Momentum = mass x velocityMomentum = mass x velocity

The equation for momentum is written The equation for momentum is written as:as: ΡΡ = mv = mv

If direction is not an important factor :If direction is not an important factor : momentum = mass x speedmomentum = mass x speed

A slow moving truck and an extremely A slow moving truck and an extremely fast roller skate can have the same fast roller skate can have the same momentum.momentum.

Question :Question :Under what circumstances would the roller Under what circumstances would the roller

skate and the truck have the same skate and the truck have the same momentum ?momentum ?

The roller skate and truck can have the The roller skate and truck can have the same momentum if the ratio of the speed same momentum if the ratio of the speed of the skate to the speed of the truck is of the skate to the speed of the truck is the same as the ratio of the mass of the the same as the ratio of the mass of the truck to the mass of the skate.truck to the mass of the skate.

A 1000 kg truck moving at 0.01 m/sec has A 1000 kg truck moving at 0.01 m/sec has the same momentum as a 1 kg skate the same momentum as a 1 kg skate moving at 10 m/sec. Both have a moving at 10 m/sec. Both have a momentum of 10 kg m/sec.momentum of 10 kg m/sec.

( ( 1000 x .01 = 1 x 10 = 101000 x .01 = 1 x 10 = 10 ) )

1000 kg1 kg .01 m/sec10 m/sec

-is defined as the product of the is defined as the product of the mass and velocitymass and velocity-is based on Newton’s 2-is based on Newton’s 2ndnd Law Law

F = mF = m aaF = mF = m ΔΔvv

ttFF tt == mm ΔΔvv

IMPULSE MOMENTUM

FOR

CE

An object at rest has no momentum, An object at rest has no momentum, why?why?

Because anything times zero is zeroBecause anything times zero is zero(the velocity component is zero for an object (the velocity component is zero for an object

at rest)at rest)To INCREASE MOMENTUM, To INCREASE MOMENTUM,

apply the greatest force possible for apply the greatest force possible for as long as possible.as long as possible.

Examples : Examples : pulling a sling shot pulling a sling shot drawing an arrow in a bow all the way back drawing an arrow in a bow all the way back a long cannon for maximum rangea long cannon for maximum range hitting a golf ball or a baseball hitting a golf ball or a baseball

. (follow through is important for . (follow through is important for these !)these !) TIME

MOMENTUMMOMENTUM

DEFINITION OF TERMSDEFINITION OF TERMS : : impulseimpulse : : impact force X time impact force X time

(newton(newton..sec)sec) . . F t = F t = impulseimpulse

impactimpact : : the force acting on an the force acting on an object (N)object (N) when it hits when it hits something. something.

impact forcesimpact forces : : averageaverage force of force of impactimpact

MOMENTUMMOMENTUM

Decreasing MomentumDecreasing Momentum Which will provide lesser impact force for the Which will provide lesser impact force for the

car ?car ?

Knowing the physics helps us understand why Knowing the physics helps us understand why hitting a soft object is better than hitting a hitting a soft object is better than hitting a hard one.hard one.

MOMENTUMMOMENTUM

mv

mv

Ft

Ft

In each case, the momentum is decreased by In each case, the momentum is decreased by the same amount or impulse (force x time)the same amount or impulse (force x time)

Hitting the haystack Hitting the haystack extendsextends the impact time the impact time (the time in which the momentum is (the time in which the momentum is brought to zero).brought to zero).

The longer impact time reduces the force of The longer impact time reduces the force of impact and decreases the deceleration.impact and decreases the deceleration.

To decrease the force of impact, the time of To decrease the force of impact, the time of impact must be extended!impact must be extended!

MOMENTUMMOMENTUM

DECREASING DECREASING MOMENTUMMOMENTUM

If the time of impact is increased by 100 times If the time of impact is increased by 100 times (for example, from .01 sec to 1 sec), then the (for example, from .01 sec to 1 sec), then the force of impact is reduced by 100 times force of impact is reduced by 100 times (relatively survivable).(relatively survivable).

EXAMPLES :EXAMPLES :Padded dashboards on carsPadded dashboards on carsAirbags in cars or safety nets in circusesAirbags in cars or safety nets in circusesMoving your hand backward as you catch a fast-Moving your hand backward as you catch a fast-

moving ball with your bare hand or a boxer moving ball with your bare hand or a boxer moving with a punch.moving with a punch.

Flexing your knees when jumping from a higher Flexing your knees when jumping from a higher place to the ground. place to the ground.

