The University of Alabama Fluid Statics & Standing Waves Simulation Paper

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The University of Alabama

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I have physics labs that are due on June 19th at 7:00pm center timezone, I attached the documents so you can see them.

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Course and Section _______ Names ___________________________ Date___________________ ___________________________ FLUID STATICS SIMULATION Introduction Fluid Statics deals with fluids at rest. In this simulation you will study the proprieties of force and pressure within a fluid and how they are related to objects submerged in the fluid. Submit your answers using Blackboard. 1 – Buoyancy Open the simulation (https://ophysics.com/fl1.html ) Archimedes' principle states that an object submerged in a fluid is buoyed by a force that is equal to the weight of the displaced fluid. 1. If you increased the mass of the object while the keeping volume constant, what happens to the density? Run the simulation . You can change the densities of the object and the fluid in the simulation. 2. What happens when the density of the object is less than that of liquid? 3. What happens when the density of the object is more than that of liquid? Set ρ 0 = 5 g/cm 3 and ρ F = 0.1 g/cm 3 . Run the simulation. Wait for the object to totally sink in the liquid. Check Show Numbers and Free-Body Diagram. 4. How does the volume of the liquid displaced compare to the volume of the object? 5. What is the volume of the liquid displaced in this case? 6. How does the mass of the liquid displaced compare to the mass of the object? 7. Which quantity is effected by a change of the fluid viscosity? As you increase the density of the fluid: 8. What happens to buoyant force of the object? 9. What happens to weight of the object? 10. What happens to the normal force? 11. When ρF = ρO what is the value of the normal force? 12. For what value of ρF are the Buoyant force and normal force equal? Set ρ0 = 2 g/cm3 and ρF 3 g/cm3. Run the simulation and wait for the object to partially float on the liquid’s surface. 13 What is the volume of the object outside of the water? 14. What is the ratio of the volume above and volume below? 15. What is the ratio ρ0 / ρF equal to? 16. What is the relation between buoyant force and weight of the object? 17. What is the relation between the weight of the liquid displaced and the weight of the object? 2 – Hot Air Balloon Open the simulation (https://phet.colorado.edu/en/simulation/legacy/balloons-and-buoyancy ) The sphere is like a hot air balloon. Its mass is not specified but assume it to be non-zero. Different molecules of air can enter and leave its volume and its temperature inside can be changed. Set Gravity to the second mark from the left (it might be already set this way). Click to hold temperature in the container constant. Use the pump to add about 400 of the heavy blue particles. 18. What happens to the balloon as the particles enter into the container? 19. Keep observing the balloon for a few minutes, does it stay afloat? 20. How is the final density inside the balloon compared to the density above it? Start over by clicking on Reset. Use the pump to add about 400 of the light red particles. 21. Observer the balloon for a few minutes, does it stay afloat? Add slowly about 400 more of the heavy blue particles. 22. What happens to the balloon as the blue particles enter into the container? 23. Keep observing the balloon for a few minutes, does it stay afloat? Keep the simulation running and increase gravity to mark midway in the bar. 24. Which statement better describes how the particles behave? 25. How does the final density inside the balloon compare to the density above it? Start over by clicking on Reset. Set gravity to the first mark and constant temperature selected. Play the simulation and add about 500 of the light red particles. Wait for the balloon to sit at the bottom. Now increase the temperature of the Hot Air Balloon. 26. What happens to the balloon? 27. Does it stay afloat? Now, visually compare the number density of particles inside the balloon vs the number density outside 28. How does the density inside compare to the density of the surrounding medium? 29. Did increasing the temperature inside the balloon decrease its density? 3 – Pressure in a Fluid Open the simulation (https://phet.colorado.edu/sims/html/under-pressure/latest/under-pressure_en.html Select to display Grid and set Atmosphere off . You can drag around the pressure ‘clock’ to read the pressure at different locations and use the ruler to measure the depth. Fill up the tank with water using the tap. Pressure and depth 30. What is the pressure on the surface of the water. 31. What happens to the pressure as you move the clock deeper? 32. Where is the maximum pressure? 33. What does the pressure clock read at depth of 1.6 m? 34. Calculate the pressure at depth 1.6 m using P = ρgh 35. What is the experimental error of the two values of the pressure? Set the pressure clock at about 2 meters. Open the valve at the bottom to decrease the amount of water. 