ImpulseAnd

Momentum

Have you ever wondered…

1. Why Neo uses “follow through” when he throws his knives?

2. Why Neo bends his knees upon landing impact?

3. Why does it hurt Neo less to fall on a wood floor than a cement one?

Momentum is a cornerstone in physics concepts.

It refers to the quantity of motion that an object has.

Conceptually, think of momentum as “inertia in motion.”

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Momentum is a vector quantity. The magnitude which is the product of mass and velocity and whose direction is that of the velocity vector.

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Newton’s first law explains that objects in motion “want” to stay in motion. But just how much do moving objects wish to stay in motion?

Does a 1 kg skate moving at 10 m/s “want” to stay in motion as much as a 10,000 kg truck moving at the same speed?

To answer, think about which one would be harder to stop. Better yet, which one would you rather have approaching you?

The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving.

In other words:

The size of the momentum is equal to the mass of the object multiplied by the size of the object's velocity.

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In physics, the symbol for the quantity momentum is the lower case letter "p“. The formula for momentum is:

The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

The standard metric unit of momentum is the kg • m/s.

P = mv

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p = momentum

m = mass

v=velocity.

From the definition of momentum (p = mv), it becomes obvious that an object has a large momentum if either its mass or its velocity is large.

Both variables are of equal importance in determining the momentum of an object.

Objects at rest do not havemomentum - they do not haveany “mass in motion."

mV or Mv

8.9

A sample momentum calculation.

Let’s say that the mass of an object is 2.0 kgand that the velocity is 4.0 m/s. That is”

M = 2.0 kgV = 4.0 m/s

p = mvp = (2.0 kg)(4.0 m/s)p = 8.0 kg•m/s

Consider a Mack truck and a roller skate moving down the street at the same speed.

The considerably greater mass of the Mack truck gives it a considerably greater momentum.

Question

If a truck is at rest it has no momentum.The momentum of an object at rest is always 0.

A truck moving very slowly and a roller skate moving very fast could have the same momentum.

Will the truck always have more momentum than theroller skate?

NO!

Momentum is not velocity.

Sometimes the concept of momentum is confused with the concept of velocity.

Momentum is made up of both mass and velocity. One must take the mass and multiply it times the velocity to get the momentum.

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Momentum is a conserved quantity in physics.

This means that if you have an object or several objects in a system, interacting with each other, but not being influenced by any forces from outside of the system, then the total momentum of the system does not change over time.

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

The momentum lost by an object in a closed system will be gained by other objects so that the totalmomentum will remain the same in the system.

Law Of Conservation Of Momentum

12, 13Closed System: No matter or energy is allowed to enter or leave the system.

The separate momenta of each object within the system may change.

One object might change momentum, while another object changes momentum in an opposite manner, picking up the momentum that was lost by the first.

Conservation of Momentum

Momentum = 0 before the shotAnd after the shot

Cannon’s momentum Shell’s momentum

(equal and opposite)

Before collision:1. The momentum of the cart is 60 kg*cm/s2. The momentum of the dropped brick is 0 kg*cm/s3. The total system momentum is 60 kg*cm/s.

After collision:1. The momentum of the cart is 20.0 kg*cm/s 2. The momentum of the dropped brick is 40.0 kg*cm/s3. The total system momentum is 60 kg*cm/s. 4. The momentum lost by the loaded cart (40 kg*cm/s) is gained by

the dropped brick.

Momentum is transferred from the stick to the puck. The momentum lost by the stick is equal to the momentum gained by the puck. The total amount of momentum stays the same.

Many violent collisions, fights, and body checks occur during an ice hockey game. That is why it is perfectly appropriate to demonstrate the rules of momentum, impulse, and collisions using examples from ice hockey.

1. If velocity changes, momentum changes, and acceleration (either + or –) occurs

2. For acceleration to occur, a force has to be applied.

3. If a given force is applied over a longer time, more acceleration occurs.

What We Know:

A force applied over time will change the momentum of an object:

Time passes as a force is applied to an object. When this happenswe say that an impulse is appliedto the object.

IMPULSE is a measure of how much force is applied for how much time, and it’s equal to the change in momentum.

Forces applied over time periods create impulses.

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I = FΔTI = impulseF = force in NewtonsT = Time over which the force is applied (usually seconds)

Impulse is measured in N-s (pronounced "Newton seconds")

Ft or Ft

Impulse is the product of the force exerted to change themomentum of an object and the time it took to do it.

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Imagine that a force of 2.0 N is applied to an object for 3.0 s. Here is how to calculate that impulse:

.

I = FΔTI = (2.0N)(3.0s)I = 6.0 N-s

An object experiences a force of 15.32 N for a time period of 3.45 s. What is the impulse on the object?

I = (15.32N)(3.45s)

I = 52.85 N-s

I = FΔT

An object experiences an impulse of 39.50 N-s for a timeperiod of 16.11 s. What is the force on the object?

