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?
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 09" 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.
