s), 1 Table 2 2 3 4 5 kavg = _________ (N/m) When t = ½ Tavg, calculate the velocity and the acceleration of the hanging mass. vmass = __________ (m/s), amass = ___________ (m/s2) Questions 1) How does the value of the spring constant found in Part 1 compare to the value found in Part 2? 2) Why was it necessary to take the mass of the spring into account? 3) When does the velocity of the hanging mass reach its maximum value? 4) When does the acceleration of the hanging mass reach its maximum value? 5) When the spring is fully stretched, does the mass have any kinetic energy at this point? The total energy of the system would then be? 6) If the spring is stretched too much, does Hooke’s Law still apply? Include all data, graphs, tables, calculations, and answers to these questions in the lab report. 8 Laboratory 2 The Simple Pendulum PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The objective of this lab is to construct and analyze a simple pendulum. Initially, the mass of the pendulum bob will be held constant while the length of the cord and displacement angle will vary. This data will be used to determine the period of the pendulum, verify the small angle approximation, which is crucial to the simple pendulum approximation, and verify that the period is independent of mass. By measuring the period and the cord length of the pendulum, the acceleration due to gravity can be determined and compared to the standard value. Fig. 1 shows a diagram of a simple pendulum in which the bob was displaced to the right. The weight of the pendulum bob is indicated. This weight has both a tangential and a vertical component. The tangential component contributes to the motion of the pendulum. The length (L) is the distance from the center of the pivot to the center of the bob. The angle (𝜃) is the angle between the pendulum cord and the dotted vertical line. Figure 1. Simple pendulum [1]. From Newton’s second law an expression for the motion of the pendulum is, 01 # −𝑚𝑔𝑠𝑖𝑛𝜃 = 𝑚 02 1 (1) The negative sign indicates that the bob swings opposite to its displacement. Notice that the mass of the bob cancels. The relation between the length of the pendulum cord and the angle is 𝑠 = 𝐿𝜃. Substituting this into Eq. (1) gives us, 01 T 02 1 U = − V 𝑠𝑖𝑛𝜃 (2) This differential equation can be simplified if the small angle approximation is utilized, which states that 𝑠𝑖𝑛𝜃 = 𝜃. Eq. (2) then simplifies to, 01 T 02 1 U =−V𝜃 (3) The solution to this differential equation has a form similar to that of simple harmonic motion. The angular frequency of the pendulum bob is, U 𝜔 = FV The period of oscillation of the pendulum is, 9 (4) 𝑇= /B C = 2𝜋F V U (5) Notice that the period of the pendulum is independent of the mass and only depends on the length of the cord and the acceleration due to gravity, both of which are constant. Accordingly, for a constant mass, the period should change when the length of the cord changes. This will also be verified in this experiment. Fig. 2 shows the experimental setup for this lab. Two cords are used so that the motion of the pendulum remains in one plane. The pendulum bob should be a flat disk or a box so that no rotational motion is developed. The photogate timer sensor is placed so that it can record the period of motion. Be careful not to swing the bob in a circular pattern. This is called a canonical pendulum. Keep the bob swinging along a vertical plane. The mass of the cord can be neglected. Figure 2. Experimental setup of the pendulum and photogate timer. The zoomed in portion illustrates pendulum bob moving past the photogate timer. As the pendulum swings upward, the bob gains gravitational potential energy, mgh. Trigonometry must be used to determine the change and is a function of the angle of displacement, 𝜃 and is given by Eq. 6. Δℎ = 𝐿(1 − 𝑐𝑜𝑠𝜃) (6) The gravitational potential energy of the pendulum bob is then, 𝑃𝐸U = 𝑚𝑔[𝐿(1 − 𝑐𝑜𝑠𝜃)] (7) After the bob is release and allowed to swing downward, 𝑃𝐸U is converted into kinetic energy. The kinetic energy can be expressed as, M M ]0 / 𝐾𝐸 = / 𝑚𝑣 / = / 𝑚 \ 2 ^ 10 (8) Laboratory 2-Prelab The Simple Pendulum PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 Why can we neglect the mass of the pendulum string? Question 2 How can the small-angle approximations be justified? Explain. Question 3 How is using the small angle approximation going to help us? Explain. Question 4 Does the period of a simple pendulum depend on the mass of the bob? Explain. Question 5 Which component of the motion of the pendulum bob is responsible for its motion? Question 6 When does the pendulum have its maximum and minimum kinetic energy? What about its maximum and minimum gravitational potential energy? 11 Lab Procedure Part 1 Step 1) Visit the website: https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulumlab_en.html Step 2) Select the Lab icon. Step 3) The mass of the pendulum bob is 0.50 kg. Step 4) Set the length of the cord to 80.0 cm. Step 5) Select the Ruler, Stopwatch and Period Timer. Step 6) Make sure that the Gravity is set to 9.81 m/s2 and the Friction is set to 1/10th the full scale. Step 7) Gently displace the bob from the vertical reference (0o) to 5o using the protractor as a guide. At this same instant start the stopwatch. By clicking on the Slow button, it will be easier to measure the period. Step 8) Record the time it takes the pendulum bob to oscillate one (1) period and record this value. Step 9) Repeat Steps 7 and 8 incrementally increasing the angle of displacement as indicated in Table 1. Step 10) Repeat Step 4 through 9 for incrementally decreasing cord lengths. Fill in Table 1. Step 11) Make a plot of the period as a function of length using the measured values. Determine the slop of the graph. Step 12) Double the mass of the bob and take 𝜃 = 10` and L = 60 cm. Does the period change? Step 13) Using the value for the period when 𝜃 = 5` and L = 4cm, calculate the value for the acceleration due to gravity. 𝜽, 𝑳 20 cm 5o Tmeas._______s Table 1 40 cm Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s Tmeas._______s 10o 20o 30o 60 cm 40 cm Tmeas._______s Tmeas._______s Questions 1) Which component of the mass of the bob contributes to the motion of the pendulum? 2) Why is the period of oscillation independent of the mass of the bob? 3) How is it that the mass of the pendulum cord can be neglected? 4) What is the purpose of using the small angle approximation? Is it a reliable approximation? 5) At what angle did the small angle approximation begin to break down? 6) Did the experimental value for (g) come close to the standard value? 7) Was mechanical energy conserved for each oscillation of the pendulum? 8) Why does the pendulum begin to slow down? Be sure to show all data, calculations, graphs and answers to these questions in the lab report. 12 Laboratory 3 Standing Waves and Resonance PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction In this lab mechanical standing waves and resonance will be studied. In Part 1, the velocity of a transverse standing wave on a taught piece of string will be determined. The source of the wave is a mechanical wave generator. The desired frequency of the wave is controllable. Using this value of frequency and accurate measurements of the string’s mass and length, the value of added mass can be calculated. Once this value is known, the wave velocity can be determined. A comparison will be made between two variations of wave velocity expressions. From this, we can more clearly see the relationship between velocity, wavelength, mass, and frequency for transverse waves. In Part 2, a piston apparatus, and a tuning fork will be used to produce standing waves in an air column. By adjusting the position of the piston, the apparent length of the tube can be changed. With an understanding of the relationship between tube length, source frequency, and the velocity of sound in air, an audible amplification, i.e. resonance of the original source frequency can be observed. In order to produce a mechanical wave, there needs to be a source. In Part 1, the source will be a mechanical wave generator supplied power from an AC function generator. A frequency of 50 Hz will be used. A calculated value of mass will be hung over a pulley. Fig. 1 illustrates the experimental setup. Figure 1. Experimental setup of the wave