MomentumMo or r

What is Momentum?

A quantity of motion

Tells that an object is on the move and hard to stop

Mass in motion

Momentum Formula

• Involves mass and velocity (so direction is important!)

• Momentum = Mass x Velocity

Mo = MV ( r = MV)• So… V = Mo/M and M = Mo/V

The unit is a mass unit x a speed unit so… kg*m/s or kg*km/hr or g*cm/s… (it can’t be simplified more than this!)

Lets Try a problem! These cars are about to collide… (on ice!)

Mass: 300 kg Mass: 250 kg

Velocity: 20 km/hr Velocity: 12 km/hr

Mo = 300 kg x 20 km/hr Mo = 250 kg x 12 km/hr

6,000 kg*km/hr 3,000 kg*km/hr

Total Mo (Mo of 2 cars combined):

6000 + 3000 = 9,000 kg*km/hr

The cars already collided. What is the total momentum after the crash?

Mass: 300 kg Mass: 250 kg

Velocity: 15 km/hr Velocity: 18 km/hr

Mo = 300 kg x 15 km/hr Mo = 250 kg x 18 km/hr

4,500 kg*km/hr 4,500 kg*km/hr

Total Mo: 4500 + 4500 = 9,000 kg*km/hr

So was momentum conserved?

• YES!! • In a collision, the TOTAL MOMENTUM of all the

objects combined is the same before and after the “crash”

• Momentum is conserved if there is no loss of mass or energy due to friction…

• Which never really happens (except when you are in happy, theoretical world).

Why did car 1’s speed decrease?

• Remember action/reaction forces – if car 1 gives a force to car 2 (making car 2 speed up), then car 2 gives the same force back to car 1 - in the opposite direction – so car 1 slows down!

• Car 1 transferred some Mo to Car 2 (1500 kg*m/s to be exact)

• The car that loses Mo loses velocity (or mass)… the car that gains Mo gains velocity (or mass)

What is the Total Mo here?

Mass: 400 kg Mass: 300 kgVelocity: 35 km/hr Velocity: 40 km/hrMo = 400 kg x 35 km/hr Mo = 300 kg x 40 km/hr

14,000 kg*km/hr 12,000 kg*km/hr

Total Mo: 14000 - 12000 = 2,000 kg*km/hr to the rightThe cars are going in opposite directions, so

subtract the Mo!

What is the total Mo after they collide?

• Momentum is conserved!• So total Mo before = total Mo after• So the total Mo is still 2,000 kg*km/hr

(to the right)

@%$&*!!!

@%$&*!!!

Mass = 10,000 kgVelocity = 5 m/sMo = ? 10,000 kg x 5 m/s =

50,000 kg x m/s

Before Collision

Mass = 5,000 kgVelocity = 0 m/s

Mo = ?

0 kg x m/s

Before Collision

Total Momentum

+

50,000 kg x m/sMomentum is Conserved – this is the total momentum before and after the crash!

Mass = 10,000 kgVelocity = 0 m/s

Mo = ?0 kg*m/s

After Collision: Total Mo = 50,000

Mass = 5,000 kgMo =

50,000 kg*m/s

The tank lost 50,000 kg*m/s of Mo – this Mo was transferred to the car

The car gained 50,000 kg*m/s of Mo from the tank

Mass = 5,000 kgMo = 50,000 kg x m/s

V = ?

V = Mo / Mass = 50,000 kg x m/s 5,000 kg

V = 10 m/s

What happened to the speed of the car?

The speed of the car increased since it gained Mo! (remember the speed of the tank decreased)

Oh nooooooooI am in sooo muuuch trouble!

Mass = 5,000 kg Mass = 6,000 kg

Velocity = 5 m/s Velocity = 0 m/s

5,000 kg x 5 m/s = 6,000 kg x 0 m/s =

25,000 kg x m/s 0 kg x m/s

Total Mo Before Collision = ?

25,000 kg x m/s

What happened to the Mo and speed of the cars after the collision?

The car lost Mo… this Mo was transferred to the cop car

So the car lost speed

The cop car gained Mo from the patriotic car

So the cop car gained speed

The total Mo remained the same

Combined Mass = 11,000 kg (6,000 +5,000)

Total Mo After Collision = 25,000 kg x m/s (Mo is conserved!)

Velocity of the wreck:2.27 m/s – the cars have the same

speed since they are moving together!

Wait, how’d you do that?

Since Mo = mass x velocity

Velocity = Mo / mass

25,000 kg x m/s

11,000 kg 2.27 m/s

What is the momentum of each individual car after the crash?

Mass = 5,000 kgVelocity = 2.27 m/sMo = 11,363.64 kg*ms

The car slowed down and lost 13636.36 kg*m/s of Mo.

Mass = 6,000 kgVelocity = 2.27 m/sMo = 13,636.36 kg*ms

The car sped up and gained 13636.36 kg*m.s of Mo

The total Mo = 25,000 kg*m/s The amount of Mo the car lost = the amount of Mo the cop car gained!