• Momentum

• Momentum is conserved – even in collisions with energy loss due to friction/deformation.

• Impulse

Chapter 9: Linear Momentum and Collisions

vmp

Reading assignment: Chapter 10.1-10.5

Homework #16 : (due Monday, Oct. 10, 2005):

Problems: Q1, Q14, 9, 14, 21, 28

Black board example 9.3

You (100kg) and your skinny friend (50.0 kg) stand face-to-face on a frictionless, frozen pond. You push off each other. You move backwards with a speed of 5.00 m/s.

(a) What is the total momentum of the you-and-your-friend system?

(b) What is your momentum after you pushed off?

(c) What is your friends speed after you pushed off?

Impulse (change in _________________)

A change in _________ is called “impulse”: if pppJ

During a collision, a force F acts on an object, thus causing a change in momentum of the object:

f

i

t

t

dtJp ______

For a constant (average) force: ___ avgFJp

Think of hitting a soccer ball: A force F acting over a time t causes a change p in the momentum (velocity) of the ball.

A soccer player hits a ball (mass m = 440 g) coming at him with a velocity of 20 m/s. After it was hit, the ball travels in the opposite direction with a velocity of 30 m/s.

(a) What impulse acts on the ball while it is in contact with the foot?

(b) The impact time is 0.1s. What is the acting on the ball?

Black board example 10.1

Elastic and inelastic collisions in one dimension

________________ is conserved in any collision, elastic and inelastic.

___________________ is only conserved in elastic collisions.

Perfectly inelastic collision: After colliding, particles __________________. There is a loss of kinetic energy (deformation).

Inelastic collisions: Particles _________________ with some loss of kinetic energy.

Perfectly elastic collision: Particles __________________ without loss of kinetic energy.

Perfectly _____________ collision of two particles(Particles stick together)

fii

fi

vvmvm

pp

(________)2211

Notice that p and v are vectors and, thus have a direction (+/-)

2222

211 (_______)

21

21

21

flossii

flossi

vEvmvm

KEK

There is a loss in kinetic energy, Eloss

Perfectly _________ collision of two particles(Particles bounce off each other without loss of energy.

ffii vmvmvmvm 22112211

222

211

222

211 2

121

21

21

ffii vmvmvmvm

Energy is _____________:

Momentum is ____________:

iif

iif

vmmmmv

mmv

vmm

vmmmmv

221

121

212

221

121

211

____

____

For elastic collisions in :

Suppose we know the initial masses and velocities.

Then:

(10.38)

(10.30)

(10.39)

(10.31)

Black board example 9.2

Two carts collide elastically on a frictionless track. The first cart (m1 = 1kg) has a velocity in the positive x-direction of 2 m/s; the other cart (m = 0.5 kg) has velocity in the negative x-direction of 5 m/s.

(a) Find the speed of both carts after the collision.

(b) What is the speed if the collision is inelastic?

(c) How much energy is lost in the inelastic collision?

Black board example 9.5

Ballistic Pendulum:

In a ballistic pendulum a bullet (0.005 kg) is fired into a block (1.0 kg) that is suspended from a light string. The block (with the bullet stuck in it) is lifted up by 0.05 m.

(a) What is the speed of the combined bullet/pendulum right after the collision?

(b) Find the initial speed of the bullet?

(c) Find the loss in mechanical energy due to the collision

_______________ collisions (Two particles)

ffii vmvmvmvm 22112211

Conservation of momentum:

Split into components:

fyfyiyiy

fxfxixix

vmvmvmvm

vmvmvmvm

22112211

22112211

If the collision is ____________, we can also use conservation of energy.

Black board example 9.3

Accident investigation. Two automobiles of equal mass approach an intersection. One vehicle is traveling towards the east with 29 mi/h (13.0 m/s) and the other is traveling north with unknown speed. The vehicles collide in the intersection and stick together, leaving skid marks at an angle of 55º north of east. The second driver claims he was driving below the speed limit of 35 mi/h (15.6 m/s).

13.0 m/s

??? m/s

Is he telling the truth?

What is the speed of the “combined vehicles” right after the collision?

How long are the skid marks (k = 0.5)