1. Linear Momentum
and Collisions

2. Momentum and Impulse m F m
A block of mass (m) is acted upon by a force (F)
After a time (D) the block acquires a velocity vf
Momentum is conserved
Momentum is a vector

3. Momentum and Impulse
Newton’s 2nd Law p
Using Calculus:
Newton’s form of his 2nd law

4. v1 u1
Fm = - FM M m FM Fm M m
v = u
FmDt = - FMDt M m v2 u2
Dpm = - DpM
m(u2 - u1) = -M(v2 - v1)
Conservation of Momentum:
Blocks have the same speed (v) at
closest approach.
mu2 - m u1 = - Mv2 + Mv1
Conservation of
Momentum
Mv1 + m u1 = Mv2 + mu2
p(before) = p(after)

5. before vo
after M m
v = ? M m
Using the conservation of momentum to find the final speed when two blocks stick together.

6. after
before v vo M m
Find the speed of the bullet and block after impact.

7. Collisions Elastic Collisions Inelastic Collisions
Momentum and Kinetic Energy
are both conserved
Inelastic Collisions
Elastic and Inelastic collisions
A perfectly inelastic collision losses as much kinetic energy as possible
Only Momentum is conserved

8. Perfectly Inelastic Collision
before v1 v2
after m1 m2 vf m1 m2
Find the final speed after a
Perfectly Inelastic Collision
Linear Momentum and Collisions.ppt

9. Elastic Collision (General Equations)
v1i
v2i m1 m2 m2 m1
v1f
v2f
General Equations for an elastic collision.
Velocity is a vector - use + and - to indicate directions.

10. Elastic Collision (v2i = 0)m2 m1
v1i m2 m1
v1f
v2f
Special Case:
Elastic collision with m2 initially at rest.

11. Elastic Collision (v2i = 0 and m1= m2)
V2f = V1i
Special Case:
Elastic collision with equal masses and with m2 initially at rest.

12. Ballistic Pendulum vo M h m v Ballistic Pendulum
Cons. Energy
Cons. Momentum vo M m v
Ballistic Pendulum
Use conservation of momentum
and energy.

13. Ballistic Pendulum Find the speed of the bullet vo M h m v
Cons. Momentum vo M m v

14. Ballistic Pendulum h
Cons. Energy M v

15. Collisions in two dimensions
p1f
p1i m1 m1 m2
p2f
Linear Momentum and Collisions.ppt

16. Collisions in two dimensionsy
p1i = m1v1i
p1f = m1v1f
p2f = m2v2f q f
P1i = P1f + P2f x
m1v1f cos(q) + m2v2f cos(f) = m1v1i
m1v1f sin(q) + m2v2f sin(f) = 0

17. END ?