(A) Both Moving, Stopping After Colliding

Collision Lab

Up to now we have been describing the motion of one object. Now we start to consider two objects colliding with each other. We want to be able to describe the motion of the two objects after the collision if we know their motions before the collision. We are trying to make predictions. For now, we will limit ourselves to straight-line (one-dimensional) motion and “inelastic” collisions, where the two objects stick to each other and travel together after the collision.

In this lab, you will be given a number of collision situations. You will first make predictions about what you think the results of the collision will be. Then, you will use the tracks and carts, along with the photogates, to test your predictions.

Part I: Predictions

(a) Both moving, stopping after colliding

For each of the situations listed in the table below, a blue cart will be moving at speed v. You will push a red cart in the opposite direction at just the right speed so that the two carts stick together and come to a complete stop. (It will obviously take some practice.) In some of the situations the carts are identical; in others, the carts have different masses. On your own paper, write down your predictions for the speed with which the red cart will have to be moving in order to have both carts come to a stop. Your predictions should be written in terms of the initial speed v; that is, if you think the red cart will have to be going three times the speed of the blue cart, you would write down 3v. Your data table should look something like this:

Your prediction / Actual results
Blue Cart / Red Cart / Blue Cart / Red Cart
mass / speed / mass / speed / mass / speed / mass / speed
m / v / m / m / m
m / v / 2m / m / 2m
m / v / 3m / m / 3m
2m / v / m / 2m / m
3m / v / m / 3m / m

(b) Initially at rest, pushing off each other

What about a collision in reverse? Called an “explosion”, you’ll start two carts at rest right next to each other, then release the spring-loaded plunger on the red cart so that carts push off of each other in opposite directions. On your paper, write down your predictions for the same five mass combinations listed above. (Again, write down your predictions in terms of v, the speed of one of the carts.) Use a data table like this:

(c) One cart moving, the other at rest

Now let’s consider a different question. For the same five mass combinations listed above, a blue cart will be moving at speed v toward a red cart at rest. The two carts will stick together after the collision. On your paper, write down your predictions for the speed of the carts after they collide and stick together. As before, your prediction should be written in terms of v.

Your prediction / Actual results
Before Collision / After Collision / Before Collision / After Collision
Blue Cart / Red Cart / Both Carts Together / Blue Cart / Red Cart / Both Carts Together
mass / speed / mass / speed / mass / speed / mass / speed / mass / speed / mass / speed
m / v / m / 0 / 2m / m / m / 0 / 2m
m / v / 2m / 0 / 3m / m / 2m / 0 / 3m
m / v / 3m / 0 / 4m / m / 3m / 0 / 4m
2m / v / m / 0 / 3m / 2m / m / 0 / 3m
3m / v / m / 0 / 4m / 3m / m / 0 / 4m

Part II: Testing Your Predictions

You should have predictions written down for fifteen different situations. Now you will use the carts and tracks to test each of your predictions. Each cart by itself is 250 g; you also have two extra 250 g masses that you can add to the cart(s) to vary their mass.

Make sure that all the cables you need are plugged in. Once the LabPro and photogates are correctly set up, open the file “collisions.cmbl” on the computer. This file will record the times measured by the two photogates and calculate the speed based upon the width of the flag on top of each cart.

Using the photogates to measure speeds, perform the collisions listed above and record the speeds of the two carts. Compare the experimental results to your predictions.

Part III: Drawing Conclusions

Our goal in this lab is to be able to make predictions about the motion of two objects after they collide if we know their motion before they collide. What we want is to be able to make one general statement that will cover all the cases you tested in Part II (and more). This should be in the form of a rule or formula: if the carts are doing X, then Y will happen.

Be careful not to stray from descriptions into explanations. We will worry about why these things happen in about two weeks. For now, all we are trying to do is describe what happens. As soon as you find yourself saying something that includes “this happens because…”, stop!

Don’t try to write down a rule that will apply to every possible situation immediately. Instead build up your rules. First figure out a rule that applies to the collisions in part (a). Then see if you can broaden your rule so that it applies to part (b) as well. After that, expand your rule so that it covers part (c) also.

Using the results from Part II, write down one general rule that applies to all (inelastic) collisions that will allow us to predict the motion of two carts after they collide.

Part IV: Elastic Collisions

Now that you have a general rule that relates the speeds of two carts before and after a collision, test your rule by using elastic (bouncing) collisions. Turn the carts around so that the magnetic sides face each other. Using a variety of initial speeds for the two carts (including zero), collide the carts and record the speeds before and after the collision. Does your general rule also apply to these collisions? If not, could you modify your rule so that it would apply to elastic as well as inelastic collisions?