1. the science of collision
MOMENTUM
the science of collision

2. = “Keep Goingness” of an object.
p = mv where
p = momentum
m = mass in kg
v = velocity in m/s
Momentum

3. They can stop dead.
i.e. mv = mv
So if a fast moving little object collides with a slow moving big object head on

7. Example: What is the momentum of a 300 g swallow going 15 m/s?
p = mv = (.300 kg)(15 m/s)
p = 4.5 kgm/s
Duh!
I can tell by the mass.

8. What is the momentum of a 0.25 kg swallow going 5.2 m/s ?
1.3 kgm/s
p = mv
p = (.25 kg )(5.2 m/s) = 1.3 kgm/s W

9. What velocity must a 275 gram bullet have for its momentum to be 126
What velocity must a 275 gram bullet have for its momentum to be kg-m/s?
460. m/s
p = mv
126.5 kgm/s = (.275kg)v
v = (126.5 kgm/s)/(.275kg) = 460 m/s W

10. A bowling ball has a momentum of 43
A bowling ball has a momentum of 43.6 kg-m/s when it is moving at 12 m/s. What is its mass?
3.6 kg
p = mv
43.6 kgm/s = m(12 m/s)
m = (43.6 kgm/s)/ (12 m/s) = 3.6 kg W

11. LAW OF CONSERVATION OF MOMENTUM
The sum of the momentum before and after the collision remains the same.
m1v1 = m2 v2

12. Elastic and inelastic collisions in one dimension
Momentum is conserved in any collision, elastic and inelastic.
Mechanical Energy is only conserved in elastic collisions.
Perfectly inelastic collision: After colliding, particles stick together. There is a loss of energy (deformation).
Elastic collision: Particles bounce off each other without loss of energy.
Inelastic collision: Particles collide with some loss of energy, but don’t stick together.

13. Perfectly inelastic collision of two particles
(Particles stick together)
Notice that p and v are vectors and, thus have a direction (+/-)
There is a loss in energy Eloss

14. Elastic collision of two particles
(Particles bounce off each other without loss of energy.
Momentum is conserved:
Energy is conserved:

15. The momenta must be equal but opposite:
60 kg Fran is running at 4 m/s when she collides with 80 kg Joe. They hit and stop dead, so how fast was Joe going?
3 m/s
The momenta must be equal but opposite:
Fran: p=mv=(60 kg)(4 m/s)=240 kgm/s
Joe: p=mv, 240 kgm/s = (80 kg)v,
v = (240 kgm/s)/ (80 kg) = 3 m/s. W

16. Consider the previous problem:
Since momentum is really a vector, the true initial momenta were:
Fran: p=mv=(60 kg)(+4 m/s)=+240 kgm/s
Joe: p=mv=(80 kg)(-3 m/s)=-240 kgm/s
The total momentum was the same before and after the collision.
This is true for every collision.
This is very useful