Impulse, Momentum, and Collisions

• Sections Covered – Physics– Chapter 7: pages 86 – 99– *Chapter 10: pages136 - 146

• Topics Covered– Linear Momentum– Impulse– Conservation of Momentum– Collisions

• Elastic• Inelastic• Total inelastic

– *Center of Mass

Impulse, Momentum, and Collisions

• What is inertia?

*Review

How much resistance an object has against a change in motion.

Mass = numerical amount of inertia

Large mass = lots of resistance Small mass = not a lot of

resistance

• Momentum is a quantity of movement or a measurement of how difficult it is to bring an object to a stop.

Momentum

Two Kinds of Momentum:

Linear Momentum-

Angular Momentum-

Momentum in a straight line

Rotational or Circular Momentum

Linear Momentum p = linear momentum m = mass

SI Units:

v = velocity

Linear momentum is a vector that points in the same direction as the velocity.

v

p

• A truck with a mass of 9000 kg moving 50 m/s?

Which Has More Momentum?

A moped with a mass of 180 kg moving 10 m/s?

OR

• For a constant force, the product of the force and time over which the force acts is the Impulse

Impulse

J = Impulse F = force Δt = time of contactSI

Units: Impulse is a vector

with the same direction as the force applied.

F

J

• The impulse exerted on an object changes the momentum of the object.

Impulse-Momentum Theory

The larger the impulse, the greater the change in momentum

• When you fall a significant distance and hit the ground, why do they tell you to tuck and roll when you hit the ground rather than just landing right on your feet?

Conceptual Question

Defining the System – Internal vs. External Forces

• Define your system (in this chapter – this will normally involve 2 objects)

The two skaters above are in a closed system

Any forces acting within your define system are internal forces

Defining the System – Internal vs. External Forces

• Forces that act on an object outside of the defined system are called external forces

Examples:

◦ Case 2

◦ Case 1:

◦ Meteor = External Force. Outside of the system

Defining the System – Internal vs. External Forces

• Forces that act on an object outside of the defined system are called external forces

Examples:

◦ Case 2

◦ Case 1:

◦ Meteor = External Force. Outside of the system

◦ Earthquake= External Force. Outside the system – changes how the problem is evaluated

• The total momentum of an isolated or closed system remains constant.

Conservation of Momentum

Isolated/Closed Systems – systems with only internal forces, no external

Total Initial momentum = Total Final Momentum

Two Object Conservation of Momentum (For Objects 1 and 2):

Conservation of Momentum

• For two objects, object A and object B:

Example:

A B

mA = 2.3 kg

vAo = 1.4 m/s

mB = 0.8 kg

vBo = 0 m/s

A B

vAf = 0.2 m/s vBf = ? m/s

A tennis player places a 55.0 kg automatic ball machine on a virtually frictionless tennis court. Both the machine and tennis balls inside are initially at rest. The machine fires a 0.0570 kg tennis ball with a positive velocity. The machine moves backwards with a velocity of -0.0373 m/s. What is the velocity of the tennis ball?

What are the two objects in this system?

Warm-Up #1

vf = 36.0 m/s

An ice skater (mass = 65.0 kg) moving to the right with a velocity of 2.50 m/s, holding a snowball (mass = 0.150 kg) which is moving with the skater. She then throws the snowball with a velocity of 32.0 m/s with respect to the ground. What is the velocity of the skater after she throws the snowball?• What are the two objects in this system?

Warm-Up #2

vf = 2.43 m/s

A boy on a skateboard is initially at rest holding an 8.00 kg jug of water. He tosses the water, giving it a positive velocity of 3.00 m/s. The boy and skateboard move backwards with the magnitude of their velocity being 0.600 m/s. What is the mass of the boy and skateboard together? • What are the two objects in this system?

Warm-Up #3

m = 40.0 kg

Collisions!!

• Three different kinds of collisions

IMPORTANT: In ALL collisions, momentum is conserved.

Elastic Collisions

Inelastic Collisions

Total Inelastic Collisions

Elastic

Collisions!Inelastic Total

Inelastic Perfect rebound,

no energy loss

Momentum conserved

KE conserved KEo = KEf

Some energy loss

Momentum conserved

KE NOT conserved

Objects are stuck together after collision

Momentum conserved

KE NOT conserved

Collision Kinetic Energy Conserved

Momentum Conserved

Elastic Collision

Inelastic Collision

Total Inelastic Collision

Collision Summary

YES YES

NO YES

NO YES