generator, string, pulley and mass system. In order to generate consistent standing waves, the string must be taught. This implies that the string must be stretched to a certain tension. The tension is simply the force due to the vertical masses, as shown in Fig. 1. Direct observation of the wavelength would be impossible. In order to determine the value of this mass, we can use the expression, 𝑚= e fg1 V1 Uh1 (1) From Eq. 1, 𝜇 is the mass per unit length of the string, in kg/m. This can be obtained by using a sensitive balance. The length is simply the measured length of the string, not including the part used for connections, or the vertical section. f is the frequency measured in Hertz. For this lab, a range of 50-100 13 Hz will be used. L is loop length from one node to the next. g is the acceleration due to gravity and n is the number of antinodes, which is illustrated in Fig. 2. In order to obtain a standing wave pattern as shown in Fig. 2, both ends of the string needs to be fixed. This is accomplished with the vertical masses. The intersection of the two sine waves is called a node. This is a region of no vibration. The antinode is the peak of the wave. This is a region of maximum vibration. Anti-Node Node Figure 2. An upright transmitted sine wave superimposed on a reflected inverted sine wave with nodes and anti-nodes. The distance from one wave crest to the next is called the wavelength 𝜆. From Fig. 2, it should be clear that, one loop is one-half of one wavelength. Eq. 2 is an expression relating the wavelength to n. This equation is necessary sine we cannot directly measure the wavelength of the string wave since a frequency of 50 Hz is too fast for us to observe. 𝜆=F /V h (2) The velocity of a transverse wave on a string is given as, k 𝑣= F f (3) This tells us that the velocity is dependent on the tension on the string, the mass of the string and the length of the string. Another expression for traveling wave velocity is expressed as, 𝑣 = 𝑓𝜆 (4) Notice that this expression is essentially distance over time and holds for all types of waves. In order to study the effects of sound waves propagating through a medium, such as air, a source of sound is required. For this part of the lab, a tuning fork will be used as the sound source. This sound wave will propagate through the air within a closed column. The velocity of this sound wave is dependent on a few factors. Since the lab is being conducted at standard room temperature, we can neglect the effects of temperature on the sound wave since the temperature of the air inside of the column will remain constant throughout the experiment. This propagating sound wave is a traveling wave since it travels from one side of the tube (the source) to the other side, the closed end, which acts as a boundary. As with any wave, this traveling wave propagates with some velocity, in this case the speed of sound in air, and some frequency. When the wave strikes the closed end (boundary), it reflects back towards the direction of the source. This reflected wave travels in the opposite direction as the wave from the source. If it reflects at a particular frequency it will produce an interference pattern, i.e. if the reflected wave is phase-shifted in such a way with respect to the incident wave from the source, a stationary or standing wave will occur. 14 Depending on how much this reflected wave is phase-shifted will determine what effects are observed. If the reflected wave has a zero displacement relative to the original wave, this is called a node. Here, the amplitude, which is a superposition of the two waves, is zero, i.e. the waves cancel out. The waves are completely out of phase. If the reflected wave has a maximum displacement relative to the original wave, this is called an antinode. Here, the amplitude is maximum and the two waves constructively add together. Depending on the length of the column of air, which can be adjusted with the piston, there can exist multiple nodes and antinodes. This is most noticeable in musical instruments. If both ends of the air column are fixed (closed), the maximum wave length can fit inside is onehalf since the wave must have nodes at both ends. Following this logically, the only allowable increments of smaller waves lengths inside of the closed column are: 1, 3/2, etc. If we count the number of antinodes on the wave, each introduction of another antinode is called a harmonic. The relationship between the frequency of the source, the tube length and the velocity of sound in air is, m 𝑓h = 𝑛 /V , n = 1, 2, 3,… (5) 𝑓h is the natural frequency, 𝑣 is the velocity of sound in the air column, L is the length of the air column, n is the number of antinodes present in the air column. When n = 1, which represents the largest wavelength that can fit inside the column, this is called the fundamental frequency. Eq. 5 therefore, represents multiples of the frequency. If one end is open, as is the case for many musical instruments, then the largest wavelength that can fit inside of the column is one-quarter. The closed end node is called the displacement node and the open end is called the pressure antinode. If a higher audible pitch is desired, waves of higher frequency inside of the column are needed. The amplification of the original frequency from the tuning fork is called resonance. Resonance occurs when there is a drastic increase in the amplitude of the propagating sound wave. These higher frequency waves need to satisfy two conditions: 1) nodes at closed end, 2) antinodes at the open end. The relationship between the frequency of the source, the tube length and the velocity of sound in air is, m 𝑓h = 𝑛 eV , n = 1, 3, 5,… (6) n is the harmonic order. Notice that only an odd-number of harmonics is present. Compare this to the closed-closed tube where all harmonics are present. 15 Laboratory 3-Prelab Mechanical Standing Waves PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What is the difference between a transverse and longitudinal wave? Question 2 What is the difference between a traveling wave and a standing wave? Question 3 How much wave vibration is there is at node? Question 4 How does the tension of the cord affect the velocity of the wave? Question 5 Does the suspended mass act as a node or an antinode? Question 6 When analyzing the standing wave, do we need to include the portion of the vertically-hanging string length? 16 Lab Procedure Part 1 Step 1) Visit the website: https://ophysics.com/w8.html Step 2) Set the function generator vibration frequency to 100.0 Hz. Step 3) Set the linear density to 0.76 x 10-3 kg/m. Step 4) Set the Tension to the value found from Table 1. Step 5) Click the Play button. Step 6) Fill in Table 1. Show all calculations. Table 1 Total Mass (kg) Tension (N) 𝑻 𝝀 (m) 𝒗 = F𝝁 (m/s) 𝒗 = 𝒇𝝀 (m/s) n 10.0 Part 2 Step 1) A resonance tube is placed on the work bench. One end is left open and the other end is closed. Step 2) Visit the website: https://ophysics.com/w10.html Step 3) The velocity of the air in the lab is measured to be 343.0 m/s at room temperature. Step 4) A 500.0 Hz tuning fork is struck and placed at the open end of the tube. Step 5) Calculate the required length of the tube in order to hear the first fundamental frequency. Step 6) The apparent length of the tube can be adjusted. The tube is doubled from its original size. What frequency of tuning fork is needed to be able to hear the third harmonic? Step 7) The tube is tripled from its original size. What frequency of tuning fork is needed to be able to hear the fifth harmonic? Step 8) Fill in Table 2. Show all calculations. Tuning Fork Frequency (Hz) Table 2 Wavelength of Sound Tube Length (m) (m) Velocity (m/s) Questions Part 1 1) Can a standing wave be produced on a string with a free end? 2) How does the mass affect the velocity of the wave on the string? 3) What effect would increasing the cord diameter have on the velocity of the standing waves? 4) What would happen if the length of the string is increased? 5) What is the relationship between energy and nodes? Part 2 1) Why are only odd harmonics present when one end of the tube is closed and the other end is open? 2) What relationship is there between the number of antinodes and the frequency of the wave? 3) If the tube is now closed on both ends, how much does the length of the tube need to be adjusted in order to accommodate one entire wavelength? Be sure to show all data, calculations, and answers to these questions in the lab report. 