Momentum and Impulse Unit 6

Momentum (p) Definition- The amount of motion an object has. (vector quantity) units- kg∙m/s p = mv

Momentum If a car has a mass of 1,500kg and is being driven with a velocity of 15 m/s, what is it’s momentum?

Momentum If a car has a mass of 1,500kg and is being driven with a velocity of 15 m/s, what is it’s momentum? m = 1,500kg v = 15 m/s

Momentum If a car has a mass of 1,500kg and is being driven with a velocity of 15 m/s, what is it’s momentum? m = 1,500kg v = 15 m/s p = mv

Momentum If a car has a mass of 1,500kg and is being driven with a velocity of 15 m/s, what is it’s momentum? m = 1,500kg v = 15 m/s p = mv p = (1,500kg) (15 m/s)

Momentum If a car has a mass of 1,500kg and is being driven with a velocity of 15 m/s, what is it’s momentum? m = 1,500kg v = 15 m/s p = mv p = (1,500kg) (15 m/s) p = 22, 500 kg m/s

Momentum A student is riding a bike down a pathway. The combined mass of the student and the bike is 120 kg. If the student and the bike have a momentum of 180 kg m/s, what is their velocity?

Momentum A student is riding a bike down a pathway. The combined mass of the student and the bike is 120 kg. If the student and the bike have a momentum of 180 kg m/s, what is their velocity? m = 120kg p = 180 kg m/s

p = mv

m = 120kgp = 180 kg m/s p = mv 180 kg m/s = 120kg v

m = 120kgp = 180 kg m/s p = mv 180 kg m/s = 120kg v v = 1.5 m/s

A cart has a momentum of 15 kg m/s. If the cart has a velocity of 3 m/s, what is the mass of the cart?

p = 15 kg m/s v = 3 m/s

A cart has a momentum of 15 kg m/s. If the cart has a velocity of 3 m/s, what is the mass of the cart? p = 15 kg m/s v = 3 m/s p = mv

A cart has a momentum of 15 kg m/s. If the cart has a velocity of 3 m/s, what is the mass of the cart? p = 15 kg m/s v = 3 m/s p = mv 15 kg m/s = m 3 m/s

A cart has a momentum of 15 kg m/s. If the cart has a velocity of 3 m/s, what is the mass of the cart? p = 15 kg m/s v = 3 m/s p = mv 15 kg m/s = m 3 m/s m = 5 kg

Do Now 1)Units for mass 2) Units for velocity 3)Units for momentum 4)Find the velocity of a 1,500kg car which has a momentum of 5,400 kg·m/s.

Answers 1)Kg 2)m/s 3)Kg·m/s 4)3.6 m/s

#4 m = 1,500 kg p = 7,500 kg·m/s v = ?

#4 m = 1,500 kg p = 7,500 kg·m/s p = mv v = ?

#4 m = 1,500 kg p = 7,500 kg·m/s p = mv 7,500 kg·m/s = 1,500kg v v = ?

#4 m = 1,500 kg p = 7,500 kg·m/s p = mv 7,500 kg·m/s = 1,500kg v v = ? 1,500 kg

#4 m = 1,500 kg p = 7,500 kg·m/s p = mv 7,500 kg·m/s = 1,500kg v v = ? 1,500 kg

#4 m = 1,500 kg p = 7,500 kg·m/s p = mv 7,500 kg·m/s = 1,500kg v 3.6 m/s = v v = ? 1,500 kg

Throwing a Tennis Ball What will happen when I throw a tennis ball against the wall?

Throwing a Tennis Ball What will happen when I throw a tennis ball against the wall? What will happen when I throw the tennis ball into the sheet?

Throwing a Tennis Ball What will happen when I throw a tennis ball against the wall? What will happen when I throw the tennis ball into the sheet? If you think something different happens, why?

Throwing an Egg During the lesson, keep the following questions in mind: 1) If I were to throw an egg against the wall, what will happen to the egg?

Throwing an Egg During the lesson, keep the following questions in mind: 1) If I were to throw an egg against the wall, what will happen to the egg? 2) If I throw the egg into the sheet, what will happen to the egg?

Throwing an Egg During the lesson, keep the following questions in mind: 1) If I were to throw an egg against the wall, what will happen to the egg? 2) If I throw the egg into the sheet, what will happen to the egg? 3) What is different?

mm

m m

t t

t

a = F Net / ma = ∆v / t F Net t = m ∆v

a = F Net / ma = ∆v / t F Net t = m ∆v F Net t = ∆p

Impulse (J) Definition- A force applied for a given time which results in a change in momentum. Units- N ∙ s J = F Net t = ∆p = m∆v ** t is the time for the object to come to a stop after hitting another object**

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car?

Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car? Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s Unknown: J = ?