Elastic cords for bungee jumpingElastic cords for bungee jumpingUsing wrestling mats instead of hardwood floors.Using wrestling mats instead of hardwood floors.Dropping a glass dish onto a carpet instead of a Dropping a glass dish onto a carpet instead of a

sidewalk.sidewalk.

EXAMPLES OF DECREASING EXAMPLES OF DECREASING MOMENTUMMOMENTUM

In boxing … In boxing …

Increased impact time reduces force of impactIncreased impact time reduces force of impact In bungee Jumping … In bungee Jumping …

Ft = change in momentum

Ft = change in momentum

Ft = Δmv applies here.mv = the momentum gained before the cord begins to stretch that we wish to change.

Ft = the impulse the cord supplies to reduce the momentum to zero.

Because the rubber cord stretches fora long time the average force on the jumper is small.

Questions Questions When a dish falls, will the impulse be less if it When a dish falls, will the impulse be less if it

lands on a carpet than if it lands on a hard lands on a carpet than if it lands on a hard ceramic tile floor ? ceramic tile floor ?

The impulse would be the same for either The impulse would be the same for either surface because there is the same momentum surface because there is the same momentum change for each. It is the change for each. It is the force force that is less that is less for the impulse on the carpet because of the for the impulse on the carpet because of the greater time of momentum change. greater time of momentum change. There is a There is a difference between impulse and impact.difference between impulse and impact.

If a boxer is able to increase the impact time by If a boxer is able to increase the impact time by 5 times by “riding” with a punch, by how 5 times by “riding” with a punch, by how much will the force of impact be reduced?much will the force of impact be reduced?

Since the time of impact increases by 5 times, Since the time of impact increases by 5 times, the force of impact will be reduced by 5 times.the force of impact will be reduced by 5 times.

BOUNCINGBOUNCINGIMPULSES ARE GREATER WHEN AN IMPULSES ARE GREATER WHEN AN

OBJECT BOUNCESOBJECT BOUNCESThe impulse required to bring an object to a The impulse required to bring an object to a

stop and then to throw it back upward again stop and then to throw it back upward again is greater than the impulse required to is greater than the impulse required to merely bring the object to a stop. merely bring the object to a stop.

When a martial artist breaks boards,When a martial artist breaks boards,does their hand bounce?does their hand bounce?Is impulse or momentum greater ?Is impulse or momentum greater ?

Example : Example : The Pelton Wheel.The Pelton Wheel.

CONSERVATION OF CONSERVATION OF MOMENTUMMOMENTUM

To accelerate an object, a force must be applied.To accelerate an object, a force must be applied. The force or impulse on the object The force or impulse on the object must comemust come

from outside the object.from outside the object.

EXAMPLES : The air in a basketball, EXAMPLES : The air in a basketball, sitting in a car and sitting in a car and pushing on the dashboard or pushing on the dashboard or sitting in a boat and blowing on the sail sitting in a boat and blowing on the sail don’tdon’t create movement. create movement.

Internal forces like these are balanced and Internal forces like these are balanced and cancel each other. cancel each other.

If no outside force is present, no change in If no outside force is present, no change in momentum is possiblemomentum is possible. .

The Law of Conservation of The Law of Conservation of MomentumMomentum

In the absence of an external force, In the absence of an external force, the momentum of a system the momentum of a system remains unchanged.remains unchanged.

This means that, when all of the forces This means that, when all of the forces are internal (for EXAMPLE: the are internal (for EXAMPLE: the nucleus of an atom undergoing nucleus of an atom undergoing radioactive decay, cars colliding, or radioactive decay, cars colliding, or stars exploding. stars exploding. The net momentum of the system The net momentum of the system before and after the event is the same.before and after the event is the same.

QUESTIONSQUESTIONS1. Newton’s second law states that if no net force 1. Newton’s second law states that if no net force

is exerted on a system, no acceleration occurs. is exerted on a system, no acceleration occurs. Does it follow that no change in momentum Does it follow that no change in momentum occurs?occurs?

No acceleration means that no change occurs in No acceleration means that no change occurs in velocity of momentum.velocity of momentum.

2. 2. Newton’s 3Newton’s 3rdrd law states that the forces exerted law states that the forces exerted on a cannon and cannonball are equal and on a cannon and cannonball are equal and opposite. Does it follow that the opposite. Does it follow that the impulseimpulse exerted on the cannon and cannonball are also exerted on the cannon and cannonball are also equal and opposite?equal and opposite?

Since the Since the timetime interval and forces are equal and interval and forces are equal and opposite, the impulses (F x t) are also equal and opposite, the impulses (F x t) are also equal and opposite.opposite.