Ch 6 - Momentum

What is momentum?

Momentum = a vector quantity defined as the product of an object’s mass and velocity

p = mv (momentum = mass x velocity)

SI Unit = kgm/s (kilogram meter per second)

A 2250 gram toy truck has a velocity of 4 m/s to the east. What is the momentum of the toy?

M = 2250 g = 2.25 kgV = 4 m/sp = mv = 2.25 x 4 = 9 kgm/s east

Momentum Continued…

A change in momentum takes force and time When a soccer ball is moving very fast, the

player must exert a large force over a short time to change the ball’s momentum and quickly bring the ball to a stop

Impulse – Momentum Theorem

Impulse = for a constant external force, the product of the force and the time over which it acts on an object; OR, the change in momentum of an object

FΔt = Δp = mvf – mvi

Impulse = change in momentum = final momentum – initial momentum

A 1400kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30s. Find the magnitude of the force exerted on the car during the collision.

M = 1400kg Δt = 0.30s Vi = 15 m/s west =

-15 m/s Vf = 0 m/s F = ?

(1400 )(0 / ) (1400 )( 15 / )0.30

21000 70,000 to the East0.30

f imv mvF

tkg m s kg m sF

s

F N

6.2 – Conservation of Momentum

Law of Conservation of Momentum

The total momentum is conserved That is, the total momentum at the beginning of the

situation has to equal the total momentum at the end

This formula can be used in lots of different examples, like collisions, explosions, or when objects push away from each other.

1 1 2 2 1 1 2 2i i f fm v m v m v m v

A 76kg boater, initially at rest in a stationary 45kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?

1

2

1

2

1

2

7645002.5 /

?

i

i

f

f

m kgm kgvvv m s

v

1 1 2 2 1 1 2 2i i f fm v m v m v m v

1 1 2 20 f fm v m v

2

2

2

2

2

0 (76 )(2.5 / ) (45 )

0 190 45

190 45

19045

4.2 /

f

f

f

f

f

kg m s kg v

v

v

v

v m s

Momentum Continued…

The conservation of momentum fits with Newton’s Third Law Every action has an equal but opposite reaction

Real World vs. Physics World

In real life, forces during collisions are not constant

In physics world, we will work as if we are using the “average force” in our calculations

6.3 – Elastic and Inelastic Collisions

Types of Collisions

Perfectly Inelastic Collisions Two objects collide and stick together, moving

together as one mass Momentum is Conserved

1 1 2 2 1 2( )i i fm v m v m m v

NOTE: You will get the same results using the equation we already learned for conservation of momentum. This just reminds you that the masses stuck together!

Perfectly Inelastic Collisions, Cont.

Kinetic Energy is NOT constant (conserved) in inelastic collisions When the two objects stick together, some energy is lost

Deformation of objects (crunching of cars) Sound Heat

2 21 1 2 2

2 21 1 2 2

1 12 21 12 2

i i i

f f f

KE m v m v

KE m v m v

Then compare the initial KE to the final KE to see how much energy was

“lost”

Type of Collisions

Elastic Collisions Two objects collide and then move separately Both Momentum and Kinetic Energy are Conserved

1 1 2 2 1 1 2 2i i f fm v m v m v m v

2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

i f

i i f f

KE KE

m v m v m v m v

Real World vs. Physics World

In the real world, most collisions are neither elastic nor perfectly inelastic

In physics world, we act as if they fall into one of the two categories

Review

Perfectly Inelastic Collision Stick together Momentum Conserved Kinetic Energy NOT

Conserved

Elastic Collision Bounce off Momentum Conserved Kinetic Energy

Conserved