1. Chapter 10
Collisions

2. Review Momentum: If Fext = 0, then momentum does not change
For continuous momentum transfer (Rockets):
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3. Rockets: Continuous Momentum Transfer
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4. Momentum in a Collision
In a collision, objects only exert forces on each other, so Fext=0.
Total momentum is conserved
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5. Impulse During a collision, the momentum on an object changes
This change in momentum is called “Impulse”
When objects A and B collide
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6. Impulse Recall: In the limit of small Dt: (constant force)
(changing force)
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7. Impulse in a Collision
Different collisions with the same total impulse:
Blue
Dp/Dt Large
Momentum
Red
Dp/Dt Small
Large F:
p changes rapidly
Small F:
p changes slowly
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8. Example: The Impulsive Spiderman
Spiderman, who has a mass of 70 kg, jumps from a train 5 meters high moving at 20 m/s (about 40 mph).
He lands standing up, taking Dt = 0.1 s to stop himself after making contact with the ground. How much force did his knees feel?
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9. Example Treat as collision between Spiderman and the ground
Get force from the impulse:
Initial: p = mvtotal
Final: p = 0
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10. Example Need to find vy:
If he wasn’t a superhero, he’d break his legs!
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11. Example What if he rolls on landing for Dt = 2 sec?
Much easier on the knees!
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12. Cannon Recoil Cannon: mc=1134 kg Ball: mb=13.6 kg
Ball shot at ~ speed of sound
 vb = 340 m/s
The cannon and ball are initially at rest:
pball = mballvball = (13.6kg)(340 m/s) = 4620 kg m/s
So, pcannon= kg m/s
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13. A rope can easily handle this much force without
Cannon Recoil T pc
Cannon recoil stopped in ~2 s by ropes. What is the tension in the ropes?
A rope can easily handle this much force without
breaking
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14. Momentum Conservation in Different Frames
Simple 1D problem v -v m m
PTOT = mv - mv =0
Stick together 2m
v=0
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15. Momentum Conservation in Different Frames
Same 1D problem viewed from right hand block, or with right hand block at rest 2v m m
PTOT = 2mv + 0 = 2mv v
2 m
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16. Changes in Momentum Independent of Frame
Case 1
Case 2 i f i f
Left mv
2mv mv
Right
-mv mv
PTf – PTi = 0 – 0 = 0
PTf – PTi = 2mv – 2mv = 0
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17. Center of Momentum Frame
There is always a frame of reference where PTOT=0.
‘Center of mass’ frame
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18. A Limitation of MomentumvT vc
V=30 MPH
V=0
BOOM!
Before
After
How do we determine the velocities?
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19. A Limitation of Momentum
ptruck
pcar
There are many possibilities
Conservation of Momentum can’t tell them apart
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20. Elastic Collisions Two equations:
Momentum and kinetic energy are conserved
Two equations:
Good approximation for a lot of collisions, and exact for some
Examples: Billiard Balls, superball on floor…
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21. Elastic Collisions in One Dimension
Before
V1,i
V2,i m1 m2
After
V1,f
V2,f
Two conservation laws
Momentum
(Always)
Energy
(Elastic only - Mechanical Energy is conserved)
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22. We now have two equations and two unknowns:
A Unique Solution
We now have two equations and two unknowns:
Lots of Algebra
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23. Limiting Cases
How do we understand what types of motion these predict?
Consider limiting case:
m1 = m2
The two objects simply trade values of velocity!
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24. Limiting Cases What if m1 >> m2?
Semi truck hits a parked VW bug:
Truck keeps going
Bug bounces off with twice truck’s speed!
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25. Demonstration
m1>>m2
A Question:
What Happens?
Before:
After:

26. The Slingshot Effect
9.6 km/s
-10 km/s

27. Car-Truck Crash
A 2000 kg car has a head-on collision with a 10,000 kg truck. They each are travelling at 10 m/s and they collide elastically (solid bumpers!).
What are their final velocities? m1
v1i
v2i m2 +x
Choose positive x direction
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28. Car-Truck Crash (continued)m1
v1i
v2i m2
v1i = 10 m/s
m1 = 2,000 kg
v2i = -10 m/s
m2 = 10,000 kg
v2f = m/s
v1f = m/s
Truck slows down
Car goes flying backwards!
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29. Car-Truck Crash (continued)
If the two vehicles are being driven by 60 kg PSU students, what are the impulses they feel?
In truck: J = Dp = mDv
= m(v2f - v2i)
= 60(-3.33 – (-10))
= 400 kg m/s
In car: J = Dp = mDv
= m(v1f – v1i)
= 60(-23.3 – (10))
= kg m/s
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30. Car-Truck (question) Which would you rather be driving?
Say collision lasts Δt = 0.2 seconds
Force on student is given by F = Δp/Δt
Student in truck feels 2,000 N (survivable)
Student in car feels 10,000 N (not good)
What if instead of a 2000 kg car, she was on a 500 kg motorcycle!
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31. Example: 2-D Elastic Collision
v1,i=(1 m/s)i+(2 m/s)j
Two billiard balls collide elastically on a table. The initial velocity of the first ball is v1,i=(1 m/s)i+(2 m/s)j. The second ball is initially at rest. Both balls have the same mass. Determine the final velocity of both after the collision.
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32. Inelastic Collisions
Momentum is conserved (NOT Kinetic Energy)
Completely Inelastic:
Two objects stick together
Examples: Spit wads, football player being tackled,…
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33. Inelastic Collisions…
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34. Car Crash
m1=750 kg
m2=1000 kg
v1=20 m/s
v2=30 m/s
Two cars collide and stick together after the collision. What is the final velocity of the system?
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35. Car Crash Using conservation of momentum: m1=750 kg m2=1000 kg
v1=20 m/s
v2=30 m/s
Using conservation of momentum:
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36. Basketball Cannon
A ball projected from a cannon hits the trash can such that:
It sticks into the trash can.
It hits the trash can and bounces back.
Will the velocity of the trash can be bigger for case 1, case 2, or exactly the same?
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37. Basketball Cannon Consider an elastic collision: M m v vtrash=0
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38. Basketball Cannon Consider a perfectly inelastic collision: M m v
vtrash=0
Consider a perfectly inelastic collision:
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39. Basketball Cannon Elastic: Inelastic:
Elastic collision results in twice the velocity!
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