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 third 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.)
2. What is the relationship between the two forces in the pair (in terms of their directions and
magnitudes)?
Consider the following scenario: Two carts undergo a collision on a frictionless track. The mass of cart #1
is twice the mass of cart #2. These two carts are moving as follows before the collision: cart #1 is moving
to the right at 5 m/s, cart #2 is stationary. The carts bounce off one another after the collision.
3. Draw a diagram of the situation and label your carts #1 and #2. Draw a freebody diagram for cart #1
before the collision. Show all forces acting on the cart, both in the vertical and horizontal directions.
4. Draw a free body diagram for cart #2 before the collision. Show all forces acting on the cart, both in
the vertical and horizontal directions.
5. Note any Newton’s third 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.
6. Repeat steps 3-5 above for the carts during the collision.
7. For each of the forces represented in your 4 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. 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 capitol (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.
8. Now consider only the cart on the right as your system. Do not include the other cart, 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.
9. 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 the TWO cart system? Why or Why not?
 1999, 2000 K. Cummings; Rev. 2003 Bedrosian
10. Would you expect the momentum in x-direction to be conserved during the entire time (before,
during and after the collision) for the ONE cart system? Why or Why not?
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 08” and click on “Video Point File A”.)
Copy it to your hard drive. Start the VideoPoint software, choose open movie and open "explosion.mov"
from the folder where you saved it.
WHEN OPENING THE MOVIE, CHOOSE TO LOCATE 2 OBJECTS,
SINCE WE WILL BE TRACKING TWO DIFFERENT CARTS
11. The first thing that must be done is to calibrate our measurement tool. (Before you do that, you might
want to make the movie larger on your screen.) There is a meter stick shown below the tracks. Use
this as your known length. Click on the ruler icon and follow the instructions that appear on the
computer screen. Do not change “scale origin” or “scale type”.
12. 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.
13. Generate (using the graph icon) and sketch plots of the x-velocity of both carts.
14. What is the approximate velocity in the x direction for each of the two carts according to your
graphs?
15. 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). What is the total final momentum of the
two cart system? Show all of your work in doing these calculations.
16. 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? Justify your answer using complete
sentences.
17. What was the momentum of the cart on the right before the explosion? (Calculate or cite a number)
What was the momentum of the cart on the right after the explosion? 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.
18. Would your answers to the question above be any different if we had discussed the cart on the left
rather the cart on the right? Why or why not?
19. Explain why we don’t worry about internal forces when considering whether momentum will be
conserved or not. Refer back to the discussion in regard to the freebody diagrams at the start of the
activity if necessary.
 1999, 2000 K. Cummings; Rev. 2003 Bedrosian