Momentum and Momentum and ImpulseImpulse

Chapter 6 Section 1Chapter 6 Section 1

Linear MomentumLinear Momentum

• Momentum can describe the motion Momentum can describe the motion of an object before and after a of an object before and after a collision takes place.collision takes place.– Examples:Examples:

•Bowling ball and the PinsBowling ball and the Pins

•Automobile AccidentAutomobile Accident

•SportsSports

•RocketsRockets

•Etc… (Basically anything that has Etc… (Basically anything that has movement)movement)

Inertia and MomentumInertia and Momentum

• Inertia is the tendency for an object Inertia is the tendency for an object to resist changeto resist change– Object at rest, stays at restObject at rest, stays at rest– Object in motion, stays in motionObject in motion, stays in motion

• Momentum is the tendency for an Momentum is the tendency for an object to stay in motionobject to stay in motion

• Momentum = Inertia in motionMomentum = Inertia in motion

MomentumMomentum

• MomentumMomentum – A vector quantity that – A vector quantity that is the product of an object’s mass is the product of an object’s mass and its velocity.and its velocity.

Momentum EquationMomentum Equation

p = mvp = mv• p = Momentum (lower case letter “p”)p = Momentum (lower case letter “p”)

• m = Massm = Mass

• v = Velocityv = Velocity

• The symbol “p” comes from the word The symbol “p” comes from the word progressprogress,, which is defined as “The quantity which is defined as “The quantity of motion with which a body proceed in a of motion with which a body proceed in a certain direction.”certain direction.”

SI Units For MomentumSI Units For Momentum

p = mv p = mv

Momentum = mass x velocityMomentum = mass x velocity

= (kg)(m/s)= (kg)(m/s)

=kgm/s=kgm/s

• SI units for Momentum – “kgm/s”SI units for Momentum – “kgm/s”

• There is no short way around the There is no short way around the units for momentum.units for momentum.

Momentum as a VectorMomentum as a Vector

• The direction of momentum is in the The direction of momentum is in the same direction as the velocity of the same direction as the velocity of the object.object.

Momentum & VelocityMomentum & Velocity• An object that has no velocity (v=0 m/s) An object that has no velocity (v=0 m/s)

has no momentum.has no momentum.

• An object that picks up speed, picks up An object that picks up speed, picks up momentum.momentum.– The more momentum an object has, the harder The more momentum an object has, the harder

it is to make the object stop.it is to make the object stop.

• An object that slows down, loses An object that slows down, loses momentum.momentum.– The less momentum an object has, the easier it The less momentum an object has, the easier it

is to make the object stop.is to make the object stop.

• Momentum is directly proportional to the Momentum is directly proportional to the velocity.velocity.

Momentum of Different Momentum of Different ObjectsObjects

• Can two different objects have the Can two different objects have the same momentum, such as a Mack same momentum, such as a Mack truck and a roller skate?truck and a roller skate?

Momentum of Different Momentum of Different ObjectsObjects• Sure they can!Sure they can!

• In order for both to have the same In order for both to have the same momentum, the Mack truck would have to momentum, the Mack truck would have to be moving really slow and the roller skate be moving really slow and the roller skate would have to be moving really fast in order would have to be moving really fast in order for both objects to achieve the same for both objects to achieve the same momentum.momentum.

Mack Truck = Roller SkateMack Truck = Roller Skate

mmvv = = mmvv

Momentum and MassMomentum and Mass

• Even objects with small masses can Even objects with small masses can have a lot of momentum, as long as have a lot of momentum, as long as the velocity is very large.the velocity is very large.– BulletsBullets– HailstonesHailstones– HammerHammer– Etc…Etc…

Example ProblemExample Problem

• An astronaut with a mass of 45 kg An astronaut with a mass of 45 kg wears a 32 kg suit and moves at 5.7 wears a 32 kg suit and moves at 5.7 m/s on the moon. What is the total m/s on the moon. What is the total momentum of the astronaut and the momentum of the astronaut and the suit?suit?

