Momentum

• Momentum is a commonly used term in sports. – A team that has the momentum is on the

move and is going to take some effort to stop. • A team that has a lot of momentum is really on

the move and is going to be hard to stop.

More force is needed to quickly stop a More force is needed to quickly stop a baseball thrown at 95 mph than to quickly stopbaseball thrown at 95 mph than to quickly stop

a baseball thrown at 45 mph, even thougha baseball thrown at 45 mph, even thoughthey both have the they both have the same masssame mass..

More force is needed to quickly stop aMore force is needed to quickly stop atrain train moving at 45 mph than to quicklymoving at 45 mph than to quickly

stop A stop A car car moving at 45 mph, even thoughmoving at 45 mph, even thoughthey both have the they both have the same speedsame speed..

BothBoth massmass and and velocityvelocity are important are importantfactors when considering the forcefactors when considering the force

needed to change the motion of an object.needed to change the motion of an object.

the product ofmass and velocity

of an object

momemtummomemtum = = massmass x x velocityvelocity

p = mvp = mvp = momentum

Units: kg m/s

Example:

• If a 100 kg person is running with a velocity of 5m/s, how much momentum does the person have?

mvp )/5)(100( smkgp

skgmp /500

Momentum is a vector,Momentum is a vector,so direction is important.so direction is important.

An object’s momentum will changeif its massmass and/or velocityvelocity

(speed or direction) changes.

According to Newton’s laws,According to Newton’s laws,a a net forcenet force causes an object to causes an object to accelerateaccelerate,,

or or change its velocitychange its velocity..

A net force, therefore, causes achange in an object’s momentum.

FNet = ma (Newton’s Second Law)(Newton’s Second Law)

Impulse = change in momentumImpulse = change in momentum

Impulse

• A force acting for a given amount of time will change an object's momentum. – Put another way, an unbalanced force always

accelerates an object – either speeding it up or slowing it down.

• If the force acts opposite the object's motion, it slows the object down.

• If a force acts in the same direction as the object's motion, then the force speeds the object up.

• Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed.

Impulse (J)

In both cases the impulse will be the same• By moving with the punch it decreases the ‘sting’

A 1000 kg car moving at 30 m/s (p = 30,000 kg m/s)A 1000 kg car moving at 30 m/s (p = 30,000 kg m/s)can be stopped bycan be stopped by

30,000 N of force 30,000 N of force acting acting for 1.0 s (a crash!) for 1.0 s (a crash!)

ororby 3000 N of force by 3000 N of force actingacting for 10.0 s (normal stop)for 10.0 s (normal stop)

Example

Formulas

mvp ptFJ net

P = momentum (kg m/s)m = mass (kg)v = velocity (m/s)J = impulse (N s)F = force (N)t = time (s)Δ = change (final – initial)

vmp

The momentum of any closed,The momentum of any closed,isolated system does not change.isolated system does not change.

The momentum before an event, p1, is equal to the momentum after the event, p2.

p1 = p2

m1v1 + m2v2 + m3v3 + … = m1V1 + m2V2 + m3V3 + …where v is the velocity before the event

and V is the velocity after

AfterBefore pp Reference Table

CollisionsCollisionsElasticElastic

Objects strike each other and bounce off.Objects strike each other and bounce off.

InelasticInelasticObjects strike each other and stick together.Objects strike each other and stick together.

ExplosionsExplosionsObjects start out together and then break apartObjects start out together and then break apart

AfterBefore pp

...)()(....)()( 22112211 AABB vmvmvmvm

...)(....)()( 212211 mmvvmvm ABB

...)()(....)()( 22112211 AABB vmvmvmvm

Elastic

Inelastic

Graphical Representation

• Momentum and Impulse can be represented in graphs.– Velocity vs. Time

– Force vs. TimeF

t

V

t

Velocity vs. Time• When the graph has

velocity vs. time remember:– mΔv = Δp = J– F*t = Δp = J

What is the change in momentum for section (A)?

What force is required to impart that change in momentum?

What is the acceleration?

m = 5 kg

Force vs. Timem = 5 kg• When the graph has force vs. time

remember:– The area under the curve represents

the impulse– F*t = Δp = J– F = m*a

What is the change in momentum for section (B)?

What is the acceleration?

What is the final velocity at the end of that section