17 Laboratory 4 Demonstrations of Static Electricity and the Electroscope PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction This lab will demonstrate some examples of static electricity. From the course lectures, we learned that there are three methods to induce electric charge: Friction, Conduction, and Induction. For Part 1, some common examples of electrostatics will be demonstrated. This includes using a balloon, the Van de Graaff generator, and water polarization. For Part 2, a simple electrostatic experiment will be conducted using an electroscope. Lab Safety Unlike PY 120, this semester’s labs deal with a great deal of potentially dangerous situations due in part to high voltages, electrical discharge, and electric current. Make sure to carefully follow the safety warnings from the instructor. Make sure to follow all steps and pay close attention during each lab. Part 1: Electrostatic Demonstrations 1) The Balloon We can use a regular balloon to demonstrate electrical induction and friction. This is a simple demonstration were the balloon and shirt (or hair) are electrically neutral. When the balloon is rubbed (electrically induced friction) charges are transferred from the shirt or hair to the balloon. Now, both objects have opposite charges. The results of this will be demonstrated in the lab. 2) The Van de Graaff Generator Van de Graaff generators are devices used to demonstrate high voltage due to static electricity. Fig. 1 shows a schematic of a Van de Graaff generator. These generators utilize both smooth and pointed surfaces, and conductors and insulators to generate large static charges and large voltages. These generators are capable of generating millions of volts. A very large excess charge can be deposited on the sphere, because it moves quickly to the outer surface. Practical limits arise because the large electric fields polarize and eventually ionize surrounding materials, creating free charges that neutralize excess charge or allow it to escape. A motor or hand crank (A) supplies excess positive charge to a pointed conductor (comb), the points of which spray charge onto a moving insulating belt near the bottom. The pointed conductor (B) on top in the large sphere picks up the charge. The induced electric field at the points is so large that it removes the charge from the belt. This is possible because the charge does not remain inside the conducting sphere but moves to its outer surface. An ion source inside the sphere produces positive ions which are accelerated away from the positive sphere. A wand, which is connected to ground, with a spherical conductor on top, is used to discharge the excess positive charges from the generator’s surface. If the electric field is great enough, the air breaks down and is ionized. An electrical discharge spark is produced. Figure 1. Schematic of a Van de Graaff generator [1]. 18 3) Water Polarization Water molecules are polarized. The hydrogen atoms have a net positive charge and the oxygen atom has a net negative charge. As the water is pulled downward due to the force of gravity the negatively charged conductor rod exerts a net attraction on the opposite charges in the stream of water, pulling the stream closer as shown in Fig. 2. Figure 2. A charged rod attracting water out of a faucet [1]. Part 2: The Electroscope The electroscope is a scientific instrument used to demonstrate static electric charges due to conduction and induction. This experiment will introduce the concept of grounding which will be utilized again for the Faraday Ice Pail experiment. Fig. 3 (a) shows the electroscope used in this lab. How an electroscope works The electroscope is a demonstration of electrical conduction and induction. We can understand how it works by looking at Fig. 3. After the electroscope has been grounded (explained below) a charged object (conducting rod) is brought into contact with the top (charge sampler) of the electroscope as shown in Fig. 3 (b). The electroscope is now net negatively charged. Negative charges on the pivoting pendulum (conducting metal) rod are repulsed away from the negative charges on the fixed stem (does not move). The greater the magnitude of negative charge on the conducting rod, the greater the pendulum rod is displaced. Even after the charged object is removed, the electroscope continues to be charged. Electrostatic repulsion on the pendulum rotates it away from the stem. The electrostatic force has a horizontal component that results in the pendulum moving up as well as a vertical component that is balanced by the gravitational force. Similarly, the electroscope can be positively charged by contact with a positively charged object. (a) (b) Figure 3. (a) Electroscope with a pivoting pendulum rod shown in the center. (b) A conducting rod making contact with the electroscope is shown [2]. 19 Laboratory 4-Prelab Demonstrations of Static Electricity and the Electroscope PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What safety precautions need to be followed in today’s lab? Question 2 What are the three methods which we can use to induce static electricity? Question 3 Where do the charges accumulate on the Van de Graaff generator? Question 4 The electroscope is a device used to demonstrate the induction of charges using what two methods? Question 5 Sketch the charge distribution on an electroscope when a negatively-charged rod is brought in close proximity to it. 20 Lab Procedure Part 1 Step 1) Visit the website: https://phet.colorado.edu/sims/html/balloons-and-staticelectricity/latest/balloons-and-static-electricity_en.html Step 2) Rub the balloon against the sweater and record the observations. Step 3) Move the balloon towards the wall and record the observations. Step 4) Watch the video: https://www.youtube.com/watch?v=XIxwYOMCCmE Step 5) Answer the questions for Part 1. Part 2 Step 1) The electroscope unit is placed on the workbench. Step 2) The charge sampler is inserted into the top of the electroscope unit. Step 3) In order to ground the electroscope a ground cable is connected to the red ground port on the electroscope and the other end to a grounded metal surface such as the workbench. Step 4) Visit the website: http://physics.bu.edu/~duffy/HTML5/electroscope_charged_rod.html Step 5) The negatively charged rod in placed in contact with the charge sampler on the electroscope and is allowed to remain there for a few seconds. Select the Negative button and slide the Charged rod position scale until the rod is in contact with the electroscope. Record and explain your observations Step 6) Remove the charged rod from the charge sampler. Record and explain your observations Questions (Explain all answers) Part 1 1) Why does the balloon stick to your shirt or hair? 2) Why does the balloon stick to the wall? 3) What causes the spark between the wand and the Van de Graaff’s surface? 4) What causes your hair to stand up? 5) Why does the water bend towards the rod? 6) What is required for the water flow to bend away from the charged rod? Part 2 1) What is the net polarity of the electroscope? 2) Why does the pendulum (conductive rod) move? 3) Is the movement of the pendulum rod proportional to the magnitude of the charge on the charge sampler? 4) Why does the electroscope no longer remain charged once the charged rod is removed? 5) What method can be used to discharge the electroscope? Explain. Be sure to show all data and answers to these questions in the lab report. 