CH 6 collision

What is a Collision?

when two objects hit each other

Collision examples

• Two cars crash

• A ball hits a wall

• You bump into someone

• Two pool balls hit

Conservation of Momentum

If nothing outside pushes on the system, the total momentum BEFORE equals total momentum AFTER.

That just means:

Add up all momentum before →
Add up all momentum after →

They MUST be equal.

Momentum is NEVER lost. It just moves around.

Freight car A is moving.
Freight car B is sitting still.

They collide and STICK together.

Inelastic Collision

Inelastic

they stick together after hitting

Since both cars they stick together, they move slower after.

Why?

Because now:

• Same momentum

• But MORE mass (both cars together)

If mass increases and momentum stays same»»

Speed must go down.

Freight car A is moving toward identical freight car B that is

at rest. When they collide, both freight cars couple together.

Compared with the initial speed of freight car A, the speed

of the coupled freight cars is

A. the same.

B. half.

C. twice.

D. None of the above.

half

mass and speed are

inverse

Elastic =

bounce

Elastic Collision examples

• Pool balls

• Super bouncy balls

Inelastic=

stick or squish

elastic and inelastics, momentum is

conserve/the same

Fish Example

A fish swims toward and swallows a smaller fish at rest. If

the larger fish has a mass of 5 kg and swims 1 m/s toward a

1-kg fish, what is the velocity of the larger fish immediately

after lunch? Ignore the effects of water resistance.

What do we have?

Big fish:

• Mass = 5 kg

• Speed = 1 m/s

Small fish:

• Mass = 1 kg

• Speed = 0 (not moving)

Big fish eats small fish

fish example: elastic or inelastic?

inelastic! They stick together

Find momentum BEFORE

Big fish:

p=5×1=5

Find momentum BEFORE

small fish:

p=1×0=0

Fish example

Total momentum before

5+0=5

Momentum after must still be ____

5

Fish example

After eating

Now total mass =

5 kg + 1 kg = 6 kg

One 6 kg fish moving at some unknown speed.

Let’s call that speed “v”.

We DON’T know it yet.

But we DO know something:

🚨 The total momentum must still be 5.

So after eating:

Momentum = mass × velocity

6 × v = 5

Because momentum must still equal 5.

Now Solve

6v = 5

Divide both sides by 6:

v = 5 ÷ 6

v = 0.83 m/s

Before eating:

• Light fish + fast-ish

• Total momentum = 5

After eating:

• Heavier fish

• But momentum must stay 5

• So speed MUST go down

Because:

If mass goes up…
Speed must go down
To keep momentum the same

m1​vi1​+m2​vi2​=m1​vf1​+m2​vf2

vf​=0.83m/s

Problem 2: Small Fish Moving Opposite Direction

Small fish swims LEFT at 4 m/s.

• Right =

• Left =

positive

negative

So small fish velocity = -4 m/s

-4 m/s

Find total momentum before

Big fish:

5×1=5

Find total momentum before

small fish:

1×(−4)=−4

total momentum before

5+(−4)=1

After they combine

Mass =

Momentum must still =

6 kg; 1

solve

answer

if final velocity is a negative number, that means

The big fish gets pushed backward

In every collision problem:

STEP 1:

Find total momentum before.

In every collision problem:

STEP 2:

Set it equal to total momentum after.

In every collision problem:

STEP 3:

Solve for unknown velocity

long story short

(total mass) × v=(momentum)