Momentum

Mr. Pacton

CMHS Physics

Goals For Today1) Be able to explain two new physics terms:

– Momentum – Impulse

2) Answer the following question:

“Why is falling on a floor with more ‘give’ like carpet, less dangerous than falling on a floor with little ‘give’ concrete?”

Momentum• Momentum is inertia in motion.• (Remember: inertia is an objects tendency for it’s

motion to remain the same.)• Every moving object that has mass, has

momentum.

• The more mass an object has, the more momentum it has. Higher velocity also means more momentum.

• In the same direction as the velocity vector

• Units are kg . m/s (kg m/s)

• Momentum is a vector

p = mv

Mathematical Definition:

Momentum = (mass x velocity)

momentum

Check Your Understanding

1. Determine the momentum of a:

a. 60-kg halfback moving eastward at 9 m/s.

b. 1000-kg car moving northward at 20 m/s.

c. 40-kg freshman moving southward at 2 m/s.

60 x 9 = 540 kg . m/s

1000 x 20 = 20,000 kg . m/s

40 x 2 = 80 kg . m/s

Probmlem 2

2. A car is moving with a large momentum. What would be the car's new momentum if:

a. its velocity is doubled.

b. its velocity is tripled.

c. its mass is doubled (by cramming in more passengers and putting dumbbells in the trunk.)

d. its velocity were tripled and its mass were doubled.

Doubled or 2p

Tripled, or 3p

Doubled, or 2p

6p

Impulse

Impulse = (F. t) F: The Net force

t : time interval over which it acts

* Impulse is a vector in the direction of the force. * units of (N.s)

An Impulse is a change in momentum.

“If the Momentum of an object is to change, then either the mass or the velocity, or both, must change.” This requires Force and time for the force to act!!!

Impulse

F = ma = m (v/ t)

F t = m v

Impulse = Change in Momentum

Newton’s 2nd Law

And so we come back to the definition of Impulse. “Impulse equals change in momentum.”

Impulse Example Problems

1.What impulse occurs when a Force of 20 N is applied to an object for 5 seconds?

2. What would be the change of momentum for the object that experiences this impulse?

3. If the object has a mass of 5 kg. and it is initially at rest, what would be the velocity of the object after the impulse occurs?

Impulse = F. t = 20N x 5s = 100 N.s

Impulse = Change in momentum! = 100

100 = 5V – 0 V = 100/5 = 20 m/s

So…

“Why is falling on a floor with more ‘give’ like carpet, less dangerous than falling on a floor with little ‘give’ concrete?”

Main Ideas:

• Momentum: p=mv

• Impulse: = Ft = m v

Law of Conservation of Momentum

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

Example: Newton’s Cradle

‘Conserved’ means constant, or unchanged.

Looking at a Collision

A

pA

Bp`B

BpB

Ap`A

A B

F-F

Three types of collisions

1. Elastic – Collision in which both objects move separately after they collide. No friction, air resistance or other external forces act during the collision and momentum is conserved.

m1vi1 + m2vi2 = m1vf1 + m2vf2

Initial Total Momentum Final Total Momentum

2. Inelastic – Collision in which objects stick together after the collision. Momentum is conserved but

energy is not.

Three types of collisions

3. Partially Elastic – Most collisions in real life have friction but do move separately after the collision just like an Elastic Collision.

m1vi1 + m2vi2 = (m1+ m2)Vf

Initial Total Momentum Final Total Momentum

Another Example

Inelastic CollisionInelastic Collision

Elastic Collision

Elastic Vs. Inelastic CollisionsElastic Vs. Inelastic Collisions

ElasticElastic

• Momentum is conserved.

• Mass does not change.

• Objects move separately.

• KE is conserved as well.

InelasticInelastic

• Momentum is conserved.

• Mass does change.

• Objects move together.

• KE Energy is NOT conserved

m1vi1 + m2vi2 = (m1+ m2)Vf

Initial Total Momentum Final Total Momentum

m1vi1 + m2vi2 = m1vf1 + m2vf2

Initial Total Momentum Final Total Momentum

Example Problem 1Example Problem 1

A 3000-kg truck moving with a velocity of 10 m/s hits a 1000-kg parked car. The impact causes the 1000-kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, determine the velocity of the truck immediately after the collision.

Solution

Example Problem 2Example Problem 2

A 0.150-kg baseball moving at a speed of 45.0 m/s crosses the plate and strikes the 0.250-kg catcher's mitt (originally at rest). The catcher's mitt immediately recoils backwards. If the catchers hand is relaxed, and it is assumed that no net external force exists, then the law of momentum conservation applies to the catcher's mitt and ball. Determine the post-collision velocity of the mitt and ball together.

Solution

Momentum Conservation Example

Momentum conservation works for a rocket as long as we consider the rocket and its fuel to be one system, and account for the mass loss of the rocket.

Determine the forward momentum and velocity of the rocket shown. Initially it is at rest, but later it has a mass of 1050 kg as it extrudes 250 kg of gas at a velocity of 350 m/s in the opposite direction.

Solution

m1vi1 + m2vi2 = mrocketvrocket + mgasvgas

Initial Total Momentum Final Total Momentum

0 = Procket – 250 x 350

Rearrange to solve for Procket

Procket = 250x350 = 87500 kg*m/s

P=mv so… v = P/m = 87500/1050 = 83.3 m/s

YouTube! (To Turn In)

1. Why does your coach tell you to follow through in tennis, golf, or baseball?

2. Why is foam placed around the Race Track and what variable does it change in the Impulse Equation?

3. What does it mean to say Momentum is Conserved?

http://www.youtube.com/watch?v=OrLcZNG0N0I

http://www.youtube.com/watch?v=KvGWlu9ItwQ

http://www.youtube.com/watch?v=T9lehHxv-C8&feature=fvw

Momentum Misconceptions

Physics Classroom Website

http://www.walter-fendt.de/ph11e/ncradle.htm

http://en.wikipedia.org/wiki/Newton's_cradle

http://www.physicsclassroom.com/mmedia/momentum/dft.html

Web Resources