36. What happen to the pressure as the water level decreases? Now select the third stage. You see a container on the left and a container on the right. The two containers have different shapes and are connected by a channel under the ground. Select to display Grid and set Atmosphere off . Keep the pressure clock at fixed depth = 2 m. 37. How does the pressure on the right compare to the pressure on the left? Drop a weight 38. What happens to the pressure on the left? 39. How does the pressure on the right compare now to the pressure on the left? (still same as left) Pressure and density and gravity Reset all. Select to display Grid and set Atmosphere off and fill the tank. Now change the density to different values and observe the pressure at a fixed depth. 40. What happens to the pressure as you increase the density? Set the density to 700 kg/m3 (gasoline) and pressure clock at depth = 2 m. Make a note of the value of the pressure. 41. Increase density to 1400 kg/m3. How does the pressure change? 42. What happens to the pressure as you increase gravity? Mystery Fluid Now select the fourth stage. You can select three different types of fluids. 43. What is the density of fluid A? 44. What is the density of fluid B? Course and Section______ Date___________ Names ___________________________ ___________________________ STANDING WAVES SIMULATION Introduction The goal of this simulation is to observe the relationships between frequency, wavelength and the speed of waves in a rope. We will explore how they are related to tension in the rope and the observation of standing waves. Submit your answers using Blackboard. 1 – Basic Interference To study the interference of two waves open th e simulation (http://physics.bu.edu/~duffy/HTML5/transverse_standing_wave.html) The wave on the top travels to the right and then is reflected back as shown by the wave in the middle which travels to the left. The wave at the bottom is the standing wave generated by the interference of the two waves present in the same rope. 1. How are the wavelengths of the three waves related? Pause the animation (it does not matter the time you pause it). Look at any two locations (for example x = 2 m and x = 7 m). 2. How is the amplitude of the standing waves related to the amplitude of the individual two waves? Increase the number of Harmonic n 3. How does the wavelength change? 4. How does the velocity change? 5. How does the frequency change? 2 – Speed of the Wave Open the simulation (https://phet.colorado.edu/en/simulation/wave-on-a-string). Run the simulation and select Pulse from the top left corner Set the parameters: Fixed End. Damping = None. Speed of the simulation: Normal. Tension = Low. Amplitude = 0.50 cm. Display Rulers and Timer. 6. What is the length of the string? Click the button on the pulse generator to send a pulse through the string. Measure the period T : how long it takes for the pulse to travel back and forth (the distance traveled by the pulse is twice the length of the rope). 7. What is the value of T? 8. From your data calculate the speed of the wave. 9. Set the tension set to Medium. Calculate the speed of the wave. 10. Set the tension set to High. Calculate the speed of the wave. 11. What is the effect of a greater Amplitude on the velocity of the wave? 3 – Standing Waves Use the same simulation entitled Wave on a String. You can restart the simulation by clicking the yellow icon located at the bottom right. Select Oscillate from the top left corner. Set the parameters: Fixed End. Damping = first line from the left (None counts as is line ‘zero’). Amplitude = 0.20 cm. Tension = Medium. Frequency = 1.66 Hz Play the simulation. In order to decide if a standing waves is generated in the string, look at the green dots: they should oscillate the least compared to their adjacent points. 12. Do you see a standing wave? A standing wave is generated if its wavelength λ satisfies the condition λ= 2L n where L is the length of the rope and the n is number of loops. The goal now is to find the appropriate frequency in order to generate standing wave. Specifically the sixth harmonic (n = 6) standing wave. 13. What is the velocity of the waves? Using the condition on λ above 14. What is the frequency in order to generate the sixth harmonic? Input this frequency into the simulator and press restart to check. You should see with the green dots oscillating the least compared to their adjacent points. If not, repeat your simulation by checking both measurements and calculations. 15. What is the frequency necessary to generate the fourth harmonic? While the simulation plays the sixth harmonics, reduce the Damping to None. 16. How does the velocity of the standing wave change? 17. How does the amplitude of the standing wave change? 18. What is the name of the physical phenomenon which describes the effect on the amplitude? Change the frequency back to 1.66 HZ and reduce the Dumpling to None 19. Is the wave now effected by what is decried in question 18? 