1. Momentum and Impulse HMH Physics Chapter 6 pages 190-223
Section 3 pages

2. Learning Objectives Identify different types of collisions.
Determine change in Kinetic Energy during perfectly inelastic collisions.
Compare conservation of momentum and conservation of kinetic energy in
collisions.
4. Find the final velocity of an object after a collision.

3. Collisions
When two moving objects make contact with each other, they undergo a collision.
Conservation of momentum is used to analyze all collisions.
Newton’s Third Law is also useful. It tells us that the force exerted by body A on body B in a collision is equal and opposite to the force exerted on body B by body A.

4. Collisions During a collision, external forces are ignored.
The time frame of the collision is very short.
The forces are impulsive forces (high force, short duration).

5. Collisions
Three types
Elastic
Inelastic
Perfectly inelastic

6. Collision Types Elastic collisions Inelastic collisions
Also called “hard” collisions
No deformation occurs, no kinetic energy lost
Inelastic collisions
Deformation occurs, kinetic energy is lost
Perfectly Inelastic (stick together)
Objects stick together and become one object

7. Elastic Collision
In elastic collisions, there is no deformation of colliding objects, and no change in kinetic energy of the system. Therefore, two basic equations must hold for all elastic collisions
Spb = Spa (momentum conservation)
SKb = SKa (kinetic energy conservation)

8. Elastic Collisions m1v1i + m2v2i = m1v1f + m2v2f
Two objects collide and move separately
m1v1i + m2v2i = m1v1f + m2v2f
1st object nd object st object nd object
initial initial final final
momentum momentum momentum momentum

9. (Perfectly) Inelastic Collisions
Simplest type of collisions.
After the collision, there is only one velocity, since there is only one object.
Kinetic energy is lost.
Explosions are the reverse of perfectly inelastic collisions in which kinetic energy is gained!

10. Inelastic Collision m1v1i + m2v2i = (m1 + m2)vf
Two objects collide and stick together
m1v1i + m2v2i = (m1 + m2)vf
1st object nd object (1st object + 2nd object)
initial initial final
momentum momentum momentum

11. A 0. 215 kg golf club is swung with a speed of 55
A kg golf club is swung with a speed of 55.0 m/s and strikes a kg golf ball at rest. After the collision, the club travels at a speed of 43.0 m/s. What is the speed of the golf ball just after the impact?

12. Sample Problem
An 80-kg roller skating grandma collides inelastically with a 40-kg kid. What is their velocity after the collision?
How much kinetic energy is lost?

13. Sample Problem
A fish moving at 2 m/s swallows a stationary fish which is 1/3 its mass. What is the velocity of the big fish after dinner?

14. A 0.25 kg arrow with a velocity of 12 m/s to the west strikes the center of a 6.9 kg target. What is the final velocity of the combined mass?

15. A 90. 0 kg fullback moving south with a speed of 5
A 90.0 kg fullback moving south with a speed of 5.0 m/s has an inelastic collision with a 95.0 kg opponent running north at 3.0 m/s. What is the velocity of the players just after impact?

16. 2D-Collisions Momentum in the x-direction is conserved.
SPx (before) = SPx (after)
Momentum in the y-direction is conserved.
SPy (before) = SPy (after)
Treat x and y coordinates independently.
Ignore x when calculating y
Ignore y when calculating x
Let’s look at a simulation:

17. Sample problem
Calculate velocity of 8-kg ball after the collision.
3 m/s
2 kg
8 kg
0 m/s
Before
2 m/s v
After
50o x y