Example Problem AnswerExample Problem Answer

• p = mvp = mv

• = (77kg)(5.7m/s)= (77kg)(5.7m/s)

• = 440 kgm/s= 440 kgm/s

• p = 440 kgm/sp = 440 kgm/s

Changing Momentum Takes a Changing Momentum Takes a ForceForce• Catching a baseball thrown very fast Catching a baseball thrown very fast

might sting the hand.might sting the hand.

• Catching a slow-moving baseball Catching a slow-moving baseball causes no discomfort when it is causes no discomfort when it is caught.caught.

• When catching a ball, the velocity When catching a ball, the velocity changes to zero once it is caught.changes to zero once it is caught.– Change in velocity is an acceleration Change in velocity is an acceleration

and if there is acceleration, then there and if there is acceleration, then there must be a force present.must be a force present.

Force and MomentumForce and Momentum

• Momentum is closely related to force.Momentum is closely related to force.

• In fact, Newton wrote his Second Law of In fact, Newton wrote his Second Law of Motion mathematically, he wrote it not Motion mathematically, he wrote it not as F=ma, but in the following form:as F=ma, but in the following form:

F = F = ΔΔp/p/ΔΔttForce = Change in momentum ÷ time intervalForce = Change in momentum ÷ time interval

Impulse-Momentum Impulse-Momentum TheoremTheorem

FFΔΔt = t = ΔΔpp

• F = ForceF = Force

• ΔΔt = Time intervalt = Time interval

• ΔΔp = Change in momentump = Change in momentum

Impulse-Momentum Impulse-Momentum Theorem ExplainedTheorem Explained

The derived version of the equation.The derived version of the equation.

Ft = Ft = ΔΔpp

Ft = mFt = mΔΔvv

Ft = m(Ft = m(vvff – – vvii))

ImpulseImpulse

• ImpulseImpulse – For a constant external force, – For a constant external force, the product of the force and the time the product of the force and the time over which it acts on an object.over which it acts on an object.

• A large force will cause a change in an A large force will cause a change in an object’s momentum in a short time, but object’s momentum in a short time, but a small force will take a much longer a small force will take a much longer time to cause the same change in time to cause the same change in momentum.momentum.

Everyday Use of The Everyday Use of The TheoremTheorem

• With out thinking, you use this With out thinking, you use this theorem in everyday activities. What theorem in everyday activities. What are some of these activities?are some of these activities?

Example ProblemExample Problem

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

Example Problem AnswerExample Problem Answer

• 70,000 N to the west70,000 N to the west

•Page 211 – Sample Problem 6BPage 211 – Sample Problem 6B

Impulse For Stopping Times Impulse For Stopping Times and Distancesand Distances

• The impulse momentum theorem is The impulse momentum theorem is the formula used by engineers and the formula used by engineers and accident investigators.accident investigators.

• Larger mass objects have larger Larger mass objects have larger momentums, therefore it takes momentums, therefore it takes longer for a larger mass object to longer for a larger mass object to stop then a small mass.stop then a small mass.

• This directly affects the distance.This directly affects the distance.– Must use the Must use the kinematic equationskinematic equations

Example ProblemExample Problem

• If the maximum coefficient of kinetic If the maximum coefficient of kinetic friction between a 2300kg car and a friction between a 2300kg car and a road is 0.50, what is the minimum road is 0.50, what is the minimum stopping distance for a car moving at stopping distance for a car moving at 29m/s?29m/s?

Example Problem AnswerExample Problem Answer

• 86 meters86 meters

More Time = Less ForceMore Time = Less Force

• A change in momentum over a A change in momentum over a longer time will require less force.longer time will require less force.

• This idea is used in all kinds of safety This idea is used in all kinds of safety equipment.equipment.

Falling EggFalling Egg

• Whether your playing a game of egg Whether your playing a game of egg toss or accidently dropped an egg. In toss or accidently dropped an egg. In order to keep the egg from breaking, order to keep the egg from breaking, the time of impact must be increased.the time of impact must be increased.

• Why?Why?