1. Momentum and Collisions
Physics 2053
Lecture Notes
Momentum and Collisions

2. Momentum and Collisions
Topics
6-01 Momentum and Impulse
6-02 Conservation of Momentum
6-03 Collisions
Momentum and Collisions

3. Momentum and Impulse Momentum is a vectorF m m
A block moving with an initial velocity vi is acted on by
a constant force F for a time Dt.
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
Momentum and Collisions

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

5. Momentum and Collisions Problem
A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms.
(a) What is the impulse given to the nail? v m
(b) What is the average force acting on the nail?
Momentum and Collisions

6. Momentum and Collisions 07-01
The area under the curve on a Force versus time (F vs. t)
graph represents
A) impulse.
B) momentum.
C) work.
D) kinetic energy.
Momentum and Collisions

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

8. Conservation of Momentum
Collision with a stationary block
before v
after M m
V = ? M m
Using the conservation of momentum to find the final speed when two blocks stick together.
Momentum and Collisions

9. Momentum and Collisions 07-08
A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car? .
Momentum and Collisions

10. Conservation of Momentum
Bullet fired into a block which is initially at rest.
after V
before v M m mv
(M + m)V
Find the speed of the bullet and block after impact.
Momentum and Collisions

11. Momentum and Collisions 07-01
A freight car moves along a frictionless level railroad
track at constant speed. The car is open on top.
A large load of coal is suddenly dumped into the car.
What happens to the velocity of the car?
A) It increases.
B) It remains the same.
C) It decreases.
D) cannot be determined from the information given
Momentum and Collisions

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

13. An Inelastic Collision
Collisions
An Inelastic Collision
before v1 v2
after m1 m2 vf m1 m2
Find the final speed after a
Perfectly Inelastic Collision
Momentum and Collisions

14. Momentum and Collisions 07-01
In an inelastic collision, if the momentum is conserved,
then which of the following statements is true about
kinetic energy?
A) Kinetic energy is also conserved.
B) Kinetic energy is gained.
C) Kinetic energy is lost.
D) none of the above
Momentum and Collisions

15. Momentum and Collisions 07-01
Two objects collide and stick together.
Kinetic energy
A) is definitely conserved.
B) is definitely not conserved.
C) is conserved only if the collision is elastic.
D) is conserved only if the environment is frictionless.
Momentum and Collisions

16. Elastic Collision (General Equations)
Collisions
Elastic Collision (General Equations) mB mA
vA1
vB1 mB mA
vA2
vB2
General Equations for an elastic collision.
Velocity is a vector - use + and - to indicate directions.
Momentum and Collisions

17. Elastic Collision (vB1 = 0) Ball B is initially at rest. vA1 mA mB
Collisions
Elastic Collision (vB1 = 0) Ball B is initially at rest.
vA1 mA mB mB mA
vA2
vB2
Special Case:
Elastic collision with m2 initially at rest.
Momentum and Collisions

18. Elastic Collision (vB1 = 0 and mA= mB)
Collisions
Elastic Collision (vB1 = 0 and mA= mB) m
vA1 m
VB2
Special Case:
Elastic collision with equal masses and with m2 initially at rest.
Momentum and Collisions

19. Momentum and Collisions 07-01
In an elastic collision, if the momentum is conserved,
then which of the following statements is true about
kinetic energy?
A) Kinetic energy is also conserved.
B) Kinetic energy is gained.
C) Kinetic energy is lost.
D) none of the above
Momentum and Collisions

20. Momentum and Collisions 07-01
When is kinetic energy conserved?
A) in inelastic collisions
B) in any collision in which the objects do not stick together
C) in all collisions
D) in elastic collisions
Momentum and Collisions

21. Momentum and Collisions 07-01
When a light beach ball rolling with a speed of 6.0 m/s
collides with a heavy exercise ball at rest, the beach ball's
speed after the collision will be, approximately,
A) 0.
B) 3.0 m/s.
C) 6.0 m/s.
D) 12 m/s.
Momentum and Collisions

22. Momentum and Collisions Problem
Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision?
Momentum and Collisions

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

24. Collisions Ballistic Pendulum Find the speed of the bullet v M h m V
Cons. Momentum v M m V
Momentum and Collisions

25. Collisions Ballistic Pendulum M h V Cons. Energy
Momentum and Collisions

26. Momentum and Collisions Problem
A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.
Momentum and Collisions

27. Momentum and Collisions Problem
A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it?
Momentum and Collisions

28. Momentum and Collisions 07-01
Two objects collide and bounce off each other.
Linear momentum
A) is definitely conserved.
B) is definitely not conserved.
C) is conserved only if the collision is elastic.
D) is conserved only if the environment is frictionless.
Momentum and Collisions

29. Momentum and Collisions 07-01
A 100 kg football linebacker moving at 2.0 m/s tackles
head-on an 80 kg halfback running 3.0 m/s. Neglecting
the effects due to digging in of cleats,
A) the linebacker will drive the halfback backward.
B) the halfback will drive the linebacker backward.
C) neither player will drive the other backward.
D) this is a simple example of an elastic collision.
Momentum and Collisions

30. Center of Mass (cm)
xcm x1 x2 x y m2 m1 cm
Momentum and Collisions

31. Location of the cm of the Earth-Moon system xcm mm me
Center of Mass (cm)
Location of the cm of the Earth-Moon system
xcm mm me x Rm
Momentum and Collisions

32. Momentum and Collisions Problem
Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass. x y
1.0 kg kg kg
0.5 m m
Momentum and Collisions

33. Momentum and Collisions 07-01
Consider two unequal masses, M and m. Which of the
following statements is false?
A) The center of mass lies on the line joining the
centers of each mass.
B) The center of mass is closer to the larger mass.
C) It is possible for the center of mass to lie within
one of the objects.
D) If a uniform rod of mass m were to join the two masses,
this would not alter the position of the center of mass of
the system without the rod present.
Momentum and Collisions

34. Momentum and Collisions 07-01
Two cars collide head-on on a level friction-free road.
The collision was completely inelastic and both cars
quickly came to rest during the collision. What is true
about the velocity of this system's center of mass?
A) It was always zero.
B) It was never zero.
C) It was not zero, but ended up zero.
D) none of the above
Momentum and Collisions

35. Total momentum of an isolated system of objects is conserved.
Chapter 7 Summary
Momentum :
Impules:
Newton’s second law:
Total momentum of an isolated system of objects is conserved.
Momentum is conserved during collisions.
Momentum and Collisions

36. In an elastic collision, total kinetic energy is also conserved
Chapter 7 Summary
In an elastic collision, total kinetic energy is also conserved
In an inelastic collision, some kinetic energy is lost.
In a completely inelastic collision, the two objects stick together after the collision.
The center of mass of a system is the point at which external forces can be considered to act.
Momentum and Collisions

37. END