Collision and momentun lab 6 (1)

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Dec 6, 2023

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Johanna Gantier Lab Partner: Simrun Karin & Averseen Sous Instructor: Professor King Leung Lab: PHYS 11000- 1L12 March 31, 2023 Laboratory #6: Collisions and Momentum Objectives: To study the relation between force and change in momentum, and to determine whether momentum is conserved in inelastic collisions Equipment: two carts, two force probes, motion detector, electronic balance, masses. Introduction: For collision and momentum, we can use Newton’s third law but instead of writing Newton’s Second Law as F=ma, we can write it as F=∆p/∆t. This means that if a constant force is acting on an object for a time ∆t , then its momentum will change by an amount F∆t . Let's assume that the force starts acting at time t0 . If we plot the force as a function of time, it will be zero until t0 . The force between t0 and t0+∆t , and then zero again after that. The area under the force versus time plot is just F∆t , which is the change in momentum . If the force is not constant, it is still true that the area under the force versus time plot will be the change in the momentum of the object. When two objects collide in the absence of external forces, Newton’s Third Law guarantees that the total momentum is unchanged. If the two colliding objects are object A and object B , then when they hit, the force exerted by A on B will have the same magnitude as the force that B exerts on A , but its direction will be opposite. This means that the change in momentum of object A will be the opposite of the change in the momentum of object B so that the sum of their changes in momentum is zero. Therefore, the total momentum before the collision is the same as the total momentum after the collision. In terms of equations, if p A =m A v A is the initial momentum of object A p B =m B v B is the initial momentum of object B, P A’ =m A’ V A’ is the final momentum of object A , and P B’ =m B’ V B’ is the final momentum of object B, then p A +p B =P A’ +P B’ . In this lab, we want to verify Newton’s Third Law, show that the change in momentum is equal to the area under the force versus time graph, and study momentum conservation in an inelastic collision. The collision will involve two carts, one initially moving and the other sitting still, that stick together when they hit. This means that if the initially stationary cart is object B , then v B =0 and V A =V B  p A +p B =P A’ +P B’ Procedure: 1. You should have two cars with force probes mounted on them. Place them both on the track with the parts sticking out of the force probes facing each other. Open the file Collisions; you should see two sets of axes on the screen, a force versus time plot for each force probe. You are going to push the carts together (gently!) so that they collide. The force probes will hit each other and measure the forces on each of the carts. Sketch predictions for what the force versus time plots for each cart will look like. Zero all sensors by 28 clicking the button “Zero all sensors” before every measurement. Now do the experiment and sketch the results.

Figure 1. The experiment was set up with two cars that move on a track and motion sensors at the end of the track. Each of these cars has a probe detector on the end of contact. Predictions: Graph 1. Prediction of Force on Cart 1 vs. Time graph before and after collision Time (s) Force on Cart 1 Graph 2. Prediction of Force on Cart 2 vs. Time graph before and after collision Time (s) F o rce o n C art 2

Resuls of the experiments in part 1 Graph 3. Experiment results of force Vs time of graph 1 (in red) and graph 2 (in blue) before and after collision. 2. Now place a mass in one of the carts and repeat step 1. What do your results tell you about Newton’s Third Law? Sketch predictions of what the force versus time plots for each cart with a mass, will look like during collision. Time (s) Force on Cart 1

Graph 4. Prediction of Force on Cart 1 vs. Time graph with 499.6g (0.4996kg) mass on cart 1, before and after collision. Time (s) Force on Cart 2 Graph 5. Prediction of Force on Cart 2 vs. Time graph with 499.6g (0.4996kg) mass on cart 1, before and after collision Part 2 Experimental results

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