phy 111 remote lab 08 - momentum

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Name: _________________________________ PHY 111: Remote Lab #8 Momentum Purpose: To investigate the concept of linear momentum Objectives:  To describe the physics of collisions  To introduce the concept of impulse  To distinguish between elastic and inelastic collisions  To describe the influence of relative masses on the outcomes of collisions  To apply the Laws of Motion to the understanding of collisions  To derive the concept of conservation of linear momentum Materials & Resources  “Collision Lab” simulation (found at http://phet.colorado.edu ) Introduction A “collision” in physics occurs when two objects get so close to each other (often to the extent of coming in contact with each other) so as to dramatically affect each other’s velocities. Collisions are often thus described as arising from the imparting of impulses , which are relatively large amounts of forces applied over small durations of time. Impulses can also be thought of as changes in momentum – momentum being the mass of an object multiplied by its velocity. Like energy, momentum can be transferred from one object to another. Also like energy, the total momentum of a system is conserved – that is, the momentum of a system of objects before a collision equals the momentum of that system after a collision. The analysis of collisions ranges from the forensics of car crashes to the discovery of new subatomic particles, and therefore is of great importance in physics. Here we will review some of the basic ideas behind momentum.

Part #1: Simulations of elastic collisions Go to phet.colorado.edu and search for the “Collision Lab” simulation (as before, it will be under “Physics” and “Motion”). We will start with the 1-dimensional simulation (“introduction”). In our 1D simulations, the mass at the left is always moving at the beginning (the “incoming” mass, or object #1) and the mass at the right is always stationary at the beginning (object #2). You may need to set the motion of the right-hand mass to zero. 1. Choose the “elastic” setting (or move the slide bar all the way to “elastic”). Set the masses both equal to 1.0 kg. There is also a tab to keep track of the system’s total kinetic energy. (a) Note the values of the objects’ masses, velocities and the total kinetic energy of the system before & after an elastic collision (Table 8-1). Table 8-1. Elastic collision between two identical masses Object #1 Object #2 System Mass (kg): 1.0 1.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ X Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (b) Next, determine the initial and final momenta of the objects and record them in Table 8-1. If the sim doesn’t provide this directly, you will have to calculate it (note that “p” represents momentum): p = mv

(c) Compare the initial velocity of object #1 to the final velocity of object #2. What appears to have happened? (d) How does the initial momentum of object #1 compare to the final momentum of object #1? Is the initial momentum greater, is the final momentum greater, or are they equal? (e) How does the initial momentum of object #2 compare to the final momentum of object #2? (f) How does the initial momentum of the system (i.e. object #1 plus object #2) compare to the final momentum of the system? (g) Finally, how does the initial kinetic energy of the system compare to the final kinetic energy of the system? 2. Leave the collision setting as “elastic”, but now make object #1 twice as massive as object #2. Run the sim again and record the values of each quantity in Table 8-2. (a) Compare the initial velocity of object #1 to the final velocity of object #2. They won’t be equal this time – what appears to have happened instead?

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Table 8-2. Elastic Collision when the incoming object has more mass Object #1 Object #2 System Mass (kg): 2.0 1.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ X Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (b) How does the initial momentum of the system compare to the final momentum of the system? (c) How does the initial kinetic energy of the system compare to the final kinetic energy of the system? 3. Leave the collision setting as “elastic”, but now make object #1 half as massive as object #2. Run the sim again and record the values of each quantity in Table 8-3. (a) Compare the initial velocity of object #1 to the final velocity of object #2. Again, they won’t be equal this time – what appears to have happened instead?

Table 8-3. Elastic collision when the incoming object has less mass Object #1 Object #2 System Mass (kg): 1.0 2.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ X Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (b) In the previous examples, both objects moved in the same direction. What has happened this time? (c) How does the initial momentum of the system compare to the final momentum of the system? (d) How does the initial kinetic energy of the system compare to the final kinetic energy of the system? (e) What is the rule (or rules) we can apply to elastic collisions?

Part #2: Simulations of inelastic collisions 1. Choose the “inelastic” setting. Set the masses both equal to 1.0 kg. (a) Note the values of the objects’ velocities, momenta and total kinetic energy of the system before & after an inelastic collision (Table 8-4). Table 8-4. Inelastic collision between two identical masses. Object #1 Object #2 System Mass (kg): 1.0 1.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ __________ Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (b) Compare the initial velocity of object #1 to the final velocity of both objects (they should be stuck together). What appears to have happened? (c) How does the initial momentum of the system compare to the final momentum of the system? (d) How does the initial kinetic energy of the system compare to the final kinetic energy of the system?

