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.
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
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.
CALIBRATE THE FORCE SENSOR BEFORE MOVING ON TO THE NEXT SLIDE.
To test your prediction, you will need:
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?
What can we say about the forces two objects exert on each other during a collision?
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.
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.
(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.
(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.
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.
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.
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.
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.
Now, play the entire video, and examine the forces exerted by the spring on the two IOLabs.
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.
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.
Test your predictions. Play the entire video, and examine the forces exerted by the IOLabs on each other.
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).
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.
1. The two IOLabs of equal mass are set up with the spring bumper attached to the one on the left.
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.
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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.
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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.
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.
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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.
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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).
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.