Lab 2 Physics

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Laboratory #2 Measurement of the Earth's Surface Gravity Authors: Lab Section #: 005 Purdue University Northwest – PHYS 15200 – Spring 2023

1. Abstract In this study, we aimed to determine the acceleration due to gravity, g, by measuring the velocity of a glider on an air track. The velocity was measured by timing the glider's descent over a known distance and using kinematic equations to calculate acceleration. The data was analyzed by calculating the uncertainty in the measurements and propagating it through the calculations. The results showed that the acceleration due to gravity was 5.391 m/s^2, with an uncertainty of approximately 0.2 m/s^2. This value did not match the accepted standard value of 9.80665 m/s^2, but the relatively high fractional uncertainty in the measurement of acceleration makes it difficult to make a strong conclusion. In conclusion, our experiment highlights the importance of accurately measuring and considering uncertainties in experimental data. 2. Introduction The Earth exerts a gravitational force on all objects. Objects under the influence of this force (and other constant forces) accelerate at a uniform rate, independent of their mass (i.e. if we ignore the effects of air resistance, a bowling ball and a ping pong ball fall at the same rate). Galileo was aware of this, but didn't have a complete answer as to why. It would be Isaac Newton who put this together with a bigger picture of how the physics of motion works. Nonetheless, Galileo made measurements of this acceleration due to gravity. Also, given that he didn't have the bigger picture, Galileo did not realize that the value of this acceleration is actually dependent on distance from the Earth's surface. It varies slowly enough that you'd need a sensitive test at sea level and again at a mountain top to see the difference. So, for our purposes, we will assume that it's a constant that has a known value of 9.80665 m/s2, the adopted International Standard. With that mentioned, you should know that the value can be as different as 9.780 m/s2 at the Earth’s equator and 9.832 m/s2 at the Earth's poles due to the oblateness of the Earth (the Earth is an oblate spheroid, flattened at the poles and slightly bulging at its equator). In this lab, you will measure the acceleration due to Earth’s gravity in Hammond Indiana 3. Experimental Procedure An air track was used to provide a ramp with an air cushion which allows a “glider” to move with very little friction. We started by leveling the air track, and then created an inclined plane along the track by raising one side by 1cm using the width of a 100g weight. We will use precise photogate devices to indirectly measure the velocity of the glider at two locations (which are 100 cm or 1 meter apart) as it slides down the track (the photogate devices measure the time it takes the cart to pass and we used this measurement to calculate the velocity at each gate). We

then used the “constant acceleration kinematic equations” to calculate the acceleration of the glider. Specifically, we will measured the position of the cart and the velocity of the cart at each photogate, then use the formula V 2 2 = v 1 2 + 2a(x 2 -x 1 ) to find the acceleration Steps for the procedure went as follows: 1. Turn on the air pressure and ensure the glider moves smoothly with minimal friction. Level the track by adjusting the height of two feet on one end until the glider stays still when released from rest. 2. Using a Vernier caliper, measure the thickness of a 100 g weight, making at least five thickness measurements in different locations, and record them in a Google Drive spreadsheet and lab notebook. Make sure to use the full precision (0.001 cm) of the Vernier caliper. 3. Place the 100 g weight under one foot of the air track. The thickness of the weight measured earlier is also the height (h) of the inclined plane. Calculate the angle of inclination of the air track using the height of the inclined plane and the distance (L) between the two feet, as shown in Figure 2. Measure the distance between the two feet of the air track using a meter stick or measuring tape, and record it in the spreadsheet and lab notebook. Discuss with your group members how to estimate the uncertainty in the measurement of L and record it. 4. Attach a flag to the top of the glider. Measure the width of the flag using a Vernier caliper, making at least five measurements in different locations. Record these values in the spreadsheet and lab notebook, and calculate the mean to determine the best estimate of the width. 5. There are two photogates on the bench, one of which has a digital display. When set to "PULSE" mode, a red LED on the top will light up when the flag on the glider moves through the gate, breaking the light beam inside. To determine the location of the gate along the track, use the leading edge of the glider to measure its position and move the photogate to the point where the flag starts to turn on the light. Repeat this process 1.00 m further along the track. The distance between the leading edges of the glider flags is

the same as the distance between the leading edges of the carts, allowing you to accurately measure the distance between the photogates. 6. Set the photogates to "GATE" mode. Release the cart from the top of the ramp and allow it to roll down the track, making sure the flag passes through both photogates without making contact. Practice reading the times measured by the photogates. In GATE mode, the photogates will record ∆t1, the time spent in the first gate, and ∆t1 + ∆t2, the combined time in both gates. After each trial, only ∆t1 will be displayed (record it). To find the time in the second gate (∆t2), subtract ∆t1 from the total (∆t1 + ∆t2) which is shown when you press the memory switch button to the "READ" position. Also, make a note of the precision of the photogate devices in your lab report. 7. Conduct an experiment with a minimum of ten trials. In each trial, let the cart go from the top of the ramp and keep track of the time it spends in the first gate (∆t1) and the total time in both gates (∆t1 + ∆t2) in a spreadsheet and lab notebook. Use the recorded information to determine the time spent in the second gate (∆t2). 4. Data Photogate Trials Attempt # T 1 (s) T 1 +T 2 (s) T 2 (s) V 1 (m/s) V 2 (m/s) A 1 .1143 .1635 .0492 .2078 .483 .0951 2 .1147 .1641 .0494 .2071 .481 .0942 3 .1148 .1635 .0487 .2068 .488 .0927 4 .1149 .1646 .0497 .2067 .478 .0924

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