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PreClass Notes: Chapter 9, Sections 9.3-9.6

• From Essential University Physics 3rd Edition

• by Richard Wolfson, Middlebury College

• ©2016 by Pearson Education, Inc.

• Narration and extra little notes by Jason Harlow,

University of Toronto

• This video is meant for University of Toronto

students taking PHY131.

Outline

“A collision is a brief, intense

interaction between objects…

External forces are… negligible… so

the total momentum of the colliding

objects remains essentially

unchanged.” – R.Wolfson

• 9.3,9.4 Impulse and

Momentum

• Energy in Collisions

• 9.5 Totally Inelastic

Collisions

• 9.6 Elastic Collisions

[Animated gif from http://giphy.com/gifs/fail-bump-chest-e95jHtB4kpM2c]

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Impulse

The impulse upon a particle is defined as

Impulse has units of N s, but you should be able to

show that N s are equivalent to kg m/s.

The impulse-momentum theorem states that the

change in a particle’s momentum is equal to the

impulse on it.

Example:

When a car is out of control, it is better to hit a haystack

than a concrete wall.

Physics reason: Same impulse either way, but

extension of hitting time reduces the force.

Impulse Changes Momentum

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Collisions: vocabulary

• Every collision or explosion involves a short, intense

interaction in which external forces are usually negligible: that

means collisions and explosions conserve momentum.

• The kinetic energy of the system before and after is not

generally conserved. There are four categories:

– If the final kinetic energy is less than the initial kinetic

energy, this is an inelastic collision (Kf < Ki). Heat or

bending of materials has absorbed energy.

– If the final kinetic energy is more than the initial kinetic

energy, this is an explosive collision, or an explosion (Kf >

Ki). Some internal chemical or elastic energy must have

been released.

– If the final kinetic energy equals the initial kinetic energy,

this is an elastic collision (Kf = Ki).

Collisions: vocabulary

• A sub-category of inelastic collisions is:

– If the two objects stick together in the end, this is a totally

inelastic collision. (Kf < Ki), ( 𝑣1𝑓 = 𝑣2𝑓) Maybe there was

Velcro or glue or they just got melded together in the

collision.

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Got it?• Classify the following collisions based on the

four categories of the previous slides:

A. Two magnets approach, their north poles

facing; they repel and reverse direction

without touching.

B. A truck strikes a parked car and the two

slide off together, crumpled metal

hopelessly entwined.

C. A basketball is dropped from 1.5 m above

the floor, and bounces up to a maximum

height of 1.2 m above the floor.

D. A toy containing a compresses spring is

dropped from 1.5 m above the floor, when

it hits the floor the spring is released,

causing it to jump to a maximum height of

2.2 m above the floor.

Totally Inelastic Collisions

• Totally inelastic collisions are governed entirely by

conservation of momentum.

– Since the colliding objects join to form a single composite

object, there’s only one final velocity:

• Therefore conservation of momentum reads

1 1 2 2 1 2 fm v m v m m v

Before collision After collision

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Inelastic collision

– occurs when colliding objects result in deformation

and/or the generation of heat.

Single car moving at 10 m/s collides with another car of the

same mass, m, at rest.

From the conservation of momentum,

(net mv)before = (net mv)after

(m 10)before = (2m V)after

V = 5 m/s

Elastic Collisions

• Elastic collisions conserve both momentum and kinetic

energy:

• Therefore the conservation laws read

1 1i 2 2i 1 1f 2 2f

2 2 2 21 1 1 11 1i 2 2i 1 1f 2 2f2 2 2 2

m v m v m v m v

m v m v m v m v

Before collision After collision

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Special Cases: 1-D Elastic Collisions;

m2 Initially at Rest

1) m1 << m2:

Incident object rebounds with

essentially its incident velocity

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Special Cases: 1-D Elastic Collisions;

m2 Initially at Rest2) m1 = m2:

Incident object stops; struck

object moves away with

initial speed of incident

object

Special Cases: 1-D Elastic Collisions;

m2 Initially at Rest

3) m1 >> m2:

Incident object continues with

essentially its initial velocity;

struck object moves away with

twice that velocity

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Got it?

• Ball A is at rest on a level floor. Ball B collides

elastically with Ball A, and the two move off

separately, but in the same direction. What can you

conclude about the masses of the two balls?

A. Ball A and Ball B have the same mass.

B. Ball B has a greater mass than Ball A.

C. Ball A has a greater mass than Ball B.

D. You cannot conclude anything without more

information.

Ela

sti

c C

ollis

ion

s i

n 2

-D

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Elastic Collisions in 2-Dimensions