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 these 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 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 3,4 and 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.
 1999, 2000 K. Cummings
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?
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.
WHEN OPENING THE FOLLOWING MOVIE, CHOOSE TO LOCATE 2 OBJECTS,
SINCE WE WILL BE TRACKING TWO DIFFERENT CARTS.
For this part of the activity you will need a movie called "explosion.mov" . You can get it off of
the CD (go to VideoPoint folder, then Movies, then look for it in the list). You can also transfer it
from the course webpage (Go to “class activities”, scroll down to the bottom of the page, RIGHT
CLICK on the movie, choose “save link as” and watch were the file get saved to. Once you have
the movie file, open the Videopoint software, chose open movie and open "explosion.mov" .
11. The first thing that must be done is to calibrate our measurement tool. 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.
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 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 discussion in regard to the freebody diagrams at the start
of the activity if necessary.
 1999, 2000 K. Cummings