S-43

A. What is the relationship between the forces when the two sumo wrestlers run into each other?

B. What is the relationship between their accelerations?

C. Is their a relationship

between their initial

velocities and their

final velocities?

Linear Momentum

AP Physics

Chapter 7

Linear Momentum

7.1 Momentum and Its Relation to Force

7.1 Momentum and Its Relation to Force

Linear momentum – product of an objects mass and its velocity

Unit is a kgm/s

The quantity is only useful when discussing collisions

7-1

vm

p

7.1 Momentum and Its Relation to Force

Impulse

7-1

maF

t

va

t

vmF

7.1 Momentum and Its Relation to Force

Impulse

7-1

t

vmF

tF

p

vmp

7.1 Momentum and Its Relation to Force

Impulse

Or

7-1

tF

p

pFt

7.1 Momentum and Its Relation to Force

In a collision, to decrease force, we increase time of the collision

Air Bags

7-1

Consumer Report

Linear Momentum

7.2 Conservation of Momentum

7.2 Conservation of Momentum

Two kinds of collisions

1. Perfectly elastic – objects bounce apart

2. Perfectly inelastic – objects stick together

7-2

7.2 Conservation of Momentum

In reality collisions are a combination of the two.

Law of Conservation of Momentum – in a closed system, momentum is conserved in a collision

7-2

0p p

7.2 Conservation of Momentum

In an elastic collision

Direction of velocity is given by the sign of the velocity.

7-2

0 0A A B A A A B Bm v m v m v m v

7.2 Conservation of Momentum

In an inelastic collision

7-2

0 0( )A A B A A Bm v m v m m v

7.2 Conservation of Momentum

In an explosion

The reverse of a

Inelastic collision

7-2

BBAABA vmvmvmm 0)(

S-44

Bart and his friends are out for a drive in their

model T. The car and the passangers have a

total mass of 560 kg. They run into an angry

cow while driving at 6.08 m/s. If the car stops

in 0.44 s

• What is the change in momentum of the car?

• What is the average

force exerted on the

cow?

S-45

Shortly after this picture was taken Mittens drove into a wall. The car had a mass of 2500 kg, was traveling at 30.2 m/s, and came to a stop in 1.9 m.

A. What was the

impulse on the car?

B. What was the

average force on

the car?

Linear Momentum

7.3 Conservation of Momentum in Collisions

7.3 Conservation of Energy and Momentum

Energy (mechanical) is conserved in an elastic collision

So

7-3

0 0A A B B A A B Bm v m v m v m v

0 0

2 2 2 21 1 1 12 2 2 2A A B B A A B Bm v m v m v m v

7.3 Conservation of Energy and Momentum

Any collision in which energy is lost, is considered inelastic.

7-3

Linear Momentum

7.4 Collisions in Two Dimensions

7.4 Collisions in Two Dimensions

inelastic collisions in two dimension

As always each dimension is treated independently

Then use vector addition to calculate the final answer

7-4

0 0( )A A x B B x A B xm v m v m m v

0 0( )A A y B B y A B ym v m v m m v

x yv v v

S-46

In what would later be called a “really sucky play” Carlos came running out of the goal at 5.6 m/s and ran into the attacking Kanu. The 65 kg Kanu was running toward Carlos at 8.4 m/s. Carlos, who is 84 kg, came to a dead stop after the collision. What was Kanu’s velocity after the collision? Did you notice that Carlos missed the ball?

Linear Momentum

7.5 Center if Mass

7.5 Center of Mass

Even if an object rotates there is one point that moves in the same that a particle would move if subject to the same force.

7-5

7.5 Center of Mass

Center of mass – the point that does not rotate

Center of gravity – the point at which the force of gravity can be considered to act

7-5

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