Impulse 冲量

y

x

Consider Δp, the change in the ball’s momentum.

Is Δpx positive, negative, or zero?

y

x

Consider Δp, the change in the ball’s momentum.

Is Δpy positive, negative, or zero?

y

x

Consider Δp, the change in the ball’s momentum.

What is the direction of Δp?

tFppp if net

This is called impulse, J. It has the same units as momentum.

Jp

Another way of writing Newton’s 2nd Law:

Example

A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction.

(a) What impulse acts on the ball while it is in contact with the bat?

Example

A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction.

(a) What impulse acts on the ball while it is in contact with the bat?

iv

fv

Example

A 140 g cricket ball, bowled with a speed of 45.0 m/s, is struck by an Australian player’s bat. After leaving the bat, the ball travels with the same speed but in the opposite direction.

(b) The impact time Δt for the collision is 1.2 ms. What average force does the bat apply to the ball?

iv

fv

An ice hockey puck (冰球 ) has an initial momentum of <0, 2, 0> kg m/s. It slides across the ice, slowing down, until it stops.

What was the impulse applied by the ice to the puck?

(1)<0, 2, 0> kg m/s (4) <0, -2, 0> kg m/s

(2)<0, -4, 0> kg m/s (5) <0, 2, 2> kg m/s

(3)<1, 2, 0> kg m/s

ip

Jumping up and down

(1)Land on your toes, with bent knees – Δt is large, so F is small.

(2)Land on your heels, with locked knees – Δt is small, so F is large (and it hurts!)

F

tΔt

tFJ

Area of the rectangle is J

F

tΔt

Area under the curve is J

What if the force changes during the time Δt?

f

i

t

t

dttFJ )(

Favg

tΔt

Average force:

t

JF

avg

Systems of many particles

System

Environment

We can still use Newton’s 2nd Law on systems of more than one particle.

We just need to be careful about the difference between internal forces (内力 ) and external forces (外力 ).

Systems of many particles

System

Environment

Internal forces are interactions between particles within the system.

External forces are interactions between the system and the environment.

Systems of many particles

System

Environment

Only external forces count towards the net force Fnet in Newton’s 2nd Law.

tFp net

External forces only!

What if there are no external forces on a system: Fnet = 0?

0p

The total momentum doesn’t change.

0p

Conservation of momentum动量守恒

0p

Example

Before After

1v

1v

2v

4545

y

x

Find the speeds of the balls after the collision.

v1 = 3.0 m/s