# Unit 5: Momentum and Collisions

### Newton's Third Law of Motion

## Learning Targets

- I can identify the action and reaction forces acting in a system.
- I can diagram and calculate the components of force and motion.
- I can calculate and compare the physical property of momentum between two objects.
- I can explain the idea of impulse as it relates to changes in momentum.
- I can apply the law of conservation to momentum of objects involved in ideal collisions.

## Questions Based Off of Learning Targets

- If a lady bug flies into a moving car, which would have a greater change in momentum and why?
- Diagram and calculate the components of force and motion.
- If a bowling ball weighing 10 kg and a baseball weighing 5 kg each roll into a set of pins, which would have more momentum when hitting the pins and why?
- If a baseball has momentum and is struck by a bowling ball or a golfball, assuming both the bowling ball and golf ball hit the baseball at the same velocity, which would cause an impulse in momentum of the baseball and why?
- If two cars of equal mass are traveling at different velocities, one at 5 m/s and the other, 15 m/s, what will be their ending velocities after colliding?

## Key Concepts

~Forces

- A force is a push or pull that acts upon an object as a result of interaction with other objects

- Contact interactions are normal, frictional, tensional and applied forces

~"For Every Action, There is an Equal but Opposite Reaction"

- In every interaction, there are a pair of forces acting on two interacting objects

- The size of the force on the initial object equals the force on the second object

- The direction of the force of the first and second object are opposite of each other

- Forces always come in equal and opposite action and reaction force pairs

Momentum:

~ Momentum

- Mass in motion

- A quantity describing an objects resistance to stopping

- If an object is in motion, it has momentum

- The amount of momentum an object has depends on how much stuff is moving and how fast it's moving

- Impulse is change in momentum

- Impulse momentum Theorem:

- Large force and small time
- Small force and long time

- Collisions: momentum is conserved, therefore before=after, supporting The Law of Conservation of Momentum

- closed systems: no changes in mass

- Isolated systems: When an external force on a closed system is equal to zero (no applied force from outside)

- No system is truly isolated on earth, so we assume ideal

- Types of Collisions:

- Assume perfect or ideal

- Inelastic- objects collide together and stick, deforming

Ex: Clay being thrown on the ground

- Elastic- objects bounce and spring back into their shape

Ex: Bumper Cars

## Vocabulary

~ Elastic- Bounce and spring back into shape

~ Inelastic- Objects that collide and stick together and objects are deformed

~ Impulse- A change in momentum

~ Momentum- Mass in Motion

## Formulas

p = m*v

Δp = FΔt = Δp = mΔv

Elastic Collisions:

m1v1 + m2v2 = m1v1+ m2v2

Inelastic Collisions:

m1v1 + m2v2= (m1 + m2)v

- P = Momentum (kg * m/s)
- M =Mass (kilograms)
- V = Velocity (meters/second)
- Δp = impulse (Newtons-seconds)

## Practice Problems

Solving:

p=m*v

M=5

V=8

5*8=40

The momentum of the bowling ball is 40 kg * m/s

2. If a car weighing 45 kg going a speed of 50 m/s runs into a car at rest weighing 70 kg and then the first car continues on at 15 m/s, assuming this is an elastic collision, solve for the final velocity of the second car.

m1v1 + m2v2 = m1v1+ m2v2

Initial:

M1=45

V1=50

M2=70

V2=0

Final:

M1=45

V1=15

M2=70

V2=?

45(50) + 70(0) = 45(15) + 70(?)

2250 = 675 + 70(?)

-675 -675

1575 = 70(?)

1575/70 = (70(?))/70

V2 = 22.5 m/s

3. If a toy car weighing 5 kg is hits another toy car at rest weighing 10 kg at the speed of 6 m/s, assuming this is an inelastic collision, find the final velocity of the two cars after colliding.

m1v1 + m2v2= (m1 + m2)v

Initial:

M1=5

V1=6

M2=10

V2=0

Final:

M=15

V= ?

5(6) + 10(0) = (5+10) v

30 = (15) v

30/15 = ((15) v) / 15

V = 2 m/s