21 Laboratory 5 The Faraday Pail PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction In this lab, we will explore electrostatics, particularly charge by induction and conduction, using what is called a Faraday pail. The pail is simply a metal wire mesh can. When a charged object is placed inside of the pail it attracts charges from the inner surface of the pail. These charges have equal magnitude, but opposite sign. On the outer surface of the pail, charges are induced which have the same sign as the object inside of the pail. This charge distribution is shown in Fig. 1. Figure 1. a) Side view of the Faraday pail and cage. b) Top view of the pail showing charge distribution. How to Use the Charge Separators There are three (3) charge separators (wands) in the kit. The metal separator disk is called the proof plane. This can be used to sample charges from the other two charge separators. The white disk separator can acquire positive charge and the gray charge separator can acquire a negative charge. For example, if the white and gray charge separators are briskly rubbed together, the white surface will acquire positive charge and the gray surface will acquire a negative charge. If at any point it is desired to remove or discharge excess charge from any of the charge conductors, touch the non-conductive (plastic) neck of the wand. In addition to this, lightly breathe on the wand neck so that the excess moisture will remove excess charges. Also be sure to keep the surface of the charge conductors clean. Expected Outcomes The purpose of this lab is to explore charge by conduction, induction and charge distribution. Inducing electric charge can be done using three methods: Friction, conduction, and induction. Charge induction occurs when the object inside of the pail induces charges of equal magnitude but opposite sign on the inside of the pail. Students will also learn about grounding, which will be useful later on when working with circuits. 22 Laboratory 5-Prelab The Faraday Pail PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 Which charge separator can acquire an excess negative charge? Question 2 Which charge separator can acquire an excess negative charge? Question 3 Why is it necessary to ground the Faraday cage? Question 4 When a charged object is placed inside of the pail where are the attracted charges located? Question 5 Do these attracted charges have a magnitude equal to the inserted charges? Question 6 Draw the charge distribution on the Faraday pail when a negatively charged rod is placed inside. 23 Lab Procedure Step 1) Watch the video: https://www.youtube.com/watch?v=608MdGHIIV4 Step 2) In order to remove excess (unwanted) charges the inner pail is grounded. Step 3) Two charge separators are rubbed together in order to induce charge. Step 4) Watch the video: https://www.youtube.com/watch?v=Q1HQjb4EwWE Step 5) The white charge separator is inserted into the pail and the charge is recorded. The white charge separator is removed from the pail. Step 6) The gray charge separator is inserted into the pail and the charge is recorded. Step 7) Use the video to fill in Table 1. Step 8) Sketch a top view of the Faraday pail and show the polarity of charges when the white charge separator is placed inside the pail. Repeat when the gray charge separator is placed inside the pail. Table 1 Wand Wand (+/-) Inner Pail Surface (+/-) Outer Pail Surface (+/-) Average Meter Reading (nC) White Gray Questions 1) What is the purpose of the wrist strap? 2) Why does the Faraday pail need to be made out of metal and not plastic? 3) What is the purpose of the grounding plane (plate)? 4) Why do we need to ground the Faraday cage? 5) What technique can be used to discharge the charge separators? 6) How is it that moisture can allow for excess charge removal? 7) The meter reading quickly indicates a depreciation of magnitude. What does this represent? Where did the charges go? Include all data, tables, sketches, and answers to these questions in the lab report. 24 Laboratory 6 Equipotential Mapping PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The purpose of this lab is to measure and plot equipotential lines. In order to do this, electrically conducting paper will be used. This paper requires a pen containing metallic conducting ink. This ink will act as a wire. In order to have charge move, a voltage source needs to be supplied. Once this source is supplied, and the conducting lines, now called electrodes, are separated some distance away from each other, an electric field is created. Charges will move from the positive (+) electrode to the negative (-) electrode, as shown in Fig. 1 (a). There is a voltage gradient (slope) from the electrode with high potential to the electrode with low potential. In other words, the voltage decreases from the positive terminal to the negative terminal. A plot of this is called an equipotential map. Using a voltage meter, the voltages at points can be determined. Once enough voltage points are known, the equipotential lines can be drawn. Consider that the electric field lines move from left to right as shown in Fig 1. By definition, equipotential lines are lines with equal potential, i.e. the change in electric potential is zero all along the length of a vertical line. The change in the electric potential is zero along a path perpendicular to the electric field. A plot of equipotential lines in a single dimension is shown in Fig. 1 b. The general relationship between the electric potential and the electric field is given by Eq. (1). y Δ𝑉 = − ∫z 𝐸u⃗ ∙ 𝑑𝑠⃗ (1) However, if we wanted to calculate the electric field from the electric potential we would need to take the derivative of Eq. (1). The electric potential between two points separated a distance (ds) can be expressed as, 𝑑𝑉 = −𝐸u⃗ ∙ 𝑑𝑠⃗ (2) If there is only one component (dimension) of the electric field, as in the case of this lab, then Eq. 2 becomes, dV = -Exdx. Solving this for Ex, we get, 𝐸* = − 0{ 0* (3) Consider that the electric field lines move from left to right as shown in Fig 1. By definition, equipotential lines are lines with equal potential, i.e. the change in electric potential is zero all along the length of the line. In order for the dot product to be zero, the angle between them must be perpendicular, i.e. 90o, as expressed in Eq. (4). 𝑑𝑉 = −𝐸u⃗ ∙ 𝑑𝑠⃗ = 0 (4) Eq. (4) tells us that the change in the electric potential is zero along a path perpendicular to the electric field. 25 A plot of equipotential lines in a single dimension is shown in Fig. 1 (b). (a) (b) Figure 1. (a) Parallel conducting plates showing the direction of the E. (b) Equipotential lines (green) and E lines (blue). Notice how the equipotential lines are evenly spaced and the E is perpendicular to the equipotential lines [1]. For charges on a spherical surface, the equipotential lines radiate outward as shown in Fig. 2. These equipotential lines are perpendicular to the electric field lines. As you rotate around a concentric equipotential line, the potential does not change. Figure 2. Equipotential lines (concentric circles) drawn around a positive point charge. The electric field lines (blue) are drawn perpendicular to the equipotential lines (green) [1]. A general expression for the electric gradient takes into account all three dimensions, e.g. a sphere, as shown in Eq. 5. 𝐸u⃗ = −∇𝑉 = − \𝚤̂ •{ •* •{ •{ + 𝚥̂ •• + 𝑘‚ •ƒ ^ (5) Eq. 5 is just an extension of Eq. 3 in the y and z coordinates. The ∇ symbol is called the gradient operator and is a vector operator of the partial derivative in each coordinate. The 𝜕 is the symbol used to indicate a partial derivative. 26 Laboratory 6-Prelab Equipotential Mapping PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 Why does the electric potential remain constant along a vertical path? Question 2 Why are equipotential lines perpendicular to the electric field? Question 3 What is the relationship between the electric field and electric potential. Question 4 Which electrode should we choose to act as the reference point? 27 Lab Procedure Step 1) Visit the website: https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-andfields_en.html Step 2) A layout of your design should look like the image below. Decide on the height and separation distance of your electrodes. In order to do this, create a column of positive charges on one side and a column of negative charges on the other side. In the lab, a DC power supply is used to accomplish this. Electrodes h d Step 3) Select the Electric Field box. Step 4) Sketch the electrodes and the electric field lines on paper (or electronically). Step 5) Click and drag the Equipotential meter in between the two electrodes. Use the cross-hairs of the meter to measure and record the readings. Step 6) Measure the electric potential at a point close to the + electrode and mark this point on your sketch. Use the tape measure to measure and record distances. Make several vertical measurements with the equipotential meter and Step 7) Move incrementally to the right and repeat Steps 5 and 6. You are trying to locate the points of equal potential. Step 8) Draw the equipotential lines on your sketch and include the values of electric potential and distance with respect to the positive electrode. Questions 1) Calculate the electric field between the parallel plate conductors. 