Physics 101 DIY : Make and Use a Barometer to Measure Air Pressure Overview Air pressure is the result of the weight of tiny particles of air (air molecules) pushing down on an area. While invisible to the naked eye (i.e. microscopic), they nevertheless take up space and have weight. For example, take a deep breath while holding your hand on your ribs and observe what happens. Did you feel your chest expand? Why did it expand? Air pressure expands because the air molecules take up space in your lungs, causing your chest to expand. Furthermore, air can be compressed to fit in a smaller volume since there's a lot of empty space between the air molecules. When compressed, air is placed under high pressure. Meteorologists measure these changes in the air to forecast weather, and the tool they use is a barometer. The common units of measurement that barometers use are millibars (mb) or inches of mercury. DIY Make a Barometer A. Materials o B. Theory How does this measure air pressure? C. Procedure 1. Place the completed barometer and scale in a shaded location free from temperature changes (i.e. not near a window as sunlight will adversely affect the barometer's results). 2. In your notebook or the table below, record the current date, time, the weather conditions, and air pressure (i.e. the level where the end of the straw measures on the scale). 3. Continue checking the barometer twice a day (if possible) each day over a four days period. Date Data Table Weather Air Time Conditions Pressure Date June 4, 2003 June 4, 2003 June 5, 2003 Sample Data Table Weather Air Time Conditions Pressure Clear and 9:30 am 4 Sunny 2:30 pm Cloudy 3 9:30 am Rainy 1 Barometer Analysis Answer the following questions in complete sentences. 1. What problem were you trying to solve with your barometer? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 2. Were there any changes in the weather during the week? __________________________________________________________________________ __________________________________________________________________________ 3. Did the barometer measurement change when the weather changed? How much? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 4. Did the barometer measurement change without a change in weather? Why do you think that happened? __________________________________________________________________________ __________________________________________________________________________ 5. How well did your barometer work? __________________________________________________________________________ __________________________________________________________________________ 6. What would you change if you could design the barometer again? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 7. How do the barometer measurements help us understand the system of weather around us? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________   Name:_________________________________ Class: ______________________________ Date: ______________________________ Adding Vectors Graphically and Component Method To learn how to add vectors graphically and component method and compare with expected resultant vector. Equipment 1. protractor 2. ruler 3. pencil 4. paper Theory DEF: A vector is a quantity that has both magnitude and direction. DEF: A scalar is a quantity that has magnitude but NO direction. Ex. Vectors Force Velocity Displacement Acceleration Ex. Scalars Temperature Time Mass Speed Vector Notation A – Boldface letters ⃑ - Arrow above letter | | – Magnitude of vector A A vector is defined graphically by an arrow whose length is proportional to the magnitude of the vector quantity. The direction of the arrow points in the direction of the vector quantity. Adding Vectors Graphically Consider adding two vectors A and B graphically. The two vectors are shown below. 1. Select an appropriate scale. (Ex. 20 cm = 5 N) 2. Draw vector A to scale and in the proper direction. 3. Draw vector B to the same scale with its tail at the tip of A and in the proper direction. 4. The resultant vector R = A + B is the vector drawn from the tail of vector A to the tip of vector B. 5. Calculate the magnitude of the resultant vector R using the selected scale and measure its direction with a protractor. 6. This same process applies if you add more than two vectors. This method of adding vectors graphically is also referred to as the i. head-to-tail method, ii. analytical method, and iii. geometric method. Example A physics student realizes that class was to start soon, the student dashes 2.0 km due east, then 1.0 km at 45o north of east, and finally 0.5 km due north. Calculate the displacement of the student. Scale: 50cm = 2 km ANS: R ≈ 2.98 km, θ ≈ 24o Adding Vectors Using Component Method Consider adding three 2-D vectors A, B, and C: A = Axx+ Ayy B = Bxx + Byy C = Cxx + Cyy 1. Add the x-components and y-components of each vector to obtain the resultant vector R in unit vector notation. R = A + B + C = (Axx+ Ayy) + (Bxx + Byy) + (Cxx + Cyy) R = (Ax + Bx + Cx) x + (Ay + By + Cy) y Rx = Ax + Bx + Cx Ry = Ay + By + Cy R = Rx x + Ry y 2. Calculate the magnitude of the resultant vector R . √ 4. Same procedure applies if you add more than 3 vectors. However, if the vectors are 3D, then you must specify the direction of the resultant vector R relative to the positive x, y, and z axis. Procedure Exercise 1 1. A car travels 20 mi at 600 north of west, then 35 mi at 45o north of east. 2. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. 3. Use the component method to obtain the resultant displacement vector in unit vector notation. Calculate the magnitude and direction. 4. Add the displacements vectors graphically using an appropriate scale and coordinate system. Obtain the resultant vector and calculate the magnitude and direction. 5. Calculate the % error between the graphical and component method. Take the component method to be the expected value.[ Exercise 2 1. Suppose a particle is acted on by the following three forces: F1=m1g @ 30o (m1 = 300 gr) F2=m2g @ 110o (m2 = 450 gr) F3=m1g @ 230o (m3 = 400 gr) Calculate the force particle 1 2 3 mass gravity Force Direction Finding resultant force using Component Method 1. Express each force F1, F2, and F3 in unit vector notation. Take the origin to be at the center of the force table (at pivot point) with the +x axis along 0o and +y-axis along 90o. 2. Use the component method to obtain the resultant force vector Fcomp in unit vector notation. Calculate the magnitude and direction. Finding resultant force using Graphically 1. Add the vectors F1, F2 and F3 graphically using an appropriate scale and coordinate system. 2. Obtain the resultant vector Fgrap. Calculate the magnitude and direction. 3. Calculate the % error between the graphical method, component method.
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