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car? Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s Unknown: J = ? Equation: J = m∆v

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car? Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s Unknown: J = ? Equation: J = m∆v J = m (v f – v i )

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car? Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s Unknown: J = ? Equation: J = m∆v J = 1,500kg (0m/s – 15m/s)

A 1,500kg car is driving East with a velocity of 15 m/s. If the driver presses the brake and stops the car, what is the impulse exerted on the car? Givens: m = 1,500kg v i = 15 m/s v f = 0 m/s Unknown: J = ? Equation: J = m∆v J = 1,500kg (0m/s – 15m/s) J = -22,500 N·s

OR If this car crashed into one of these two objects, which object would cause a greater change in momentum?

OR If this car crashed into one of these two objects, which object would cause a greater change in momentum? Hint: ∆p = m∆v

OR If this car crashed into one of these two objects, which object would cause a greater change in momentum? Hint: ∆p = m∆v They cause the same ∆p

OR If this car crashed into one of these two objects, which object would cause a greater impulse?

OR If this car crashed into one of these two objects, which object would cause a greater impulse? They cause the same impulse

OR If this car crashed into one of these two objects, which object would cause a greater impulse? J = ∆p

OR Which object will cause more damage to the car? Why?

OR Which object will cause more damage to the car? Why? J = F t If J stays the same, and t is increased, F must decrease

What safety devices keep us safe in the event of an accident? How does each one work?

How does a parachute work? What physical value(s) does a parachute change to keep you safe?

Throwing an Egg If I were to throw an egg against the wall, what would happen? If I throw the egg into the sheet, what will happen? What is different?

Conservation of Momentum In a closed system (free from outside forces) the total momentum of the motion does not change. p before = p after “before” and “after” refer to before and after the collision.

Bouncy (Elastic) Collisions Objects start out separate and end separate. ex: a bat hitting a baseball

For bouncy collisions: p before = p after

For bouncy collisions: p before = p after p 1before + p 2before = p 1after + p 2after

For bouncy collisions: p before = p after p 1before + p 2before = p 1after + p 2after m 1 v 1before + m 2 v 2before = m 1 v 1after + m 2 v 2after

For bouncy collisions: p before = p after p 1before + p 2before = p 1after + p 2after m 1 v 1before + m 2 v 2before = m 1 v 1after + m 2 v 2after These are interchangeable

Cart A has a mass of 10kg. Cart B has a mass of 12kg. Cart A is moving East with a velocity of 5 m/s. Cart B is moving West with a velocity of 3 m/s and collides with cart A. If cart B is moving 1 m/s East after the collision, what is the velocity of cart A after the collision?

Givens: m A = 10kg m B = 12kg v Abefore = 5m/sv Bbefore = -3m/s v Aafter = ?v Bafter = 1 m/s

Givens: m A = 10kg m B = 12kg v Abefore = 5m/sv Bbefore = -3m/s v Aafter = ?v Bafter = 1 m/s

Givens: m A = 10kg m B = 12kg v Abefore = 5m/sv Bbefore = -3m/s v Aafter = ?v Bafter = 1 m/s m 1 v 1before + m 2 v 2before = m 1 v 1after + m 2 v 2after

Givens: m A = 10kg m B = 12kg v Abefore = 5m/sv Bbefore = -3m/s v Aafter = ?v Bafter = 1 m/s m 1 v 1before + m 2 v 2before = m 1 v 1after + m 2 v 2after 10kg·5m/s + 12kg·-3m/s = 10kg v1 + 12kg·1m/s

Givens: m A = 10kg m B = 12kg v Abefore = 5m/sv Bbefore = -3m/s v Aafter = ?v Bafter = 1 m/s m 1 v 1before + m 2 v 2before = m 1 v 1after + m 2 v 2after 10kg·5m/s + 12kg·-3m/s = 10kg v kg·1m/s 50kg·m/s – 36kg·m/s = 10kg v kg·m/s

14kg·m/s = 10kg v kg·m/s kg·m/s = 10kg v 1 V 1 = 0.2 m/s

Sticky (inelastic) Collisions Objects start separate, but end together. ex: Jumping onto a skateboard

For sticky collisions: p before = p after p 1 + p 2 = p 1,2 m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v after These are interchangeable

Lab cart A is 5kg and moving 4m/s East. Lab cart B is 10kg and moving 4m/s West. The two lab carts collide and become stuck together. What is the velocity (including direction) of the carts after the collision?

Givens: m 1 = 5kgm 2 = 10kg v 1 = 4m/sv 2 = -4m/s

Givens: m 1 = 5kgm 2 = 10kg v 1 = 4m/sv 2 = -4m/s m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v after

Givens: m 1 = 5kgm 2 = 10kg v 1 = 4m/sv 2 = -4m/s m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v after 5kg·4m/s + 10kg·-4m/s = (5kg + 10kg) v after

Givens: m 1 = 5kgm 2 = 10kg v 1 = 4m/sv 2 = -4m/s m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v after 5kg·4m/s + 10kg·-4m/s = (5kg + 10kg) v after 20kg·m/s – 40 kg·m/s = 15kg v after

-20 kg·m/s = 15kg v after

20kg·m/s – 40 kg·m/s = 15kg v after -20 kg·m/s = 15kg v after v = m/s

20kg·m/s – 40 kg·m/s = 15kg v after -20 kg·m/s = 15kg v after v = m/s 1.33 m/s West