2) For this electric field, calculate the force acting on a single electron. 3) Treat a circular electrode as a point source. What is the electric field due to this point source? Include all data, sketches, and answers to these questions in the lab report. 28 Laboratory 7 DC Circuits PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The purpose of this lab is to learn how to assemble and analyze a direct-current (DC) resistive circuit. This circuits consists of two main types of components: A voltage source and multiple resistors. Once the circuit is assembled a multi-meter can be used to determine the voltage drop across and the current through each resistor. From this data, Ohm’s Law can be applied to determine the voltage drops, current and power dissipation for each circuit component. Resistors A resistor (Fig. 1 a) is an electrical component used to resist the flow of current. The value of a resistor is given in Ohms Ω. This value is not listed on the resistor. Instead a color band system is used. Refer to Fig. 1b which shows the color bands. The gap between the 3rd band and the 4th indicates the reading direction. Read each color band going from left to right. Observe the color from the 1st band, e.g. red and refer to the table. Observe the color from the 2nd band, e.g. violet and refer to the table. Observe the color from the 3rd band, e.g. green and refer to the table. This 3rd band is the multiplier. The multiplier value represents the order of magnitude. For the resistor from Fig. 1b) its value is: 1st band red = 2, 2nd band violet = 7, 3rd band green = 7. R = 27 x 107 Ω. Note that this is an unusually large resistor. The last band is the tolerance of the resistor. From the table, a gold band indicates a 5% tolerance. This indicates the percent error in the resistor value and must be included when stating any resistor value. Tolerance Multiplier 1st Band 2nd Band (a) (b) (c) Figure 1. a) Standard carbon or film resistor. The color bands indicate the value of resistance and tolerance. b) Resistor color bands. c) Circuit schematic symbol of a resistor. Assembly of Circuit In order to avoid permanently connecting electrical components together with solder we will utilize a solderless breadboard. This is a segmented flat box with internal connections. The wire terminals of each component are connected (inserted) into the breadboard. Most components have a positive and a negative terminal. A resistor, however, does not. It does not matter which way it is inserted into the breadboard. Once the circuit is assembled, a power supply is required. In this lab, one 1.5 V battery will be used. Once the battery is snapped into the battery patch the leads can be connected to the breadboard. How to Measure Current Using a multi-meter to measure the current through a resistor is very different than measuring the voltage across it. The multi-meter probes need to be in series with the circuit as shown in Fig. 2. Be sure to set the meter dial to the current (A) side and the range selector to the mA range. The instructor will demonstrate how to measure current using the multi-meter. 29 Figure 2. Multi-meter set up to measure current. The probes are in series with the circuit. How to Measure Voltage Measuring voltage is much easier than measuring current. You should be familiar with measuring voltage from Lab 3. The lab probes are placed across the component. Be sure to turn the dial to the voltage (V) side and select a voltage range within the voltage of the source, e.g. a 1.5 V battery. Ohm’s Law Ohm’s Law is a linear relationship between the voltage and current in a circuit. It states that the voltage drop across a resistor is equal to the current through the resistor multiplied by the resistance of the resistor. V = IR (1) Kirchhoff’s Rules Kirchhoff’s Current Rule states that the net current entering and leaving a circuit node is equal to zero. This can be expressed as, ∑𝑖 = 0 (2) Kirchhoff’s Voltage Rule states that the net voltage drops around a closed path is equal to zero and can be expressed as, ∑𝑉 = 0 (3) Electric Power The voltage across a resistor is the product of the current flowing through the resistor multiplied by the value of the resistor. By using the probe leads of the multimeter you can determine the voltage across the resistor and the current through it. Electric power can be calculated as, P = IV = V2/R = I2R The power dissipated by the resistor is simply the voltage drop across it multiplied by the value of current flowing through it. A resistor is a passive device. It does not produce power. It only uses (dissipates) power. Much of this power is lost (transferred) into heat. 30 (4) Laboratory 7-Prelab DC Circuits PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 A resistor has the following color bands: red, red, black. The fourth band is gold. What is the nominal value of this resistor? Question 2 Two 100 Ω resistors are connected in parallel. Determine the equivalent resistance. Question 3 How can we measure the voltage across a component with a voltmeter? Explain. Question 4 How can we measure the current through a component with an ammeter? Explain. Question 5 Explain how to apply Kirchhoff’s Voltage Law and Kirchhoff’s Current Law. Question 6 The summation of the power dissipated by the resistors should be equal to the power delivered by what? 31 Lab Procedure Fig. 3 shows the DC circuit that will be used for this lab. It consists of a voltage source (battery) and three resistors. The values of these resistors will be different for each group. Figure 3. Schematic of the DC circuit for this lab. Steps Step 1) Visit the website: https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuitconstruction-kit-dc_en.html Step 2) Select the Lab icon. Step 3) Assemble the circuit shown in Fig. 3. The values of the source and resistors are your choice. Record and clearly indicate your values of resistors and the source in the lab report. Step 4) Click and drag each component. Use wires to connect each component. Step 5) For each resistor double click and slide the scale at the bottom of the screen to change its resistance. Record the colors on the color band for each resistor and their tolerance. Step 6) Slide the Battery Resistance scale to 0. Step 7) Slide the Wire Resistivity scale to “tiny.” Step 8) Use the Voltmeter to measure the voltage across each component in the circuit. Record all values. Step 9) Use the Ammeter to measure the current through each component in the circuit. Record all values. Fill in Table 1. Step 10) Include a screen shot of your circuit in your lab report. Step 11) Calculate the voltage drop across each resistor, current through each resistor, power supplied by the source and the power dissipated by each resistor. Fill in Table 2. Show all calculations. Step 12) Compare the values of voltage drops, currents, and power to the calculated values. Table 1 Measured Values Voltage Drop (V) Current (A) Vs R1 R2 R3 Table 2 Calculated Values Voltage Drop (V) Current (A) Vs R1 R2 R3 32 Power (W) Questions 1) Why do we need to connect the meter probes in series with the resistor and not across the resistor when measuring current? 2) What does the fourth color band indicate on the resistor? 3) Calculate the theoretical value of the equivalent resistance? Be sure to include the tolerance. 4) Calculate the measured value of the equivalent resistance using the measured value of electric potential of the source and the current delivered by the source. 