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2. Let’s repeat the case where object #1 is twice as massive as object #2, but now for an inelastic collision. Record your results in Table 8-5 below: Table 8-5. Inelastic Collision when the incoming object has more mass Object #1 Object #2 System Mass (kg): 2.0 1.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ __________ Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (a) Compare the initial velocity of object #1 to the final velocity of both objects (they should be stuck together). What appears to have happened? (b) How does the initial momentum of the system compare to the final momentum of the system? (c) How does the initial kinetic energy of the system compare to the final kinetic energy of the system?

3. Finally, let’s repeat the case where object #1 is half as massive as object #2, but now for an inelastic collision. Record your results in Table 8-6 below: Table 8-6. Inelastic Collision when the incoming object has more mass Object #1 Object #2 System Mass (kg): 1.0 2.0 __________ Initial velocity (m/s): __________ __________ X Final velocity (m/s): __________ __________ __________ Initial Kinetic Energy (J): X X __________ Final Kinetic Energy (J): X X __________ Initial momentum (kg . m/s): __________ __________ __________ Final momemtum (kg . m/s): __________ __________ __________ (a) Compare the initial velocity of object #1 to the final velocity of both objects (they should be stuck together). What appears to have happened? (b) How does the initial momentum of the system compare to the final momentum of the system? (c) How does the initial kinetic energy of the system compare to the final kinetic energy of the system?

(d) What is the rule (or rules) we can apply to inelastic collisions? Part #3: 2D Collisions Now it’s time to look at two-dimensional collisions. Change to the “Advanced” page. We’ll leave the masses as their default values - ball #1 should be 0.5 kg and ball #2 should be 1.5 kg. We’ll also start with elastic collisions; please set the sim to 100% elasticity if it hasn’t defaulted here. 1. Before we take data, watch how this works. Run the sim and watch the collision. Briefly describe what happens: 2. Click on the “kinetic energy” button – you should see a reading to the lower left. How does the kinetic energy of the system of objects before the collision compare to the kinetic energy of the system after the collision? 3. Click on the button toward bottom left that asks for “More Data”. Copy the values of the individual momenta into Table 8-7 below: Table 8-7. Momenta in Two Dimensions (Before elastic collision) Momentum (kg . m/s) In x-direction In y-direction Ball #1 ____________ ____________ Ball #2 ____________ ____________ Total ____________ ____________

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4. Run the sim. Pause the sim after the collision (if you don’t, the balls bounce off the walls, which throws off our answers). Copy the values of the individual momenta into Table 8-8 below: Table 8-8. Momenta in Two Dimensions (After elastic collision) Momentum (kg . m/s) In x-direction In y-direction Ball #1 ____________ ____________ Ball #2 ____________ ____________ Total ____________ ____________ 5. How do the individual values of the momenta for each ball behave – are they the same before and after the collision? 6. Add up the momenta for both cases (before and after) and record the totals in Tables 8-7 and 8-8. How do the total values of the momenta behave – are they the same before and after the collision? Now reset the sim, but this time choose a 0% elasticity (i.e. inelastic) collision. Note you may need to alter the elasticity each time you run the sim. 7. Again track the total kinetic energy of the system. Run the sim. Is the total kinetic energy the same before and after the collision? If not, how did it change – did the total kinetic energy increase or decrease? 8. Again click on the “More Data” button and copy the amounts of momenta for both balls before and after the collision in Tables 8-9 and 8-10 below:

Table 8-9. Momenta in Two Dimensions (Before inelastic collision) Momentum (kg . m/s) In x-direction In y-direction Ball #1 ____________ ____________ Ball #2 ____________ ____________ Total ____________ ____________ Table 8-10. Momenta in Two Dimensions (After inelastic collision) Momentum (kg . m/s) In x-direction In y-direction Ball #1 ____________ ____________ Ball #2 ____________ ____________ Total ____________ ____________ 9. How do the individual values of the momenta for each ball behave – are they the same before and after the collision? 10. Add up the momenta for both cases (before and after) and record the totals in Tables 8-9 and 8-10. How do the total values of the momenta behave – are they the same before and after the collision?

Part #4: Summary The term conservation in physics means that the total amount of a quantity before an event equals the total amount of that quantity after the event. 1. Which system quantities are conserved during a collision? Simply check each option that applies in Table 8-11: Table 8-11. System quantities conserved during collisions Elastic Collision Inelastic Collision Velocity ________ ________ Momentum ________ ________ Kinetic Energy ________ ________ 2. Note that in question #1 above, we requested “system” quantities? Why? Are individual quantities ever conserved? (And what is a “system”, anyway?) 3. Which quantity(s), if any, is always conserved during a collision? 4. What is the difference between an elastic and inelastic collision? Briefly answer in terms of conservation. 5. We didn’t include mass in Table 8-11, because our objects never had the opportunity to change their individual masses during a collision. What might be a situation where mass can change? Hint: what is the opposite of a collision?

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