Collision and Momentum Lab PDF

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Summary

OBJECTIVE: The purpose of this experiment is to explore conservation of momentum for elastic
and inelastic collisions and to use the interactive simulation to generate data to test whether the
momentum of system is conserved in each type of collision....

Description

Name: ___________________

Conservation of Momentum in Collisions (1-Dimension) - Simulation OBJECTIVE: The purpose of this experiment is to explore conservation of momentum for elastic and inelastic collisions and to use the interactive simulation to generate data to test whether the momentum of system is conserved in each type of collision. THEORY: If we consider the two carts and the track as the system, when the two carts collide with each other, the total vector momentum, 𝑝 = 𝑚𝑣, is conserved (remains constant before and after the collision) regardless of the type of collision. In general, this means that we must consider each direction separately and conserve momentum in each direction (by component). However, in this lab we are limiting the interactions to one-dimension which we will call the x-direction. An elastic collision is one in which the two carts bounce off each other. A perfectly inelastic collision is one in which the two carts stick together and move together with the same final velocity. An explosion is a perfectly inelastic collision going backwards in time. PROCEDURE: Go to the following website and read the instructions for “Using the Interactive.” https://www.physicsclassroom.com/Physics-Interactives/Momentum-and-Collisions/CollisionCarts/Collision-Carts-Interactive You can resize the window as desired and click and drag the carts to move them. You can select the type of collision (elastic, inelastic or explosion), the mass of each cart by selecting different options for each cart, and the initial velocity of each cart (by using arrows on either direction).

Use subscripts in your equations and diagrams as follows: x for direction (+x is to the right), 1 for the red cart and 2 for the blue cart, i for initial and f for final velocities and momenta before and after each collision.

Attention: Throughout this lab, you need to pay attention to the directions of vector quantities, like velocity and momentum. Even if this is a one-dimensional simulation, you need to be careful about the directions. +x direction is to the right and -x direction is to the left.

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Part I: Elastic Collisions For Part I, select “Elastic Collision”. Please refer to below illustration and formula for before and after collision in one dimensional elastic collisions (along the x-axis). m1 (v1)i

Before Collision m2

After Collision m2 (v2)f m1 x

𝑝𝑖,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑖 + 𝑝2𝑖 = 𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖

x 𝑝𝑓,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑓 + 𝑝2𝑓 = 𝑚1 𝑣1𝑓 + 𝑚2 𝑣2𝑓

A. Carts with Equal Masses Case 1: 1. Place the red cart on the left end of the track and the blue cart in the middle of the track. 2. Set the velocity of the blue cart to 0 m/s and set the velocity of the red cart to 10 m/s and both masses to 1 kg. 3. Click “Start” to run the simulation and find the velocities of each cart after the collision, then use the values to calculate the momentum of each cart before and after the equation. 4. Record the results in the data table including units. (Do not write the calculations in the table.) Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total 5. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

6. Show your calculation for final momentum of each cart and find the total final momentum of the system.

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Case 2: 1. Place the carts at opposite sides of the track. 2. Keep the masses the same and set the velocity of the red cart to 10 m/s (+x direction) and the blue cart to -10 m/s (-x direction). 3. Run the simulation and record the final velocities. 4. Calculate the initial and final momenta of each cart and record the values in the data table. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total

5. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

6. Show your calculation for final momentum of each cart and find the total final momentum of the system.

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Case 3: 1. Place the red cart at the left end of the track and move the blue cart a little left of center. 2. Set the velocity of the red cart to 10 m/s and the velocity of the blue cart to 5 m/s. 3. Record and calculate the momenta before and after the collision as before. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total 4. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

5. Show your calculation for final momentum of each cart and find the total final momentum of the system.

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B. Carts with Unequal Mass Case 1: 1. Set the red cart mass to m1 = 3 kg, mass of the blue cart to m2 = 1 kg. 2. Place the red cart at the far left with initial velocity of +10 m/s and the blue cart in the middle with zero velocity. 3. Run the simulation, calculate the momenta of each cart before and after, and record your results in the table. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total

Case 2: 1. Start the carts at opposite ends of the track. 2. Set the red cart m1 = 1 kg with velocity +10 m/s and the blue cart m2 = 3 kg with -10 m/s. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total

Part I Summary: Summarize the results of Part I. Use your data as evidence to discuss if momentum is conserved in elastic collisions. What happened to the momentum of each cart as the result of the collision? How about the total momentum of the system?

