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Chapter 6 Momentum and Collisions

Objectives

- Understand the concept of momentum.
- Use the impulse-momentum theorem to solve

problems. - Understand how time and force are related in

collisions.

Momentum

momentum inertia in motion the product of mass

and velocity

p m v

How much momentum does a 2750 kg Hummer H2

moving at 31 m/s possess?

Note momentum is a vector units are kgm/s

Impulse Changes Momentum

Newton actually wrote his second law in this form

SF Dt m Dv

The quantity SFDt is called impulse.

The quantity mDv represents a change in momentum.

Thus, an impulse causes a change in momentum

SF

SFDt mDv Dp

impulse-momentum theorem

Highway Safety and Impulse

Water-filled highway barricades increase the time

it takes to stop a car. Why is this safer?

They reduce the force during impact!

SF (m Dv) / Dt

Seatbelts and airbags also increase the stopping

time and reduce the force of impact.

Impulse Problem

- A car traveling at 21 m/s hits a concrete wall.

If the 72 kg passenger is not wearing a seatbelt,

he hits the dashboard and stops in 0.13 s. - What is the Dp?
- How much impulse is applied to the passenger?
- How much force does the
- dashboard apply to the passenger?

What is the force applied to the passenger if he

is wearing a seatbelt takes 0.62 s to stop?

Impulse Problem

The face of a golf club applies an average force

of 5300 N to a 49 gram golf ball. The ball

leaves the clubface with a speed of 44 m/s. How

much time is the ball in contact with the

clubface?

SFDt mDv

SF

Bouncing

Which collision involves more force a ball

bouncing off a wall or a ball sticking to a wall?

Why?

The ball bouncing because there is a greater Dv.

SF Dt m Dv

SF Dv

so

Pelton wheel

Objectives

- Understand the concept of conservation of

momentum. - Understand why momentum is conserved in an

interaction. - Be able to solve problems involving collisions.

Conservation of Momentum

conservation of momentum in any interaction

(such as a collision) the total combined

momentum of the objects remains unchanged (as

long as no external forces are present).

system all of the objects involved in an

interaction

system

Conservation of Momentum

mavai mbvbi Spi

mb

ma

vai

vbi

SF

-SF

-Dp -SF Dt

Dp SF Dt

Dt

DpTOTAL ( -SFDt ) ( SFDt ) 0

mavaf mbvbf Spf

mb

ma

S pi S pf

vaf

vbf

Law of Conservation of Momentum

mavai mbvbi mavaf mbvbf

Slingshot Manuever

The spacecraft is pulled toward Jupiter by

gravity, but as Jupiter moves along its orbit,

the spacecraft just misses colliding with the

planet and speeds up.

The spacecraft substantially increased its

momentum (as speed) and Jupiter lost the same

amount of momentum, but because Jupiter is so

massive, its overall speed remained virtually

unchanged.

Jupiter

S pi S pf

Conservation of Momentum Problem

A 0.85 kg bocce ball rolling at 3.4 m/s hits a

stationary 0.17 kg target ball. The bocce ball

slows to 2.6 m/s. How fast does the target ball

(pallino) move? Assume all motion is in one

dimension.

mavai mbvbi mavaf mbvbf

Objectives

- Understand the difference between elastic and

inelastic collisions. - Solve problems involving conservation of momentum

during an inelastic collision.

Collisions

- elastic objects collide and rebound, maintaining

shape - both KE and p are conserved (DEMONewton spheres)
- perfectly inelastic objects collide, deform, and

combine into one mass - KE is not conserved (becomes sound, heat, etc.)
- real collisions are usually somewhere in between

Types of Collisions

elastic

mavai mbvbi mavaf mbvbf

perfectly inelastic

mavai mbvbi (ma mb) vf

Conservation of Momentum Problem

Victor, who has a mass of 85 kg, is trying to

make a get-away in his 23-kg canoe. As he is

leaving the dock at 1.3 m/s, Dakota jumps into

the canoe and sits down. If Dakota has a mass

of 64 kg and she jumps at a speed of 2.7 m/s,

what is the final speed of the the canoe and its

passengers?

Conservation of Momentum in Two-Dimensions

Collisions in 2-D involve vectors.

paf

ma

initial

ma

mb

final

Spi

mb

pbf

Equal Mass Collision

A cue ball (m 0.16 kg) rolling at 4.0 m/s hits

a stationary eight ball of the same mass. If the

cue ball travels 25o above its original path and

the eight ball travels 65o below the original

path, what is the speed of each ball after the

collision?

Unequal Mass Collision

A 0.85 kg bocce ball rolling at 3.4 m/s hits a

stationary 0.17 kg target ball. The bocce ball

slows to 2.8 m/s and travels at a 15o angle above

its original path. What is the speed of the

target ball it travels at a 75o below the

original path?