Momentum and CollisionsMomentum and Collisions

MomentumMomentum► From NewtonFrom Newton’’s laws: force must be present to change s laws: force must be present to change

an objectan object’’s velocity (speed and/or direction)s velocity (speed and/or direction)

Method to describe is to use concept of Method to describe is to use concept of linear linear momentummomentum

scalar vector

Linear momentum = product of mass velocityLinear momentum = product of mass velocity

Golf ball initially at rest, so some of the KE of club transferred to provide motion of golf ball and its change in velocity

MomentumMomentum

► Vector quantityVector quantity, the direction of the , the direction of the momentum is the same as the velocitymomentum is the same as the velocity’’ss

► Applies to two-dimensional motion as wellApplies to two-dimensional motion as well

yyxx mvpandm vp

vmp

Size of momentum: depends upon mass depends upon velocity

ImpulseImpulse

► In order to In order to changechange the momentum of an the momentum of an object (say, golf ball), a object (say, golf ball), a force must be force must be appliedapplied

amt

vvm

t

pF

ifnet

)(

tFpor net:

Impulse Cont’dImpulse Cont’d

Gives an alternative statement of NewtonGives an alternative statement of Newton’’s s second lawsecond law

(F Δt)(F Δt) is defined as the is defined as the iimpulsempulse

Impulse is a Impulse is a vector quantityvector quantity, the direction is the , the direction is the same as the direction of the forcesame as the direction of the force

Finding Impulse using F-t Finding Impulse using F-t GraphGraph

►Usually force is Usually force is not constant, but not constant, but time-dependenttime-dependent

► If the force is not If the force is not constant, use the constant, use the average forceaverage force appliedapplied

Graphical Interpretation of Graphical Interpretation of ImpulseImpulse

► The average force can be The average force can be thought of as the thought of as the constant force that would constant force that would give the same impulse to give the same impulse to the object in the time the object in the time interval as the actual interval as the actual time-varying force gives time-varying force gives in the intervalin the interval

If force is constant: impulse = F t

Example: Impulse Applied to Example: Impulse Applied to Auto CollisionsAuto Collisions

► The most important factor is the The most important factor is the collision timecollision time or or the time it takes the person to come to a restthe time it takes the person to come to a rest

►Ways to Ways to increase the timeincrease the time Seat beltsSeat belts Air bagsAir bags

The air bag increases the The air bag increases the time of the collisiontime of the collision and and absorbs some of the energyabsorbs some of the energy from the from the bodybody

To Do….To Do….

In the first section of the Momentum In the first section of the Momentum chapter in your SNAP (Impulse and chapter in your SNAP (Impulse and Momentum):Momentum):

►Read Example problemsRead Example problems►Do Practice Exercises (odds) Do Practice Exercises (odds)

►Next: 2-D collisions; Elastic vs. Inelasctic Next: 2-D collisions; Elastic vs. Inelasctic CollisionsCollisions

ConcepTest1ConcepTest1

Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?

1. It takes less time to stop the ping-pong ball.2. Both take the same time.3. It takes more time to stop the ping-pong ball.

ConcepTest1ConcepTest1

Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?

1. It takes less time to stop the ping-pong ball.2. Both take the same time.3. It takes more time to stop the ping-pong ball.

Note: Because force equals the time rate of change of momentum, the two balls loose momentum at the same rate. If both balls initially had the same momenta, it takes the same amount of time to stop them.

Problem:Problem: Teeing Off Teeing Off

A 50-g golf ball at rest is hit by “Big Bertha” club with 500-g mass. After the collision, the golf ball leaves with velocity of 50 m/s.

a) Find impulse imparted to ballb) Assuming club in contact with

ball for 0.5 ms, find average force acting on golf ball

Problem:Problem: teeing offteeing off

Given:

mball = 50 g = 0.050 kgv = 50 m/s

Find:

Impulse = ?Faverage = ?

1. Use impulse-momentum relation:

2. Having found impulse, find the average force from the definition of impulse:

N

s

smkg

t

pFthustFp

3

3

1000.5

105.0

50.2,

Note: according to Newton’s 3rd law, that is also a reaction force to club hitting the ball:

of club

CONSERVATION OF MOMENTUM