Momentum and Impulse Unit 6. Momentum (p) Definition- The amount of motion an object has. (vector...

Momentum and ImpulseUnit 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


m = 1,500kgv = 15 m/s

Momentum


m = 1,500kgv = 15 m/s

p = mv

Momentum


m = 1,500kgv = 15 m/s

p = mv

p = (1,500kg) (15 m/s)

Momentum


m = 1,500kgv = 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

m = 120kg p = 180 kg m/s

m = 120kg p = 180 kg m/s

p = mv

m = 120kg p = 180 kg m/s

p = mv

180 kg m/s = 120kg v

m = 120kg p = 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/sv = 3 m/s


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

p = mv


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

p = mv

15 kg m/s = m 3 m/s


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

p = mv

15 kg m/s = m 3 m/s

m = 5 kg

Do Now

1) Units for mass2) Units for velocity3) 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 kgp = 7,500 kg·m/s

v = ?

#4

m = 1,500 kgp = 7,500 kg·m/s

p = mvv = ?

#4

m = 1,500 kgp = 7,500 kg·m/s

p = mv

7,500 kg·m/s = 1,500kg v

v = ?

#4

m = 1,500 kgp = 7,500 kg·m/s

p = mv

7,500 kg·m/s = 1,500kg v

v = ?

1,500 kg 1,500 kg

#4

m = 1,500 kgp = 7,500 kg·m/s

p = mv

7,500 kg·m/s = 1,500kg v

3.6 m/s = v

v = ?

1,500 kg 1,500 kg

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?



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



2) If I throw the egg into the sheet, what will happen to the egg?

Throwing an Egg



2) If I throw the egg into the sheet, what will happen to the egg?

3) What is different?

a = FNet / m a = ∆v / t

FNet t = m ∆v

a = FNet / m a = ∆v / t

FNet t = m ∆v

FNet t = ∆p

Impulse (J)

Definition- A force applied for a given time which results in a change in momentum.

Units- N ∙ s

J = FNett = ∆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 = 1,500kgvi = 15 m/svf = 0 m/s


Givens:

m = 1,500kgvi = 15 m/svf = 0 m/s

Unknown:

J = ?


Givens:

m = 1,500kgvi = 15 m/svf = 0 m/s

Unknown:

J = ?

Equation:

J = m∆v


Givens:

m = 1,500kgvi = 15 m/svf = 0 m/s

Unknown:

J = ?

Equation:

J = m∆v

J = m (vf – vi)


Givens:

m = 1,500kgvi = 15 m/svf = 0 m/s

Unknown:

J = ?

Equation:

J = m∆v

J = 1,500kg (0m/s – 15m/s)


Givens:

m = 1,500kgvi = 15 m/svf = 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


They cause the same impulse

OR


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.

pbefore = pafter

“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:

pbefore = pafter


pbefore = pafter

p1before + p2before = p1after + p2after


pbefore = pafter


m1v1before + m2v2before = m1v1after + m2v2after


pbefore = pafter



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?

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: mA = 10kg mB = 12kg

vAbefore = 5m/s vBbefore = -3m/s

vAafter = ? vBafter = 1 m/s

Givens: mA = 10kg mB = 12kgvAbefore = 5m/s vBbefore = -3m/svAafter = ? vBafter = 1 m/s



10kg·5m/s + 12kg·-3m/s = 10kg v1 + 12kg·1m/s



10kg·5m/s + 12kg·-3m/s = 10kg v1 + 12kg·1m/s

50kg·m/s – 36kg·m/s = 10kg v1 + 12kg·m/s

50kg·m/s – 36kg·m/s = 10kg v1 + 12kg·m/s

14kg·m/s = 10kg v1 + 12kg·m/s-12 -12 .

2kg·m/s = 10kg v1

V1 = 0.2 m/s

Sticky (inelastic) Collisions

Objects start separate, but end together.ex: Jumping onto a skateboard

For sticky collisions:

pbefore = pafter

p1 + p2 = p1,2

m1v1 + m2v2 = (m1 + m2)vafter

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?

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:

m1 = 5kg m2 = 10kgv1 = 4m/s v2 = -4m/s

Givens:

m1 = 5kg m2 = 10kgv1 = 4m/s v2 = -4m/s


Givens:

m1 = 5kg m2 = 10kgv1 = 4m/s v2 = -4m/s


5kg·4m/s + 10kg·-4m/s = (5kg + 10kg) vafter

Givens:

m1 = 5kg m2 = 10kgv1 = 4m/s v2 = -4m/s


5kg·4m/s + 10kg·-4m/s = (5kg + 10kg) vafter

20kg·m/s – 40 kg·m/s = 15kg vafter


-20 kg·m/s = 15kg vafter



v = -1.33 m/s



v = -1.33 m/s

1.33 m/s West

Momentum and Impulse Unit 6. Momentum (p) Definition- The amount of motion an object has. (vector...

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Transcript of Momentum and Impulse Unit 6. Momentum (p) Definition- The amount of motion an object has. (vector...