5) When this experiment is performed in the lab, there a discrepancy between the power delivered by the source and the total power dissipated by the resistors? Where did this energy go? Include all data, images, calculations, and answers to these questions in the lab report. Helpful Websites https://wiki.analog.com/_media/university/courses/electronics/abb_f2.png?cache= https://upload.wikimedia.org/wikipedia/commons/6/6e/4-Band_Resistor.svg https://upload.wikimedia.org/wikipedia/commons/7/73/400_points_breadboard.jpg 33 Laboratory 8 RC Circuits PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The purpose of this lab is to construct and operate an RC circuit containing one resistor (R), one capacitor (C), one DC voltage source and a switch. The switch is needed in order to demonstrate the charging and discharging capability of a capacitor. This lab will introduce the concept of the time constant as well as the exponential functions necessary in order to analyze RC circuits. Fig. 1 (a) illustrates the RC circuit that will be constructed for this lab. When the switch is initially open, no current can flow and the capacitor cannot charge. Fig. 2 (b) verifies this through a PhET simulation which shows that when the switch is open, no current flows and hence no charge accumulates on the plates of the capacitor. (a) (b) Figure 1. (a) RC circuit with the switch open. No current flows. (b) Simulation of circuit demonstrating that there is no charge on the capacitor, since the voltage source is not connected [3]. When the switch is closed, current (I) flows as shown in Fig. 2 (a). As charge accumulates on the plates of the capacitor, there is an increasing opposition to the flow of charge. One plate will accumulate (+) charges and the other will accumulate (-) charges as shown in Fig. 2 (b). (a) (b) Figure 2. (a) RC circuit with the switch closed. Current (I) flows. The capacitor begins to charge. (b) PhET simulation showing the charges across the plates of the capacitor [3]. 34 The current in the circuit at the instant the switch is closed is Io = VS/R. This is called the initial current. Once the capacitor is fully charged, no current can pass through it. The capacitor acts as an open circuit. If we were to measure the voltage across the capacitor, we would see that it is not constant. For example, when the capacitor is initially uncharged, the voltage across it is zero. As time passes, the voltage across the capacitor (VC) increases until it reaches a maximum value VS. When the capacitor is discharging, the voltage across it starts from this maximum value and steadily decreases once the switch is opened. The voltage across the capacitor is a function of time. Charging a Capacitor 𝑄,ˆ* = 𝐶𝑉 G (1) G 𝑞(𝑡) = 𝐶𝑉 \1 − 𝑒 Œ• ^ = 𝑄,ˆ* \1 − 𝑒 Œ• ^ (2) The symbol 𝜏 is called the time constant of the circuit. It is the product of the capacitance and the value of resistance the capacitor charges and discharges through. 𝜏 = 𝑅𝐶 (3) As soon a s the switch is closed, before the capacitor has a chance to charge, the maximum value of { current through the capacitor is 𝐼` = ’‘. As the capacitor charges, the current will exponentially decay, { 𝑖(𝑡) = ’ 𝑒 Œ2/” (4) The voltage across the capacitor steadily increases until it reaches its maximum possible value, VS. The voltage across the capacitor will remain there until it is discharged. A plot of this is shown in Fig. 3. 𝑉• (𝑡) = 𝑉` –1 − 𝑒 Œ2/” — (5) As an example to understand what the time constant represents, plug in t = 1𝜏 into Eq. 5. 𝑉• (𝑡 = 1𝜏) = 𝑉` (1 − 𝑒 ŒM ) 𝑉• (𝑡 = 1𝜏) = 𝑉` (1 − 0.368) 𝑉• (𝑡 = 1𝜏) = 0.632𝑉` For 1𝜏 the voltage across the capacitor is 63.2% of its maximum possible value VS (the battery). Assemble the circuit shown in Fig. 1. Initially, the capacitor has no charge. The action starts when the switch is closed (Fig. 2) in which the voltage source charges the capacitor. As current starts to flow, the capacitor will begin to charge. After some time, the capacitor will be fully charged. How long will it take to charge the capacitor? From Fig. 3, about 4𝜏. When the switch is opened again, the capacitor discharges. The time is takes the capacitor to charge or discharge can be determined from the time constant, and denoted as 𝜏 = RC. This is a constant, since the value of resistor and capacitor do not change. The values of resistors are more abundant than capacitors. So, start with a readily available value of capacitor, 35 for example, C = 10 uF. You will be able to observe that once the capacitor is fully charged, the voltage across it is approximately equal to VS. Figure 3. Voltage across the capacitor, when charging, as a function of time. VC will increase until the maximum possible value is reached (Vs). The dotted lines indicate the time constant and the corresponding voltage [1]. Discharging a Capacitor When the switch is opened, the capacitor begins to discharge. The charge on the capacitor plates exponentially decreases with time. 𝑞(𝑡) = 𝑄𝑒 Œ2/” › 𝑖(𝑡) = − ’• 𝑒 Œ2/” (6) (7) The voltage across the capacitor steadily decreases until it reaches its minimum possible value, 0 V. A plot of this is shown in Fig. 4. As an example, plug in t = 1𝜏. 𝑉• (𝑡) = 𝑉` 𝑒 Œ2/” (8) 𝑉• (𝑡 = 1𝜏) = 𝑉` 𝑒 ŒM 𝑉• (𝑡 = 1𝜏) = 0.368𝑉` For 1𝜏 the voltage across the capacitor is 36.8% of its maximum possible value VS (the battery). Figure 4. Voltage across the capacitor, when discharging, as a function of time. VC decays until the smallest possible value is reached (0 V). The dotted lines indicate the time constant and the corresponding voltage [1]. 36 Laboratory 8-Prelab RC Circuits PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What does a capacitor act as when it is fully charged? Question 2 What is the maximum possible value of voltage across the capacitor? Question 3 How do we determine the time constant of the capacitor? Question 4 How many time constants are required to charge and discharge a capacitor? Question 5 How can we determine the electric energy stored in a capacitor? 37 Lab Procedure Step 1) Visit the website: http://www.falstad.com/circuit/ Step 2) Assemble the circuit as shown in Fig. 1 a. If there is already a circuit present on the drawing board, click the Run/Stop button and click on each component to delete it. Step 3) For the time constant, it is recommended to use a value of a few seconds, so you can easily observe the charging and discharging of the capacitor. Fill in Table 1. Step 4) In order to add components, click on the Draw tab from the menu. The parameters of the RC circuit are completely up to each group. Step 5) A switch and capacitor can be found under the Draw tab. Select Passive Components. Step 6) Change the value of a component by double clicking on it. Step 7) When you are finished assembling your circuit, click on the Run/Stop button. Select the capacitor and closely watch the value of the voltage drop across it. Step 8) You may to adjust the Simulation Speed. Step 9) Record all of your data and fill in Table 2. Step 10) Discharge the capacitor by opening the switch. Select the capacitor and closely watch the value of the voltage drop across it. Step 11) Record all of your data and fill in Table 2. Step 12) Calculate the theoretical values for the voltage across the capacitor when it is charging and discharging and fill in Table 2. Step 13) Make a plot of the voltage across the capacitor as a function of time. Table 1 Parameter R C 𝜏 Value Table 2 Vc(t) Capacitor Charging Vc(t) Capacitor Discharging Time (s) Theoretical Measured Time (s) Theoretical Measured Value of Vc Value of Vc Value of Vc Value of Vc t =0𝜏 t =0𝜏 t =1𝜏 t =1𝜏 t =2𝜏 t =2𝜏 t =3𝜏 t =3𝜏 t =4𝜏 t =4𝜏 Questions 1) What is the general purpose of using a capacitor in a circuit? 2) What is the significance of the time constant? 3) Why does the capacitor act as an open circuit when it is fully charged? 4) Calculate the energy stored in the capacitor when it is fully charged. 5) What circuit element does the capacitor discharge through? Include all data, graphs, calculations, and answers to these questions in the lab report. 