Linear Mom

entum

5-1 Linear Momentum

Linear Momentum, p – defined as mass x velocity

The unit is kg·m/s

A quantity used in collisions

So a small object with a large velocity could have the same momentum as a large object with a small velocity

vmp

9-1 Linear Momentum

5.2 Momentum and Newton’s Second Law

Newton’s Second Law is

This is only true for objects with a constant mass

The original form of the equation was

This statement is true even if the mass varies

amF

5.2 Momentum and Newton’s Second Law

t

pF

5.3 Impulse

A baseball player hits a pitch

Bat delivers an impulse

We actually only

consider average force

Impulse is define as

5.3 Impulse

ptF

An increase in time produces a decreases in force

A decrease in time produces an increase in force

5.3 Impulse

Airbag

5.4 Conservation of Linear Momentum

If no net external force is applied to a system

Then momentum is conserved

5.4 Conservation of Linear Momentum

pp

0

External Forces will result in a change in momentum, so no conservation

1.Force added in

2.Force removed

5.4 Conservation of Linear Momentum

Shuttle Launch

5.5 Inelastic Collisions

Inelastic collision – momentum is conserved, but energy is lost

Momentum is conserved

5.5 Inelastic Collisions

pp

0

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Completely (or perfectly) Inelastic collision – two objects collide and stick together

5.5 Inelastic Collisions

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Example: On a touchdown attempt, a 95 kg running back runs toward the end zone at 3.75 m/s. A 111kg linebacker moving at 4.10 m/s meets the runner in a head on collision. If the two players stick together what is their velocity immediately after the collision?

5.5 Inelastic Collisions

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v

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If the collision occurs in two dimensions

We need to consider the x

and y axis separately

5.5 Inelastic Collisions

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)(00

yBABBAA vmmvmvmyy

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Then we use vector addition to calculate the magnitude and velocity.

5.5 Inelastic Collisions

x

y

yx

v

v

vvv

1

22

tan

Example: A 950kg car traveling east at 16m/s collides with a 1300 kg car traveling north at 21 m/s. If the collision is completely inelastic, what is the magnitude and direction of the cars’ velocity after the collision?

5.5 Inelastic Collisions

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x

x

/76.6

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y

y

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x

y

yx

v

v

vvv

1

22

tan

o

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8.6076.6

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1

22

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5.6 Elastic Collisions

Elastic collision – two objects collide and bounce apart

Elastic Collisions

Momentum is conserved

Kinetic energy is conserved too

5.5 Elastic Collisions

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2212

212

212

21

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A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?

5.5 Elastic Collisions

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212

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21

00 BBAABBAA vmvmvmvm

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A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?

5.5 Elastic Collisions

BA vv 51020

22 51040 BA vv

BA vv 5.2

22 5)5.2(1040 BB vv

A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?

5.5 Elastic Collisions

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22 5)4225(.1040 BBB vvv 22 540205.240 BBB vvv

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A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision?

Confirm

5.5 Elastic Collisions

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5.7 Center of Mass

The point where the system can be balanced in a uniform gravitational field

Uniform objects

center of mass is in the

center

5.7 Center of Mass

Motion of CM

Center of mass ofTriangle

Center of mass is not always in the object

Objects balance if supported at their center of mass

5.7 Center of Mass