Chapter 6

Impulse and Momentum

DEFINITION OF LINEAR MOMENTUM

The linear momentum of an object is the product of the object’s mass times its velocity:

vpm

Linear momentum is a vector quantity and has the same direction as the velocity.

m/s)(kg ndmeter/secokilogram

Do these objects have the same momenta?

Can these objects have the same momenta?

How can momentum change?

Two billiard balls collide and bounce back with the same speed. Does their momenta change? Why?

A a rocket is leaving the atmosphere, moving at a constant velocity. Is its momentum changing? Why?

A a rocket is leaving the atmosphere, moving at a constant velocity. Is its momentum changing? Why?

If velocity (or speed) of the object changes, then the object…

tFJ

There are many situations when the force on an object is not constant and we have to talk about average force. As a result of the force applied (the bat), the momentum of the ball changed.

Calculate the change of momentum, in SI units, if the ball was pitched at 60 mph and pounced off the bat 70 mph. The mass of the ball is 145 g.

DEFINITION OF IMPULSE

The impulse of a force is the product of the averageforce and the time interval during which the force acts:

tFJ

Impulse is a vector quantity and has the same directionas the average force. The unit of impulse is

s)(N secondsnewton

If the ball was in contact with the bat for 0.5 s, what was the average force delivered by the bat?

IMPULSE-MOMENTUM THEOREM

When a net force acts on an object, the impulse ofthis force is equal to the change in the momentumof the object

Example 2 A Rain StormRain comes down with a velocity of -15 m/s and hits theroof of a car. The mass of rain per second that strikesthe roof of the car is 0.060 kg/s. Assuming that rain comesto rest upon striking the car, find the average forceexerted by the rain on the roof.

Conceptual Example 3 Hailstones Versus Raindrops

Instead of rain, suppose hail is falling. Unlike rain, hail usuallybounces off the roof of the car.

If hail fell instead of rain, would the force be smaller than, equal to, or greater than that calculated in Example 2? Explain.

Explain the physics (Impulse – momentum theorem) behind air bags

Compare change of momentum for each egg if they were dropped from the same height. Compare impulses applied to each. Explain why one egg breaks and the other one doesn’t

Why do we instinctively squatwhen landing after a jump? (Explain the physics of this instinct).

Conservation of Momentum

Collisions

Momentum is conservedIn the absence of friction, air resistance and

other external forces.

The only forces that are exerted on the objects are the action-reaction pairs

Collisions

Types of collisions(Nearly) elastic

Inelastic

Perfectly inelastic

Perfectly inelastic

Objects collide – ‘stick together’ and move as one

MOMENTUM IS CONSERVED

Example 1A 1500 kg car traveling at 15.0 m/s to the south collides with a 4500 kg truck that is initially at rest at a stoplight. The car and truck stick together and move together after the collision. What is the final velocity of the two-vehicle mass?

Example 2A 1.50 × 104 kg railroad car moving at 7.00 m/s to the north collides with and sticks to another railroad car of the same mass that is moving in the same direction at 1.50 m/s. What is the velocity of the joined cars after the collision?

Is KE conserved in PIC?A 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target.a. What is the final velocity of the combined mass?

Elastic CollisionsObjects collide and move separately without any damage or loss of momentum or KE.

Note: some energy is converted into sound (negligible compared to KE of the balls) + there is friction, but we look at the very short moment – right before and right after the collision. So, we can disregard any loss of energy and consider this collision (nearly) elastic.

Example 1A 0.015 kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a 0.030 kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 18.0 cm/s.

Find the velocity of the second marble after the collision.

Example 1A 0.015 kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a 0.030 kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 31.5 cm/s.

Inelastic collisionsMost of every day collisions: car accidents,

bumping into a table (door, wall, or whatever you prefer to bump into)

Objects do not lock together and move (rest) separately.

Momentum is conserved.

Energy is lost (to deformations, sound, thermal energy, etc.)