4 – Questions Use the information learned from the simulations to answer the following questions. It can be shown that the wavelength depends on the tension in the string as λ= 1 T f μ √ where μ is the mass per unit length of the string and T is the tension in the string. 20. Suppose you have established a standing wave on a string. If you increase the tension until another standing wave is created, how will the new wavelength compare to the original? 21. If the tension is tripled will you get a standing wave? A standing wave with 5 loops is created on a string of length 2.0 m and mass 2.5 g 22. What is its wavelength? 23. If the tension in the string is measured to be 290 N what is the wave frequency? 24. What is the speed of the wave? Course and Section_______ Names ___________________________ Date__________ _______________________________ SIMPLE HARMONIC MOTION SIMULATION Introduction In this experiment you will measure the spring constant using two different methods and compare your results. Hooke’s law for a spring states that (1) F = −k x where x is the displacement of the spring from equilibrium, F is the force exerted by the spring, and k is the spring constant. The negative sign means that the restoring force is opposite in direction to the displacement. If a spring obeys Hooke’s law, then a mass attached to it moves in a simple harmonic motion when displaced from equilibrium and released. That is, (2) x( t ) = A c o s( ω t +φ ) where A is the amplitude of oscillation (maximum displacement from equilibrium), ω is the angular frequency (rad/s) related to the frequency (Hz) and the period (T) by ω = 2πf = 2π/T. The quantity φ is the phase which depends on when the timing starts. By substituting Eq. (2) into Eq. (1) and using Newton’s 2nd law of motion, it can be shown that ω= √ k m. , and T = 2 π m k √ (3) Thus, k can be measured statically using Eq. (1) or dynamically using Eq. (3). Input your answers in Blackboard. 1 – Preliminary Questions 1. Which has a longer period of oscillation T, a mass of 0.6 kg or a mass of 0.7 kg (same spring)? 2. From Eq. 2, x varies from -A to +A. At which location(s) does the mass have its greatest speed? 3. At which location(s) does the mass have its greatest potential energy? 2 – Static measurement of k Open the simulation (https://phet.colorado.edu/en/simulation/masses-and-springs-basics). Run the simulation and select Stretch. Set the value for the Spring Strength 1 to the second line: Hang the block of mass 50 g to the spring on the left and measure the vertical displacements Δy by using the ruler located on the right of the screen (you can drag it). Repeat for the block of m = 100 g and m = 250 g. Calculate F (= mg) for each mass and make a plot of F vs Δy. Use g = 9.81 m/s2. 4. Determine k from the slope of the line (see Eq 1). Using the value of k find, 5. What is the unknown mass of the red block? 6. What is the unknown mass of the blue block? 7. What is the unknown mass of the green block? 3 – Dynamic measurement of k Open the simulation (https://phet.colorado.edu/en/simulation/masses-and-springst). Run the simulation and select Intro. Set the Spring Constant to the first line: Hang the block of mass 50 g to the spring on the left and measure the period of oscillation T using the stop watch located on the right of the screen (drag the stop watch outside its box). It might be easier if Slow speed is selected. Repeat ten times your measurements of the period and record your data. 8. What is average value of T? 9. What is the standard deviation of T? 10. Use your average value of T and Eq. (3) to find the sprint constant k (N/m) 4 – Spring on the Moon Use the same simulation entitled Masses and Springs. You can restart the simulation by clicking the yellow icon located at the bottom right. Use the same spring constant set at the first line. Hang the block of mass 100 g to one of the spring and compare the oscillation on Earth with the oscillations as the spring was placed on the Moon (select Moon in the tab under Gravity). 11. How is the mass different on the Moon? 12. How is the force F acting on the mass different on the Moon? 13. How is the displacement Δy different on the Moon 14. How is the period of oscillation T different on the Moon? 5 – Pendulum Open the simulation (https://phet.colorado.edu/en/simulation/pendulum-lab). Run the simulation and select Intro. Move (drag) the pendulum about 14 degrees away from its equilibrium position and observe the motion. Do not include friction. 15. How does the period T change as you increase the mass ? 16. How does the period T change as you increase the length ? 17. How does the period T change as you increase gravity ? 18. How does the period T change if you start over and move the pendulum at about 5 degrees away from its equilibrium position? (you might want to use the Stopwatch and the Slow motion).
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Explanation & Answer

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1 – Basic Interference
1. The wavelength of all 3 waves are the same.
2. The amplitude of standing wave is the sum of amplitudes of 2 individual waves.
3. Wavelength decreases as harmonics increases
4. Velocity does not c...


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