# Unit 5: Momentum and Collisions

## Learning Targets

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

## Questions Based Off of Learning Targets

1. If a lady bug flies into a moving car, which would have a greater change in momentum and why?
2. Diagram and calculate the components of force and motion.
3. 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?
4. 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?
5. 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

Newton's Third Law:

~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
Conservation of Momentum:

- 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

~ Conservation- Closed system, no change in total

~ 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

1. If the mass of a bowling ball is 5 kg and is rolling down a lane at 8 m/s, what is the momentum of the bowling ball when rolling into the pins?

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