PCS211 Lab Report 3

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Toronto Metropolitan University *

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211

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Physics

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Apr 3, 2024

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Newton’s Second Law

Introduction This experiment analyzes the motion of a cart being pulled along a track by a weight being pulled towards the ground by gravity. Friction in this experiment is considered negligible. The acceleration and velocity of the cart are measured with different masses (applied in different combinations to the cart and the hanger) using photogates which note the time and distance traveled by the cart. The information gathered is then used to calculate the acceleration. There will be two different setups used to collect data in this experiment and the information collected will be compared and analyzed. Setup 1: Experiment 1) Setup 2: Experiment 2)

Theory This lab relates to concepts found within Newton’s second law, which states that an object will only accelerate in the situation that there is a net force acting upon it which is not balanced by an opposite force. In this experiment we see that since there is no frictional force preventing the cart from gliding along the rail it will accelerate in the direction it is pulled with no resistance. Newton’s second law also states that the acceleration of an object in any direction is inversely proportional to the net force acting on the object, and the mass of the object. We expect that as mass increases, the acceleration decreases, and as force increases, acceleration also increases. The equation that we will be using to calculate the carts acceleration over a period of time is one of the 5 kinematic equations: 𝑎 = 𝑣 2 − 𝑣 1 𝑡 2 − 𝑡 1 The other equation that will be considered with the object’s mass (m), acceleration (a), and the force acting upon it (F), is:

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𝐹 = 𝑚𝑎 Or when rearranged for acceleration: 𝐹 𝑚 = 𝑎 The final equation which will be used to estimate the slope of our graphs is: 𝑎 𝑐𝑐 = 𝑀 ℎ 𝑀 ℎ +𝑀 𝑔 𝑔 Procedure List of Equipments used: Experiment 1) - Air Cushioned Track - Glider - Hanger - 7 Weights of 5g - Pulley & Clamps - String - Vernier Lab Pro Software - 2 Vernier Photogates Experiment 2) - Vernier dynamics cart & track - Photogate trigger - Hanger - 3 Weights of 50g - Pulley & Clamps - String - Vernier Lab Pro Software - 2 Vernier Photogates For experiment 1, the first thing you would do is measure the masses of the items used in the experiments. These items would be the glider, the hanger and the weights. Once you have recorded the masses you would then measure the plate above the glider. After that you would launch the Vernier Lab Pro software on your device. Once launched, open the file from D2L onto the software. Then you would set up the software by replacing the ‘Object Length’ with the

length you measured earlier. You would then make sure the two photogates are set up properly 60cm apart. Connect the glider with the hanger with a sting that is placed over the pulley. Make sure that the string is long enough to cross both photgates. Add 30g of weight to the glider (make sure you add 15g to each side so it’s properly balanced) and 10g of weight onto the hanger. Set a starting position which you will use for the rest of the experiment. Have the glider ready and hit play on the software and turn on the air pump and release. On the software, the timer should have given you the two lengths of time. The software also gives you the average velocity through each gate. Don’t forget to record your data. Repeat these steps two more times. Once done, remove 10g from the glider and add it on the hanger. Now repeat all the process until you run out of weight to move. For the second experiment, you will be repeating a lot of the same steps. Start with measuring all the lengths and weight as you did in the last experiment. For this system you will need a hanger and 3, 50g weights. Set up the software and photogates as you did before. Connect the cart with the hangers with a strong over the pulley. Add 50g of weight to the hanger and 150g of weight to the cart. Set a starting position for the cart that you will be using for the rest of the experiment. Once ready hit play on the software and release the cart. The software will give you the timing lengths and the average velocity through each gate. Make sure to record it. Now repeat the process two more times. Once done remove 50g from the cart and place it on the hanger. Now repeat all the process until there are no masses left to remove. Results & Calculations We did the experiment 2) with a cart and a hanger.

Data : Distance of object’s length: 11.93 ± 0.25cm Distance between the sensors: 50.37 ± 0.25cm Mass of Cart: 535.44 ± 0.05g Mass of Hanger & String: 48.33 ± 0.05g Trial 1 Trial 2 Trial 3 V1 (m/s) V2 (m/s) Δ T (s) V1 (m/s) V2 (m/s) Δ T (s) V1 (m/s) V2 (m/s) Δ T (s) 0g 0.252 0.555 0.9957 99 0.196 0.498 1.0863 36 0.200 0.428 1.2845 50g 0.335 0.864 0.6804 81 0.310 0.864 0.6835 28 0.299 0.791 0.7411 01 100g 0.387 1.030 0.5727 93 0.359 1.029 0.5774 32 0.378 1.029 0.5750 98 150g 0.439 1.183 0.5014 01 0.399 1.183 0.5053 0.380 1.171 0.5127 4 Calculations: We use one of the 5 formulas of kinematics to solve the acceleration

