CHAPTER 6Momentum

• Momentum = mass x velocity • Momentum is a measure of inertia in motion

– how much motion an object has

• p = mv

• A really slow moving truck (mv) and an

extremely fast roller skate (mv) can have the same momentum.

• Units for momentum are kg*m/s

Momentum (p)

Example Questions

• A 100 kg cart is moving with a velocity of 5 m/s, what is its momentum?

• 500 kg*m/s• A 2 kg bowling ball is rolling with a speed

of 5 m/s, what is its momentum?• 10 kg*m/s

Change in Momentum (Δp)

• A change in ‘p’ can only be caused by a change in v (Δv) Δp = mΔv– Change in mass, WILL NOT change ‘p’

Δp Examples

• A 100 kg car increases its speed from 5 m/s to 15 m/s, what is its change in momentum?

• Δp =mΔv = (100kg) (15m/s – 5m/s)

• = (100kg)(10m/s) = 1000 kg*m/s

Δp examples• A 2 kg bowling ball slows down from 8 m/s

to 3 m/s, what is its change in momentum?• Δp=mΔv = (2kg) (3m/s – 8m/s)

• = (2kg)(-5m/s) = -10 kg*m/s

What causes a Δp?

• Δp is only caused by a change in velocity (Δv)

• Δv means acceleration (a)• Aaand Acceleration is caused by a Net Force

(Fnet)

• Sooo Fnet causes Δp

• Applying a net Force for some time to an object creates an acceleration which changes the momentum

• Impulse = Force x time (Ft)• (Ft) = Impulse = Δp = mΔv

Impulse & Momentum

Impulse – Momentum Theorem

• Impulse (Ft) = Change in Momentum (Δp)

• Ft = mΔv• The impulse (Ft) is equal to the change in

momentum

FO

RC

E

• An object at rest has no momentum, why?• Because anything times zero is zero

– If v= 0 then p=0• To INCREASE MOMENTUM,

apply the greatest force possible for as long as possible.

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

. (follow through is important for these !)

TIME

MOMENTUM

• https://www.youtube.com/watch?v=As3NzDQknVc

• Decreasing Momentum • Which would it be more safe to hit in a car ?

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

MOMENTUM

mv

mv

Ft

Ft

• In each case, the momentum is decreased by the same

amount --- Δp is same for both, sooo impulse (Ft) is same for both

• Hitting the haystack extends the impact time

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

• Whenever it is desired to decrease the force of impact, extend the time of impact !

MOMENTUM

DECREASING Impact ForceDECREASING Impact Force

• If the time of impact is increased by 100 times (say from .01 sec to 1 sec), then the force of impact is reduced by 100 times (say to something survivable).

• EXAMPLES :• Padded dashboards on cars• Airbags in cars or safety nets in circuses• Moving your hand backward as you catch a fast-moving ball

with your bare hand or a boxer moving with a punch.• Flexing your knees when jumping from a higher place to the

ground. or elastic cords for bungee jumping• Using wrestling mats instead of hardwood floors.• Dropping a glass dish onto a carpet instead of a sidewalk.

EXAMPLES OF DECREASING MOMENTUM

• Increased impact time reduces force of impact• 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 : • When a dish falls, will the impulse be less if

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

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

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

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

• IMPULSES ARE GREATER WHEN AN OBJECT BOUNCES, b/c greater Δp when v goes from + to - than from + to 0

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

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

• Example : • The Pelton Wheel.

Bouncing

The Law of Conservation of Momentum

• Unless there is an external force acting on a system, the momentum of the system remains unchanged.

• If there are no outside forces, total momentum of a system remains constant

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

Difference between internal & external forces…

• The force or impulse on the object must come

from outside the object. (we talked about this with Newton’s 3rd Law )

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

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

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

QUESTIONS• 1. Newton’s second law states that if no net force is

exerted on a system, no acceleration occurs. Does that also mean that no change in momentum occurs?

• No acceleration means that no change occurs in velocity and therefore no change in momentum.

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

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

The Law of Conservation of Momentum

• No change in momentum occurs unless outside force acts

• Initial total momentum = Final Total Momentum• For a collision between 2 objects...• Ʃpbefore = Ʃpafter

• Ʃmvbefore = Ʃmvafter

• P1i + p2i = p1f + p2f

• Or m1v1i + m2v2i = m1v1f + m2v2f

• ELASTIC COLLISIONS

• INELASTIC COLLISIONS

COLLISIONS

Momentum transfer from one Object to another .

Is a Newton’s cradle like the one Pictured here, an example of an elastic or inelastic collision?

Problem Solving #1(write this down)

• A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after “lunch”.

• System is both fish, so …..• net momentum initial = net momentum final

• (6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vf)

• 6 kg.m/sec = (8 kg)(vf)

• vafter = 6 kg.m/sec / 8 kg

• 8 kg• vf = ¾ m/s

vf =

Problem Solving #2• Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg

fish that is swimming towards it at 2 m/sec. Find the velocity of the fish immediately after “lunch”.

• System is both fish, so….• net momentum initial = net momentumfinal

• (net mv)i = (net mv)f

• (6 kg)(1 m/s) + (2 kg)(-2 m/s) = (6 kg + 2 kg)(vafter)

• 6 kg.m/sec + -4 kg.m/sec = (8 kg)(vafter)

• vafter = 2 kg.m/sec / 8 kg

• 8 kg• vafter = ¼ m/sec

vafter =

Problem Solving #3 & #4• Now the 6 kg fish swimming at 1 m/sec swallows a 2

kg fish that is swimming towards it at 3 m/sec. • (net mv)i = (net mv)f

• (6 kg)(1 m/sec) + (2 kg)(-3 m/sec) = (6 kg + 2 kg)(vf)

• 6 kg.m/sec + -6 kg.m/sec = (8 kg)(vf)

• vafter = 0 m/sec

• Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is swimming towards it at 4 m/sec.

• (net mv)i = (net mv)f

• (6 kg)(1 m/sec) + (2 kg)(-4 m/sec) = (6 kg + 2 kg)(vf)

• 6 kg.m/sec + -8 kg.m/sec = (8 kg)(vf)

• vf = -.25 m/sec

MOMENTUM VECTORS• Momentum can be analyzed by using vectors• The momentum of a car accident is equal to the

vector sum of the momentum of each car A & B before the collision.

A

B

MOMENTUM VECTORS (Continued)

• When a firecracker bursts, the vector sum of the momenta of its fragments add up to the momentum of the firecracker just before it exploded.

• The same goes for subatomic elementary particles. The tracks they leave help to determine their relative mass and type.

CHAPTER #8 - MOMENTUM• Finish