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Part II: Perfectly Inelastic Collisions For Part II, select “Inelastic Collision”. Please refer to below illustration and formula for before and after collision in one dimensional inelastic collisions (along the x-axis). Note that carts stick and have a common final velocity. m1 (v1)i

Before Collision m2

After Collision m1 m2

(v)f

x 𝑝𝑖,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑖 + 𝑝2𝑖 = 𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖

x 𝑝𝑓,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑓 + 𝑝2𝑓 = (𝑚1 + 𝑚2 )𝑣𝑓

Case 1: 1. Set the type of collision to Inelastic. 2. Give the carts equal masses of 1kg. 3. With the blue cart at the center of the track at rest and red car at the left end, set the initial velocity of the red cart to +10 m/s. 4. Run the simulation and record your results in the table. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total 5. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

6. Show your calculation for final momentum of each cart and find the total final momentum of the system.

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Case 2: 1. Give the red cart a mass of 3kg and blue a mass of 1kg. 2. With the blue cart at the center of the track at rest and red car at the left end, set the initial velocity of the red cart to +10 m/s. 3. Run the simulation and record your results in the table. Cart

Initial Momentum (before collision) (px)i

Final momentum (after collision), (px)f

Change in momentum, Δpx

Red (1) Blue (2) System Total Case 3: 1. Give the carts equal masses of 1kg. 2. Place them at opposite ends of the track starting with equal and opposite velocities towards each other. 3. Record your observations and results. Cart

Initial Momentum (before collision) (px)i

Final momentum (after collision), (px)f

Change in momentum, Δpx

Red (1) Blue (2) System Total

Case 4: 1. Give the red cart a mass of 3kg and blue a mass of 1kg. 2. Place them at opposite ends of the track starting with equal and opposite velocities towards each other. 3. Record your observations and results. Cart

Initial Momentum (before collision) (px)i

Final momentum (after collision), (px)f

Change in momentum, Δpx

Red (1) Blue (2) System Total

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4. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

5. Show your calculation for final momentum of each cart and find the total final momentum of the system.

Part III: Explosions For Part III, select “Explosions”. Another type of inelastic collision occurs when an object breaks up into 2 or more fragments. This type of collision is called an explosion, which looks like a perfectly inelastic collision going backward in time. Please refer to below illustration and formula for before and after collision in one dimensional explosions (along the x-axis). Note that carts are initially stuck together and have a common initial velocity. Before Explosion

𝑝𝑖,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑖 + 𝑝2𝑖 = (𝑚1 + 𝑚2 )𝑣𝑖

After Explosion

𝑝𝑓,𝑡𝑜𝑡𝑎𝑙 = 𝑝1𝑓 + 𝑝2𝑓 = 𝑚1 𝑣1𝑓 + 𝑚2 𝑣2𝑓

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Case 1: 1. Place the two carts at the center with equal masses of 1kg. 2. Run the simulation and record your observations and results. Cart

Initial Momentum (before collision) (p)i

Final momentum (after collision), (p)f

Change in momentum, Δp

Red (1) Blue (2) System Total 3. Show your calculation for initial momentum of each cart and find the total initial momentum of the system.

4. Show your calculation for final momentum of each cart and find the total final momentum of the system.

Case 2: 1. Place the two carts at the center and set the red cart mass to 3 kg and blue to 1 kg. 2. Run the simulation and record your observations and results. Cart

Initial Momentum (before collision) (px)i

Final momentum (after collision), (px)f

Change in momentum, Δpx

Red (1) Blue (2) System Total

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Parts II&III Summary: 1. Is momentum conserved in inelastic collisions? Explain your answer.

2. Is momentum conserved in explosions? Explain your answer.

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