F = 39.50 N-s / 16.11 s

F = 2.54 N

I = FΔT

Impulse Changes Momentum

• 1) Apply 10 N for 10 minutes• 2) Apply 10 N for 5 minutes

Which scenario produces more momentum change?

I = Ft I = Ft

(10 N)(600 s) (10 N)(300 s)

6000 N-s 3000 N-s

Impulse changes momentum.

A greater impulse exerted on an object

A greater change in momentum

OR

Impulse = Change in momentum

Impulse can be exerted on an object to either INCREASE or DECREASE its momentum.

Impulse = Δ(mv)Greek symbol “Delta”Means “the change in…”

I =F∆t = (m∆v)

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ImpulseThe formula for impulse can also be written as

F∆t = (m∆v)

I = ImpulseF = ForceForce Newtonst = Time seconds Units: N-s (Newton seconds)m = Mass kilogramsv = Velocity m/s

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An object is moving with a velocity of 4.23 m/s, and it speeds up to a velocity of 14.18 m/s in 11.23 s. If its mass is 7.31 kg, what force acted upon it?

f = 72.72 kg•m/s / 11.23 s

f = 6.47 N

fΔt = mΔv

A small force acting for a long time can be as effective as ahuge force acting for a short time. 

fT or Ft1. To decrease momentum, reduce the force applied or

extend the time over which the force is applied.2. To increase momentum, increase the force and shorten

the time over which it is applied. 20, 21

Air bags can save your life in an auto accident.

Air bags increase the time your body gets to stop during a collision.

Another way to change momentum is to change the factors that determine momentum; mass and velocity.

A second way to increase momentum, is by increasing either the mass or velocity (or both) of an object.

A second way to decrease momentum is to decrease either the mass or velocity (or both) of an object.

mV vM

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Crash Cushion (or Crash Attenuators) are rubber devices that protects the motorist from a blunt object such as concrete wall or guard rail.

Inside of the cushions is a very high density foam.  As the vehicle hits the front of the system, the system collapses. This increases the time over which the force of the car is applied, thus reducing the force applied by the collision with a car..

To increase impulse, either the force or time interval must be increased. In baseball, this is done by hitting harder or following through with the swing.

To decrease impulse, either the applied force is reduced or the time of contact is shortened.

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For example,

A bat stays in contact with the ball for 1.6 s causing an impulse of 13.44 N-s. The average force of the bat on the ball is:

F = Impulse/time = (13.44 N.s)/(0.0016 s) = 8,400 N

Increase the time over which the an impulse is acts:

F = Impulse/time = (13.44 N.s)/(0.0032 s) = 4,200 N

If the time over which an impulse acts (ballstays in contact with the bat), the forceapplied will decrease.

1. Friction between wheels and track not enough to set entire train in motion

2. But enough locomotive friction to set one car in motion

• Coupling tightens

Next car is in motion

Impulse vs. ImpactSlack between coupling in RR cars allows the required impulse to be broken into a series of smaller impulses so friction between locomotive wheels and track can pull the entire train.

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Bouncing• Impulses are greater when bouncing takes place

• Ft = ∆(mv)• Falling flower pot hits your head • Falling flower pot hits your head and bounces off • Momentum is reversed. Impulse to stop< impulse

to “throw it back again” – 2(∆mv)– Karate chop– Pelton wheel

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Bouncing

Important point: It only takes an impulse of mv to stop the ball. It takes twice the impulse (2mv) to make it bounce)

Think about a bouncing ball:

Before it hits the ground:Speed = v

Momentum = mv

At the moment it hits the ground:Speed = 0

Momentum = 0

After it leaves the ground:Speed = v

Momentum = mv

Impulse needed to stop the ball = mv

Total Impulse = 2mv

Impulse needed to accelerate the ball upwoard = mv

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If the time of impact is long, the force will be milder. If the time is very short, the force is powerful. When things bounce off an object after hitting them, it is even more deadly in force magnitude.

Momentum Vectors• Momentum is conserved even when interacting objects don’t

move in a straight line.

• We can use our previously learned vector techniques to anlayze these problems.

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Momentum Vectors

Momentum is a vector quantity. The momentumof the wreck is equal to the vector sum of carA and B before the collision.

Question2 cars are involved in a collision. Which would be more damaging - if the cars collide and bounce or collide and

crumple?

Collide and bounce. The momentum change is larger and therefore there is a greater impulse and greater force.

Question

What are two ways that crumple zones in cars minimize the effect of force in a collision?

1. Crumpling increases the time over which the momentum is changed, thus decreasing the force.

2. Crumpling means less likely to rebound, thus less impulse.

Question

Why is falling on a floor with more give less dangerous than falling on a floor with less give?

The floor with more give allows a greater time for the impulse that reduces the momentum of the fall. A greater time for changing momentum means less force.

Impulse: A one inch punch!

Momentum and impulse in action.

A lot of momentum, impulse anda whole bunch of other fun stuff.

TheEnd

Resources:

The Phsics ClassroomYouTubeNational Transportation Safety BoardConceptual Physics: Paul HewittThe Matrix websiteThe Matrix Revolution website