LAB 7: NEWTON’S THIRD LAW AND CONSERVATION OF MOMENTUM

Please list the members of your group:

OBJECTIVES

OVERVIEW

Interactions like collisions and explosions never involve just one object. Therefore, we turn our attention to the mutual forces of interaction between two or more objects. This will lead us to a very general law known as Newton’s third law, which relates the forces of interaction exerted by two objects on each other. Then, you will examine the consequences of this law and the impulse–momentum law, when they are applied to collisions between objects. In doing so, you will arrive at one of the most important laws of interactions between objects, the conservation of momentum law.

As usual you will be asked to make some predictions about interaction forces and then be given the opportunity to test these predictions.


Copyright © 2018 John Wiley & Sons, Inc.

INVESTIGATION 1: REVIEW: WHAT DOES THE FORCE IN A COLLISION LOOK LIKE?

A ball is thrown at a wall and bounces off. During the time that the ball is in contact with the wall, the wall exerts a force on the ball. What does this force look like over time? You can simulate such an interaction with the IOLab.

The setup will look like this.


First a prediction

INVESTIGATION 1

Prediction 1-1: Choose from the graphs below your prediction for the force exerted by the book on the IOLab force sensor as a function of time.


1 2 3 4 5 Explain your prediction—why do you think that the graph will have this shape? From the graph, how do you know the time interval during which the IOLab spring is in contact with the book?

CALIBRATE THE FORCE SENSOR BEFORE MOVING ON TO THE NEXT SLIDE.

INVESTIGATION 1

To test your prediction, you will need:

  1. Zero the force sensor with nothing pushing or pulling on it by clicking Rezero sensor.
  2. Press Record and give the IOLab a short push toward the book. Let it hit the book and rebound.
  3. Use the to clearly display the shape of the force-time graph. If necessary, also adjust the Force axis by selecting to the lower left of the axes, and typing in values.
Question 1-1: Which prediction graph does your graph resemble? Does this agree with the prediction you chose?

INVESTIGATION 1

Question 1-2: : Identify on your graph the time interval during which the spring was in contact with the book. How do you know? Question 1-3: Explain why the Force-time graph has this shape. Hint: what happens to the force as the spring bumper compresses and then stretches back again?

INVESTIGATION 2:

FORCES BETWEEN INTERACTING OBJECTS

There are many situations where objects interact with each other, for example, during collisions. In this investigation we want to compare the forces exerted by the objects on each other. In a collision, both objects might have the same mass and be moving at the same speed, or one object might be much more massive, or they might be moving at very different speeds. What factors might determine the forces the objects exert on each other? Is there some general law that relates these forces?

Activity 2-1: Collision Interaction Forces

What can we say about the forces two objects exert on each other during a collision?

Prediction 2-1: Suppose two cars have the same mass and are moving toward each other at the same speed so that and



Choose your prediction for the relative magnitudes of the forces between car A and car B durring the collision Car A exerts a larger force on car B. The cars exert the same size force on each other. Car B exerts a larger force on car A.

Activity 2-1: Collision Interaction Forces

Prediction 2-2: Suppose the masses of two cars are the same and that car A is moving toward car B, but car B is at rest. and



Choose your prediction for the relative magnitudes of the forces between car A and car B durring the collision Car A exerts a larger force on car B. The cars exert the same size force on each other. Car B exerts a larger force on car A.
Prediction 2-3: Suppose the mass of truck A is greater than that of car B and that it is moving toward car B, which is at rest. and



Choose your prediction for the relative magnitudes of the forces between car A and car B durring the collision Car A exerts a larger force on car B. The cars exert the same size force on each other. Car B exerts a larger force on car A.

Activity 2-1: Collision Interaction Forces

Summarize your predictions: What are the circumstances under which you predict that one object will exert a greater force on the other object?

If you have two IOLabs, you can test the predictions you made by studying gentle collisions between the two force sensors on the two IOLabs. However, since you probably have only one IOLab, this lab includes videos of collisions between two IOLabs that you can examine.

Activity 2-1: Collision Interaction Forces

Examine collisions (a)–(c) listed below.

(a) Two carts of the same mass moving toward each other at about the same speed.

Play the entire video, and examine the forces the two carts exert on each other.



Activity 2-1: Collision Interaction Forces

(b) Two carts of the same mass, one at rest and the other moving toward it.

Play the entire video, and examine the forces the two carts exert on each other.


Activity 2-1: Collision Interaction Forces

(c) One cart twice or three times as massive as the other, moving toward the other cart, which is at rest.

Play the entire video, and examine the forces the two carts exert on each other.



Activity 2-1: Collision Interaction Forces

Question 2-1: Did your observations agree with your predictions? What can you conclude about forces of interaction during collisions? Under what circumstances does one object experience a different force than the other during a collision? How do forces compare on a moment by moment basis during each collision? Question 2-2: You have probably studied Newton’s third law in lecture or in your text. Do your conclusions have anything to do with Newton’s third law? Explain. Question 2-3: Recall that the impulse is defined as the area under the force vs.time graph. How does the impulse due to cart A acting on cart B compare to the impulse of cart B acting on cart A in each collision? Are they the same in magnitude or different? Do they have the same sign or different signs?

