PHYS 211 - Lab 6 - Instructions - Fall 2023.docx

Jaquan Pope October 30, 2023 Dr. Otim Odong Lab 6: Conservation of Linear Momentum Fundamentals of Physics 1 Lab Section 11 Lab 6: Conservation of Linear Momentum Instructions Background A collision is an event in which two or more moving bodies exert forces on each other for a relatively short time or ongoing depending on the relationship of the collisions. Collisions are classified as either elastic or inelastic, meaning an elastic collision is a collision in which objects don’t stick to each other after a collision for example a bowling ball and bowling pins. As for the other option listed above , an inelastic collision is a collision in which objects stick to each other after a collision. An example of such a collision includes a car hitting and sticking to another car after collision. Here, in this experiment with the help of scotch tape, it focuses on the collision of two objects sticking together in an inelastic collision. Objective To show that linear momentum is conserved when two objects collide, inelastically or not. Ideally we will see a once stationary object moved due to the collision One of Newton's laws was an object in motion will stay in motion until and force counteracts that of the original. With that said another object will be to see the statically data change from before and after the collision. Theory The theory is that once cart 1 collides with cart 2 the momentum will slow but the transfer of energy and that it is and inelastic crash, the carts will continue down the track with no delays. Let two objects (carts), labeled 1 and 2, collide into each other along the x-axis. Then for an: ● Elastic collision:

Linear momentum is conserved. That is: ̅P→ i = ̅P→ f (1) where: P̅ → i = ̅P→ 1ix + ̅ P → 2ix = m 1 ̅v→ 1ix + m 2 v ̅ → 2ix (2) and: P̅ → f = ̅P→ 1fx + P ̅→ 2fx = m 1 v ̅ → 1fx + m 2 v ̅ → 2fx (3) m 1 = mass of cart 1, m 2 = mass of cart 2, v ̅ → 1ix = initial linear velocity of cart 1 along the x-axis = (v 1ix ) ı^ , v 1ix = component of v ̅ → 1ix v ̅ → 2ix = initial linear velocity of cart 2 along the x-axis = (v 2ix ) ı^ , v 2ix = component of ̅v→ 2ix , v ̅ → 1fx = final linear velocity of cart 1 along the x-axis = (v 1fx ) ı^ , v 1fx = component of v ̅ → 1fx , v ̅ → 2fx = final linear velocity of cart 2 along the x-axis = (v 2fx ) v 2fx = component of v ̅ → 2fx , ̅ P → 1ix = initial linear momentum of cart 1 along the x-axis, ̅ P → 2ix = initial linear momentum of cart 2 along the x-axis, ̅ P → 1fx = initial linear momentum of cart 1 along the x-axis, ̅ P → 2fx = initial linear momentum of cart 2 along the x-axis, ̅ P → i = initial linear momentum of the system, ̅ P → f = final linear momentum of the system.

Let R be the ratio: R = ̅P→ i ̅P→ 𝐹 = (m1v1ix+ m2v2ix) ı^ (m1v1 𝐹 x+ m2v2 𝐹 x) ı = (m 1 v 1ix + m 2 v 2ix ) (m 1 v 1 𝐹 x + m 2 v 2 𝐹 x ) (8) Then, theoretically, for both elastic and inelastic collisions, R = 1. This also means that linear momentum is conserved. We next test whether this is true experimentally, but only for the case of inelastic collision. Experiment A. Procedure 1. Get two carts and a cart track. 2. Determine the mass of each cart. Record the result. 3. Attach a motion sensor to one end of the track, and connect it to a data acquisition device. 4. Make sure that the track is completely level such that it is horizontal to the table. 5. Place one cart on the track and close to the end near the sensor. 6. Put the second cart on track and some distance away from the first cart. Note: the first cart should be the closest to the sensor. 7. Put a sticky material (such as folded scotch tape) on the second cart and on the end facing the first cart. 8. Set the data acquisition program to collect data in a table for time vs. position. 9. Start the data acquisition program. 10. While the program runs, gently tap the first cart and let it collide and stick with the second cart that is stationary. 11. Stop the data acquisition shortly after the collision. 12. At this point, the data acquisition program should have data in a table for time and position 13. Save, copy, and paste the data in the table into Excel. Save the Excel file. 14. From the position time graph, determine the initial and final velocity of each cart. Note: The initial velocity of cart 1 is the slope of the linear fit of the graph portion before a slight bend of the plot, and the final velocity of the carts is the slope of the linear fit of the portion following the slight bend in the plot. These are the experimental values of velocities. 14. Repeat steps 1 to 13 for a total of 5 trials. 15. Create a table as shown below and populate it with all data obtained.

matter the velocity, we were able to get a good yield.