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This equation will be used to calculate the acceleration of the cart. Trial 1 (m/s^2) Trial 2 (m/s^2) Trial 3 (m/s^2) 0g 0.304278273 0.2779987039 0.1775009731 50g 0.7773912865 0.8105008134 0.6638771234 100g 1.122569584 1.160309785 1.131980984 150g 1.483842274 1.551553533 1.542692203 The table below is to calculate the average acceleration between all 3 trials Mass (g) Acceleration (m/s^2) 0 0.2532593167 50 0.7505897411 100 1.138286784 150 1.526029337

The line of the best fit has a slope of 0.008412 ± 0.0003797 We use this formula to predict the slope of the graph Acc = (48.33)/(48.33+535.44+150)(9.80) Acc = 0.64548

%Error = %Error = %Error = 98.96% Wrap up Questions 1) [Discussion] After completing the lab, answer again the question posed in the pre-lab: If the glider/cart and the hanger had equal masses, will the magnitude of the acceleration of the glider/cart be g, less than g , or bigger than g ? Explain why in words. If, after doing the lab, your answer changed, explain what you had wrong when you first made your prediction. If the glider and the cart had equal masses, we can expect that the acceleration of the cart will be less than the acceleration caused by gravity. This conclusion is drawn using the following equation as a baseline: 𝑚𝑔 − 𝑇 = 𝑚𝑎 Where m represents mass, T represents tension, and a represents acceleration. We would substitute T to be equal to mass times the force of gravity and further rearrange. The resulting equation would allow us to conclude that the magnitude of acceleration would be less than the magnitude of the force of gravity.

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2) [Theory] In the special case where mh is much larger than mG, what do you expect the acceleration of the system to be? Does your formula agree with this special case? In the situation that mh is much larger than mG, we can expect that the acceleration of the cart will be larger. The forces acting on the cart (or the net force) will now be even more unbalanced with no resistance/opposite force which will cause the cart to accelerate faster. In this situation the acceleration will be greater than the acceleration caused by gravity. 3) [Theory] In the special case where mh is much smaller than mG, what do you expect the acceleration of the system to be? Does your formula agree with this special case? In the situation that mh is much smaller than mG, we expect the acceleration of the cart to be significantly less than that of gravity. This is due to the fact that the net force acting on the cart is much less than if the mass of the glider was larger. We also know that the acceleration of an object is related to both its mass and the forces acting upon it, in this case the force acting upon it is much smaller than its weight, therefore the hanger's ability to move the cart is weaker. This results in a slower acceleration of the cart. This idea was observed during the experiment when mass was added to the cart, it was seen that the acceleration of the cart was smaller. 4) [Discussion] Throughout this lab, we neglected friction. If friction were present (it always is to some degree), how would the results be affected? Would the slope of your measured line be larger or smaller than the predicted slope?

If friction was accounted for in this experiment we can expect that the acceleration of the cart will be smaller. This would be because there is a force opposite to the acceleration acting on the cart. This is also dependent on the coefficient of friction between the two surfaces, if the coefficient is large enough it may require more force to move the cart or the cart may not move at all. The slope of the measured line would be smaller than the predicted slope as our predicted slope does not account for friction being present, whereas if friction was present in this experiment the acceleration of the cart would be smaller. 5) [Discussion] Conceptually, what differences would you expect to see between the two apparatus (Air Track & Glider vs. Rail & Cart)? Comment on the need for different weights between the two systems. While in the lab: discuss your results with the group sitting across from you, are there any noticeable differences? Try to provide some explanation for these differences. After discussing the two experiments with the group across we conducted that the two experiments are very different and use different masses for a reason. The air track experiment would have a higher acceleration than the cart experiment as there is no friction as it glides and doesn’t come in contact with anything. There are different weights used as the cart system would have a lot of friction with the railing and the glider doesn’t have any friction and would need a lighter weight for it to glide smoothly. The cart on the other hand is going down a slight slope and we increase the weight of the cart and hangers.

Bibliography ● G. Pearson (2021). 3 Laboratory Guide - Physics . Toronto Metropolitan University. ● Uncertainty Of Measurement and Report Writing (2022). Toronto Metropolitan University. ● Newton’s Second Law. (n.d.). Toronto Metropolitan University

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PCS211 Lab Report 3

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