Activity 2-2: Interactive Forces During an Explosion

An explosion usually involves a number of pieces of matter (often a large number!) flying apart, caused by the internal forces between them produced by a violent chemical reaction. Sometimes, as in the firing of a gun, the event can be considered as two objects flying apart, caused by the internal forces between them.




Activity 2-2: Interactive Forces During an Explosion

In this activity, you will simulate an explosion by compressing a spring between two IOLabs, and then letting the spring force (“the explosion”) push the IOLabs apart.


First a prediction.

Prediction 2-4: Suppose the two IOLabs have equal mass, and that both IOLabs are at rest with the spring compressed between them before they are released. The force sensors can measure the forces exerted on IOLab A and on IOLab B. Choose your prediction for the relative magnitudes of the forces as the spring pushes the IOLabs apart. The force on IOLab A is larger than the force on IOLab B. The forces on both IOLabs are the same. The force on IOLab B is larger than the force on IOLab A.

Activity 2-2: Interactive Forces During an Explosion

Once again, you will view a video of the “explosion.” Play the entire video, and examine the forces exerted by the spring on the two IOLabs.


Question 2-4: Compare the two forces. Did this agree with your prediction?

Activity 2-2: Interactive Forces During an Explosion

Now suppose that the two pieces that fly apart in the explosion do not have equal mass. We can simulate this by adding mass to one of the IOLabs.


Prediction 2-5: The spring between the two IOLabs is compressed. Choose your prediction for the relative magnitudes of the forces as the spring pushes the IOLabs apart. The force on IOLab A is larger than the force on IOLab B. The forces on both IOLabs are the same. The force on IOLab B is larger than the force on IOLab A. Explain your prediction

Activity 2-2: Interactive Forces During an Explosion

Now, play the entire video, and examine the forces exerted by the spring on the two IOLabs.


Question 2-5: Compare the two forces. Does the result agree with your prediction? Question 2-6: Explain your observation. Could it have something to do with Newton’s Third Law?

Activity 2-3: Other Interaction Forces

Interaction forces between two objects occur in many other situations besides collisions and explosions. For example, suppose that a small car pushes a truck with a stalled engine, as shown in the picture. The mass of object A (the car) is much smaller than object B (the truck).




At first the car doesn’t push hard enough to make the truck move. Then, as the driver pushes harder on the gas pedal, the truck begins to accelerate. Then, the car and truck are moving along at the same constant speed. Finally, the car pushes with a smaller force, and the car and truck slow down and come to rest.

Activity 2-3: Other Interaction Forces

You can again simulate the car pushing the truck with two IOLabs.



The IOLabs have been turned over so that there is larger friction, and a mass has been placed on top of IOLab B to double its mass.

First some predictions. There are three parts to the motion as IOLab A is pushed against IOLab B: the IOLabs begin speeding up, they move at a constant speed, and then they slow down. Make a prediction for each part of the motion.

Prediction 2-6: As the IOLabs begin to speed up, choose your prediction for the relative magnitudes of the force exerted by IOLab A on IOLab B and the force exerted by IOLab B on IOLab A. IOLab A exerts a larger force on IOLab B. Both forces are the same. IOLab B exerts a larger force on IOLab A.

Activity 2-3: Other Interaction Forces

Prediction 2-7: As the IOLabs move together at a constant speed, choose your prediction for the relative magnitudes of the force exerted by IOLab A on IOLab B and the force exerted by IOLab B on IOLab A. IOLab A exerts a larger force on IOLab B. Both forces are the same. IOLab B exerts a larger force on IOLab A. Prediction 2-8: As the IOLabs slow down, choose your prediction for the relative magnitudes of the force exerted by IOLab A on IOLab B and the force exerted by IOLab B on IOLab A. IOLab A exerts a larger force on IOLab B. Both forces are the same. IOLab B exerts a larger force on IOLab A.

Activity 2-3: Other Interaction Forces

Test your predictions. Play the entire video, and examine the forces exerted by the IOLabs on each other.


Question 2-7: How do your results compare to your predictions? Is the force exerted by car A on truck B (reading of force sensor B) significantly different from the force exerted by truck B on car A (reading of force sensor A) during any part of the motion? Explain any differences you observe between your predictions and your observations. Question 2-8: Explain how truck B is able to accelerate. Use Newton’s second law, and analyze the combined (net) force exerted by all the forces acting on truck B. Is there a nonzero net force?

INVESTIGATION 3: NEWTON’S LAWS AND MOMENTUM CONSERVATION

Your work in Investigation 1 should have shown that interaction forces between two objects are equal in magnitude and opposite in sign (direction) on a moment by moment basis for all the interactions you studied. This is a testimonial to the universal applicability of Newton’s third law to interactions between objects.