38 Laboratory 9 Magnetic Fields and Ampere’s Law PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The purpose of this laboratory is two-fold. For Part 1, the magnetic field lines emanating out a magnet will be sketched. It will be experimentally verified that magnetic field lines point out of the north pole of a magnet and terminate on the south pole of a magnet. In Part 2, Ampere’s law will be verified for a solenoid. According to Ampere’s law, when a current is supplied to the wound copper wire of a solenoid the current induces a magnetic field that circulates around the wire according to the right-hand rule. A teslameter will be used to detect the induced magnetic field inside of the solenoid. Part 1 Fig. 1 (a) illustrates a typical bar magnet. The red top is the north pole and the lower half is the south pole. Iron filings are used to show how the magnetic field points out of the north pole and terminates on the south pole. Fig. 1 (b) is a simplfied sketch of the magnetic field lines. Fig. 1 (c) is a practial sketch similar to the one that is required for this lab. (a) (b) (c) Figure 1. (a) Magnetic field lines of a bar magnet. (b) and (c) Simplified sketches of the magnetic field lines [1]. As might be predicted from the diagram in Fig. 1, the magnetic field sketch is greater the closer one is to the magnet. As one moves further away from the magnet, the magnetic field lines depreciate in magnitude. A teslameter can measure the magnitude of the magnetic field. The meter should indicate a high reading near the magnet and depreciate in value as the meter moves further away from the magnet. Part 2 Ampere’s Law states that when a conductor has a current flowing through it, this current produces a magnetic field. Fig. 2 (a) shows a current (I) flowing through the wire. Around the wire is the induced magnetic field (B). The direction of the magnetic field is given by the right-hand rule as shown in Fig. 2 (b). If a compass, for example, which contains an internal magnet, is placed near the current carrying wire, the compass needle will be deflected as shown in Fig. 2 (c). This experiment will verify Ampere’s law for the magnetic field strength inside of a solenoid. 39 (a) (b) (c) Figure 2. (a) Magnetic field produced by a current-carrying wire. (b) Right-hand rule for determining the direction of the magnetic field. (c) Compass needle placed near the current-carrying wire is deflected [1]. In this experiment, current will supplied to a device called a solenoid. A solenoid is simply a long wire wrapped into a coil around a core as shown in Fig. 1 (a). The purpose of this device is to obtain a dense, large magnetic field strength inside of the coil. A solenoid normally has many loops of wire wrapped around its core (typically iron). A cut-away view of the solenoid illustrating the magnetic field lines is shown in Fig. 3 (b). These magnetic field lines are generated by the current supplied by the battery. Figure 3. (a) A battery supplying power (voltage and current) to a solenoid. (b) A cut-away view of the solenoid indicating the magnetic field lines (as generated by the current) [1]. The magnetic field inside (center) of the solenoid can be derived from Ampere’s law and is given by, 𝐵 = 𝜇` 𝑛𝐼 (1) k, 𝜇` is the permeability of free space which has a constant value of 4𝜋 𝑥 10Œž z . n is the number of turns (loops) of wire per unit length as given by Eq. 2. N is the number of turns and L is the length of the solenoid not the length of the wire prior to being wrapped into a coil. Be sure to use units of meters. I is the current flowing through the solenoid. This can easily be measured using a multimeter. 𝑛 = 𝑁/𝐿 40 (2) Laboratory 9-Prelab Magnetic Fields and Ampere’s Law PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What is the direction of the magnetic field lines coming out of the north pole of a magnet? Question 2 Why does a compass needle move when placed near a magnet? Question 3 What does a teslameter measure? Question 4 What is Ampere’s law? Give an example and explain. Question 5 How are you going to determine the number of turns of the solenoid? 41 Lab Procedure Part 1 Step 1) A bar magnet is placed onto the workbench. Step 2) Visit the website: https://www.physics-chemistry-interactive-flashanimation.com/electricity_electromagnetism_interactive/bar_magnet_magnetic_field_lines.htm Step 3) Sketch the magnetic field lines due to the bar magnet. Indicate on the sketch how the magnitude of the magnetic field decreases further away from the magnet. Include this sketch or screenshot in your lab report. Part 2 Step 1) Watch the video: https://www.youtube.com/watch?v=EsJXZLwSCdA Step 2) Watch the video: https://www.youtube.com/watch?v=FzPO92Jxxt8 We want to calculate the theoretical value of the magnetic field inside of the coil and compare this to the measured value to verify Ampere’s law. The difficulty in calculating the theoretical value of the magnetic field strength inside of the solenoid using Eq. 1 is that we do not know the number of turns. However, we can use the following technique. The resistance of a material is given by, 𝑅= 𝜌𝐿 𝐴 The coil wire is copper. The area can easily be measured. Here, the length (L) is not the length of the solenoid coil, it is the length of the wire. This is not known. Step 3) Visit the website: https://www.physics-chemistry-interactive-flashanimation.com/electricity_electromagnetism_interactive/solenoid_magnetic_field_parameters_current _number_turns.htm Step 4) Select the solenoid with a length of 20.8 cm. Step 5) Connect the red and black probes into the board which are connected to the solenoid. Step 6) Apply a voltage of 10.0 V by selecting and turning the voltage knob. Step 7) Record the value of current through the solenoid from the multimeter. Step 8) Determine the resistance of the wire. Record this in Table 1. Step 9) Using Vernier calipers, the diameter of the coil wire is measured to be 0.5 mm. Step 10) Determine the value for the resistivity of copper from the textbook or online. Step 11) From this information calculate the length of the solenoid wire. The number of turns is equal to the total length of the wire divided by the circumference of the coil. Step 12) Calculate the number of turns of the coil and record this value in the Table 1. Comment if this value matches the value as indicated at the bottom of the screen. 42 Step 13) Calculate the magnetic field strength inside of the solenoid and compare this to the value obtained from the teslameter. Make sure the teslameter probe is fully inserted into the solenoid. Step 14) While 10.0 V is still applied across the solenoid, record the current and magnetic field strength and record this in Table 2. V (v) I (A) Table 1 Theoretical Value of the Magnetic Field in a Solenoid Length N Length R (Ω) Area (m2) 𝜌 (Ω ∙ 𝑚) wire (m) coil (m) Binside (T) Table 2 Measured Value of the Magnetic Field in a Solenoid Boutside (T) Binside (T) Step 15) Calculate the percent difference between the theoretical and measured values of the magnetic field inside of the solenoid. Questions 1) If a more powerful magnet were used, how would the sketch of the magnetic field lines in part 1 change? 2) Why does a current-carrying wire deflect a compass? Explain. 3) For the same current and number of turns of wire, does a toroid or solenoid produce a greater magnetic field? 4) Why is the magnetic field outside of the solenoid zero? 5) If a solenoid coil of one-half the diameter but twice as many turns were used instead, would the magnetic field produced be greater, less than etc.? Be sure to include all data, calculations, sketches and answers to these questions in your lab report. 43 Laboratory 10 Faraday’s Law of Induction and Lenz’s Law PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Introduction The purpose of this experiment is to verify Faraday’s and Lenz’s law of induction by performing three experiments. For the first experiment, a bar magnet will be placed inside of a large solenoid coil. According to Faraday’s law, a change in the magnetic flux will induce a current in the coil. By connecting an ammeter in series with the solenoid coil, this current can be measured. For the second experiment, an attempt will be made to power a small light bulb using only a bar magnet and a large solenoid. For the third experiment, a rail circuit will be placed in the presence of a magnetic field. A conducting bar will be placed across these rails. When this bar is moved with some velocity, to the right for example, then according to Faraday’s law of induction, the change in magnetic flux will induce a circuit in the circuit. The right-hand-rule can be used to determine the direction of this induced current. However, according to Lenz’s law, the induced current in the circuit will flow in the opposite direction as predicted. Part 1: Faraday’s Law of Induction Eq. 1 is Faraday’s law of induction, which states that a changing magnetic flux induces an electromotive force (electric potential). The negative sign is Lenz’s law, which states that there is an opposition to the change in magnetic flux. From Eq. 2, flux can change due to a change in the magnetic field, area of the loop, or angle between the surface area and the magnetic flux. In this lab, the cross-sectional area of the solenoid remains constant as does the angle between this area and the magnetic field. What varies is the magnetic field as a function of time. 