Conservation of Momentum in One Dimension
Studio Physics I
Part I – Internal and External Forces,
Newton’s Third Law and Conservation of Momentum
1. Write down the definition of a Newton’s 3rd Law force pair as presented to you in the lecture. (Hint:
This is not “two equal, oppositely directed forces,” or something about forces summing to zero.)
Two carts undergo a collision on a frictionless track. The mass of cart #1 is half the mass of cart #2.
Before the collision, cart #1 was moving to the right at 3 m/s and cart #2 was stationary. After the
collision, cart #1 was moving to the left at 1 m/s and cart #2 was moving to the right at 2 m/s.
2. Draw a free-body diagram for each cart during the collision. Show all forces acting on the carts, both
in the vertical and horizontal directions. (Hint: There are three on each cart.)
3. Note any Newton’s 3rd Law force pairs present in these two freebody diagrams (if any) by putting the
same number of lines through the force vectors on the diagrams. For example, these two vectors are
marked as being a pair:
Also, make a list of those force pairs here. Verify that every force pair that you have identified is
consistent with the definition that you wrote down in question #1.
4. For each of the forces represented in your freebody diagrams, you are to determine whether the force
is an internal force or an external force. Carefully refresh your memory as to the definitions of these
classifications of forces from the lecture. Consider the two carts as your system, call it System A.
Do not include the track, earth or anything else in your system. Based on this definition of your
system, place a capital (I) next to the force vector if the force is an internal force. Place a capital (E)
next to the force vector if the force is an external force. Every force vector in your freebody diagrams
should have one or the other letter next to it.
5. Now consider only the cart #2 as your system, call it System B. Do not include cart #1, the track,
earth or anything else in your system. Based on this definition of your system, place a lowercase (i)
next to the force vector if the force is an internal force. Place a lower case (e) next to the force vector
if the force is an external force.
6. Recall that the momentum will be conserved in the X-direction if there is no net external force on
your system in the X-direction. Based on this and your freebody diagrams above, would you expect
the momentum in X-direction to be conserved during the entire time (before, during and after the
collision) for System A? How about System B? Explain your answers.
Have one person on your team start the exercise while the others do Part II. Discuss the results for Part II
and the exercise with each other when you are done. All team members must answer all questions.
Part II – Conservation of Momentum During An “Explosion”
For this part of the activity you will need a movie called "explosion.mov". You can get it from the Studio
Physics CD. (Go to the Physics 1 folder, then look for “explosion.mov”.) You can also transfer it from
the course web site. (Go to “Activities”, scroll down to “Class 07” and click on “Video Point File A”.)
Start the VideoPoint software, choose open movie and open "explosion.mov" from where you stored it.
WHEN OPENING THE MOVIE, CHOOSE TO LOCATE 2 OBJECTS,
SINCE WE WILL BE TRACKING TWO DIFFERENT CARTS
 1999, 2000 K. Cummings; Rev. 2004 Bedrosian
7. Make the video image window larger. Calibrate the length scale by using the ruler icon and clicking
on either end of the meter stick shown below the tracks. Do not change “scale origin” or “scale type”.
8. Collect position data for each cart by first clicking on one cart and then clicking on the other cart.
After the second click, the movie frame will advance. You need to always click on the carts in
the same order. Take data carefully – try to click on the centers of the “dots”. The carts you are
interested in are on the top track, where the instructor is releasing a spring on one of them.
9. Generate (using the graph icon) and sketch plots of the X-velocity of both carts.
10. What was the total momentum of the system before the explosion? (Calculate a number or justify
your answer.) Calculate the final momentum of the cart on the left (m= 510.2 grams). Calculate the
final momentum of the cart on the right (m = 1020.2 grams) after the spring “explosion”. What is the
total final momentum of the two-cart system? Show all of your work in doing these calculations.
11. Is momentum conserved in this case? In light of the fact that there was an “explosion” (a spring
popping open) in this system, does your answer make sense? Explain.
12. If you chose only the cart on the right as your system, would momentum have been conserved in the
explosion? Explain why your answer makes sense in terms of internal and external forces.
13. Explain why we don’t worry about internal forces when considering whether momentum will be
conserved or not. Refer back to the discussion in Part I if necessary.
Exercise
In this exercise, we will continue with the example of the cart collision in Part I. Let moving to the right
be the + direction of velocity and momentum. For ease of calculation, let the mass of cart #1 be 0.5 kg
and the mass of cart #2 be 1.0 kg. Assume the system consists of cart #1 and cart #2. Ignore friction.
14. What was the momentum of the system before the collision?
15. What was the impulse on cart #1 from cart #2 during the collision?
16. What was the impulse on cart #2 from cart #1 during the collision? How does that relate to 15?
Explain using Newton’s 3rd Law and the definition of impulse.
17. What was the momentum of the system after the collision?
18. Explain why the answers to 14 and 17 are or are not the same.
We will next assume that the track has magnetic bumpers on either end that change the directions of the
respective carts but retain the same speed. After hitting the bumpers, cart #1 will be going 1 m/s to the
right and cart #2 will be going 2 m/s to the left, and the carts will collide a second time.
19. What was the impulse on cart #1 from the bumper on the left end of the track?
20. What was the impulse on cart #2 from the bumper on the right end of the track?
21. What was the momentum of the system after hitting the bumpers?
22. Explain why the answers to 17 and 21 are or are not the same.
23. Relate the answers to 17, 19, 20, and 21 in an equation and justify your equation using principles we
discussed today and/or in previous classes.
24. After the second collision between the carts, cart #1 is moving to the left at 3 m/s. What is the
velocity of cart #2?
 1999, 2000 K. Cummings; Rev. 2004 Bedrosian