As a consequence of the forces between two colliding objects being equal and opposite at each moment, the impulses of the two forces are always equal in magnitude and opposite in direction. This observation, along with the impulse–momentum theorem that you studied in Lab 6, is the basis for the derivation of the conservation of momentum law, which you may have seen in lecture or in your text. (The impulse–momentum theorem is really equivalent to Newton’s third law since it can be derived mathematically from this law.) The argument is that the impulse acting on object A during the collision equals the change in momentum of object A, and the impulse acting on object B during the collision equals the change in momentum of object B:

and

But, as you have observed, as a consequence of Newton’s third law, if the only forces acting on the objects are the interaction forces between them, then By simple algebra

or

i.e., there is no change in the total momentum of the system (the two objects).

Note: It is important to know what system you are examining. In this discussion, the system includes the two objects. While neither the momentum of object A nor the momentum of object B is conserved during the collision between them, the momentum of the system including both of them is conserved, when there are only internal forces acting on the objects that make up the system (or no net external force on the system).

INVESTIGATION 3: NEWTON’S LAWS AND MOMENTUM CONSERVATION

Suppose that the two objects are IOLabs. If the momenta of the two IOLabs before (initial—subscript i) and after (final—subscript f) the collision are represented in the diagrams below, then:


Where

and

In the next activity you will examine the conservation of momentum in a simple elastic collision between two carts of equal mass. If you have two IOLabs, you can carry out the collisions yourself. Since you probably don’t have two IOLabs, you have been provided videos of the collisions.

Activity 3-1: Conservation of Momentum in an Elastic Collision

1. The two IOLabs of equal mass are set up with the spring bumper attached to the one on the left.



Prediction 3-1: In the video, IOLab A is given a push toward IOLab B, which is initially at rest. The IOLabs bounce off each other during the collision. Suppose that you measure the total momentum of IOLab A and IOLab B before and after the collision. How do you think that the total momentum after the collision will compare to the total momentum before the collision? Prediction 3-2: Given that the IOLabs have the same mass, if the initial velocity of IOLab A is , what do you predict for the values of and ? Explain the basis for your prediction.

Activity 3-1: Conservation of Momentum in an Elastic Collision

Test your prediction.

2. View the entire video. Record the velocities measured in the video just before the collision and just after the collision below.

3. Calculate the total momentum of the system consisting of IOLabs A and B before the collision and after the collision in terms of their masses m. show your calculations below. See Slide 23 if you need a reminder of how to calculate these.


Momentum calculations

Activity 3-1: Conservation of Momentum in an Elastic Collision

Question 3-1: Was momentum for the system consisting of the two IOLabs conserved during the collision? Did your results agree with your prediction? Explain. Question 3-2: Did the final velocities of IOLab A and IOLab B agree with your prediction? Explain why the measured values are what is needed for momentum to be conserved in the collision.

Activity 3-2: Conservation of Momentum in an Inelastic Collision

In this activity, you will examine an inelastic collision in which the two IOLabs stick together after they collide. This can be accomplished by putting a loop of tape with its sticky side facing outward on the front of each of the IOLabs. See the figures below. Again, you will view a video of the collision.


Prediction 3-3: In the video, IOLab A is given a push toward IOLab B, which is initially at rest. The IOLabs stick together after the collision. Suppose that you measure the total momentum of IOLab A and IOLab B before and after the collision. How do you think that the total momentum after the collision will compare to the total momentum before the collision? Prediction 3-4: Given that the IOLabs have the same mass, if the initial velocity of IOLab A is , what do you predict for the value of their velocity ? Explain the basis for your prediction.

Activity 3-2: Conservation of Momentum in an Inelastic Collision

Test your predictions.

1. View the entire video. Record the velocities measured in the video just before the collision and just after the collision below.

2. Calculate the total momentum of the system consisting of IOLabs A and B before the collision and after the collision in terms of their masses m. show your calculations below. See Slide 23 if you need a reminder of how to calculate these.


Momentum calculations

Activity 3-2: Conservation of Momentum in an Inelastic Collision

Question 3-3: Was momentum conserved for the system consisting of the two IOLabs during the collision? Did your results agree with your prediction? Explain. Question 3-4: Did the final velocities of IOLab A and IOLab B agree with your prediction? Explain why the measured values are what is needed for momentum to be conserved in the collision.

Comment: Momentum is conserved for the system consisting of the two IOLabs whether the IOLabs bounce off each other during the collision (elastic collision) or stick to each other (inelastic collision).

ALL DONE!

Please remember to edit the report (insert your name - and if necessary your partners), export the report and submit it on D2L.


Now do the homework associated with this lab.


Copyright © 2018 John Wiley & Sons, Inc. and David Sokoloff, Erik Jensen, and Erik Bodegom.
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