𝑉¡,g = − ¢£¤ (1) £2 ΔΦ = ΔBAcos(θ) (2) A solenoid, which is just a coiled wire with many turns, will be used for this experiment. When a bar magnet is thrust inside of the solenoid, there is a change in the magnetic field of the system (solenoid and magnet). A change in magnetic field, according to Faraday’s Law, induces an emf in the solenoid. Since the solenoid is simply a wire, and all wires have some resistance, there is also an induced current in the wire, given by Ohm’s Law. The magnetic field induced by the current in the solenoid is given by, 𝐵¬`-¡h`®0 = fH ¯¢ V (3) 𝐵`°2#®0¡ = 0 𝜇` is the permittivity of free space, I is the current supplied (flowing through) the solenoid coil, N is the number of turns, and L is the length of the solenoid. Be aware that 𝐵¬`-¡h`®0 is the induced magnetic field due to a current supplied to the solenoid and not the magnetic field strength of the bar magnet. 44 Part 2: Induction and Lightbulb From Part 1, a changing magnetic field induced an emf across the solenoid. This also implied there is an induced current flowing through the coil as well. Since power is the product of electric potential and current, we should be able to power a small light bulb simply by placing a bar magnet into the center of the solenoid. In reality, the magnets available, as well as the size of the solenoid may be limiting factors. Part 3: Motional EMF and Lenz’s Law Fig. 1 illustrates a simple circuit consisting of a conducting wire. The resistance of the conducting wire is modeled by the resistor, R. This circuit is placed inside of a magnetic field pointing into the page. A bar of length L is placed across these rails. No current is induced because there is no change in the magnetic flux. When the bar is displaced by an amount Δ𝑥, to the right for example, the area changes. This also exposes more of the magnetic field. According to Eq. 2, a change in the area and the magnetic field in this case, results in a change in the magnetic flux. A change in the magnetic flux, from Eq. 1, induces an emf (electric potential) across the bar. A current is also induced in the bar, which flows through the circuit as well. The direction of this current can be determined from Lenz’s law. Figure 1. Conducting bar placed across wire The length of the bar is L. The displacement of the bar is rails and pulled to the right in the presence of a Δ𝑥. The exposed area is then, L Δ𝑥. Substituting this into Eq. 2 magnetic field [1]. gives us, ΔΦy = 𝐵𝐴𝑐𝑜𝑠θ = BLΔ𝑥𝑐𝑜𝑠𝜃. (4) We will assume the magnetic field is perpendicular to the area as shown in Fig. 2, then 𝜃 = 0o and Eq. 4 becomes, ΔΦy = 𝐵𝐿Δ𝑥 (5) Substituting this into Eq. 1 and noting that N = 1 (only one coil) gives us, 𝑉¡,g = − ¢£¤ £2 = − yV]* = −𝐵𝐿𝑣 ]2 (6) Notice how the induced emf is related to the velocity, hence the term motional emf. From Ohm’s law, the induced current flowing through the wire is, 𝐼= {²³´ ’ = yVm ’ (7) The minus sign was neglected because we only care about the magnitude of the current. 45 Figure 2. A conducting square wire of area A is in the presence of a magnetic field. 𝜃 is the angle between the magnetic field and the normal to the loop [4]. Laboratory 10-Prelab Faraday’s Law of Induction and Lenz’s Law PY-121 Physics II Laboratory Passaic County Community College Professor: Wayne Warrick Question 1 What does the negative sign in Faraday’s Law of Induction represent? Question 2 Explain Lenz’s law. Question 3 Which variables can cause a change in magnetic flux? Question 4 𝜃 is the angle between what two quantities? Question 5 If the magnetic field through a coil remains constant and the area of the coil also remain constant, can there still be a change in magnetic flux? 46 Lab Procedure Part 1 Step 1) A copper wound solenoid, bar magnet, and multimeter are placed on the workbench. The solenoid has a diameter of 5.0 cm. The length of the solenoid is 25.0 cm. The magnetic field produced by the bar magnet is 10.0 mT. Step 2) N of the solenoid is needed. Instead of counting the number of turns, there is an easier way. Step 3) Connect the DC power supply to the solenoid coil and supply a small current of 2.0 A to the coil and record this value. Step 4) The length of the solenoid has already been recorded. Step 5) Using the teslameter, the measured induced current due to the magnet is 5.0 mT. Step 6) From Eq. 3, calculate the number of turns N. Step 7) The DC power supply is removed and the solenoid is connected to a voltmeter. Step 8) The bar magnet is placed inside of the solenoid with time horizontally oscillating time intervals of 1.0 s. Step 9) The induced current of the solenoid is measured to be 100.0 𝜇𝐴. Step 10) Calculate the induced emf across the solenoid. Fill in Table 1. Show all calculations. Bmagnet (T) 2 A (m ) N Table 1 Iind (A) 𝜃 Δt (s) Vemf (v) Rwire (Ω) Steps-Part 2 Step 1) Watch the video: https://www.youtube.com/watch?v=Hh58afwzHfA Step 2) Watch the video: https://www.youtube.com/watch?v=shJAV59NS6k The voltage supplied by a battery is 1.5 V. When the light bulb is heated up and producing light, its resistance is 150.0 𝛺 . When cold, and producing no light its resistance is 10.0 𝛺 . Step 3) Using the same solenoid from Part 1, calculate the required magnetic field necessary to induce the needed emf to light up this lightbulb. Steps-Part 3 Step 1) For the magnetic strength of the bar magnet, use the value from Part 1. Step 2) The length of the conducting bar is 10 cm. The resistance of the rails is 0.10 Ω. The bar is pulled to the right with a velocity of 2 m/s. Calculate the induced current in the rails. Questions 1) Why do we need to move the magnet back and forth through the solenoid (i.e. why can’t we just let the magnet sit there?) 2) What is the magnetic field due to the induced current outside of the solenoid 5 cm away? 3) In order to determine the number of turns, N, how much current was supplied to the solenoid? 47 4) How is it possible the bulb can light up without being connected to any type of power source? 5) Calculate the power needed to operate the light bulb. 6) Using the right-hand-rule, determine the direction of induced current in Part 3. 7) What is the actual direction of the induced current in the rails according to Lenz’s law? 8) If the magnetic field in Part 3 were removed and replaced with a large power supply which supplied a large current to the rails, what effect would this have on the conducting bar? Explain. Be sure to include all data, calculations and answers to these questions in your lab report. 48 References [1] Paul Peter Urone, Roger Hinrichs, OpenStax, College Physics, Jun 21, 2012, Houston, Texas, Book URL: https://openstax.org/books/college-physics/pages/1-introduction-to-science-andthe-realm-of-physics-physical-quantities-and-units. [2] PASCO Electroscope SF-9069 [3] https://phet.colorado.edu/ [4] Serway and Jewett, Physics for Scientists and Engineers with Modern Physics, 10th Ed. Cengage Learning. 49
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached.

1

Running Head: EQUIPOTENTIAL MAPPING

The Equipotential Mapping
Lab 6
First name Last name
Institution

2

EQUIPOTENTIAL MAPPING
Abstract
The objective of measuring the electric potential and plotting of equipotential lines was
successfully determined. The experiment also determined that the electric field would always be
perpendicular to the equipotential lines.

Introduction
Calculation of the electrical potential throughout the points in space is generally precise, if not
inherently simple, when dealing with known charge distributions. Also, the same would not be
determined for conductor configurations. Conductor’s surface needs to be an equipotential if not;
the currents would flow until it acquires the same. When a conductor has an irregular form, it is
not easy to evaluate the final charge distribution.
Determination of electric field from elect...


Anonymous
I was struggling with this subject, and this helped me a ton!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags