IMPULSE AND MOMENTUM

Agop-op Kadaok

Momentum

called as “inertia in motion”The difficulty encountered by a moving body to come to rest.

The product of body’s mass and velocity vmp

Factors Affecting Momentum:MassVelocity

Anything stationary has a zero momentum.

A car moving downhill gains momentum.

Impulse-Momentum Theorem

The impulse on a body is equal to the change in the body’s momentum.

Impulse

The equation in the left is Impulse ( J ).

vmp

dt

vdmF

t

va

t

vmF

pvmtF

Sample Problems:

1. A 45-g golf driven from a tee has a velocity with a magnitude of 40m/s immediately after being hit. If the club is in contact with the ball for 0.10s, what is the magnitude of the average impulse force?

2. Suppose the golf ball in the previous example were given an applied average impulse force of 25N. What would be the magnitude of the ball’s velocity immediately after being hit?

3. An estimated force–time curve for a baseball struck by a bat is shown in the figure below. From this curve, determine (a) the impulse delivered to the ball, (b) the average force exerted on the ball, and (c) the peak force exerted on the ball.

F(N)

20000         

15000            

           

10000            

           

5000           

            t(ms)0 1 2                3

F= 18 000 N

4. A pitched 140-g baseball, in horizontal flight with a speed of vi of 39m/s, is struck by a batter. After leaving the bat, the ball travels in the opposite direction with speed vf, also 39m/s.a. What impulse (J) acts on the ball while it is in contact

with the bat?b. The impact time Δt for the baseball-bat collision is

1.2ms, a typical value. What force acts on the baseball?c. What is the average acceleration a of the baseball?

5. Crash testing of cars produced the following data. During crash testing, cars are driven into a solid concrete wall, which does not move at all during the collision.

Crumple ZoneCrumple Zone

Steel Safety Cage

Car Mass (kg)

Velocity on motion (ms-1)

Crumple Zones

Time for car to stop in collision 

(s)A 915 10.0  Yes 4.40

B 1250 7.32 No 0.44

What is the impulse of both cars A and B started at rest?

What force, assumed constant, acted on the car A and B during impact?

Seatwork

Suppose you throw a ball with a mass of 0.40kg against a brick wall. It hits the wall moving horizontally to the left at 30m/s and rebounds horizontally to the right at 20m/s. a. Find the impulse of the net force on the ball during its collision with the wall.b. If the ball is in contact with the wall for 0.010s, find the average horizontal force that the wall exerts on the ball during the impact.

Conservation of Momentum m1v1+m2v2 = m1v’1+m2v’2

When no net external force acts on a system, its momentum is conserved.

Sample Problem

A 30-kg boy on roller skates is at rest when he throws a 0.40-kg ball horizontally at a speed of 10 m/s. Find the velocity of the boy right after the ball leaves his hand.

Inelastic Collision

The colliding bodies: 1. combine after collision 2. are deformed, generate heat and sound 3. do not conserve the kinetic energy of the

system 4. conserve the momentum of the system

m1v1+m2v2 = (m1+m2)v’

Inelastic Collision

Elastic Collision

The colliding bodies: 1. do not combine 2. are not deformed 3. does not make sound or generate heat 4. conserve the kinetic energy of the

system 5. conserve the momentum of the system m1v1+m2v2 = m1v’1+m2v’2

v1-v2 = -(v’1-v’2)

Elastic Collision

Sample Problem

A 0.50-kg iron ball moving at 1.0 m/s hits a 0.40-kg iron ball moving in the opposite direction at 2.0 m/s. Find the velocities of the ball after an elastic collision.