Extra Practice Problems: 5.1, 5.7, 5.9, 5.11, 5.13, 5.15, 5.17, 9.3, Conceptual 9.1

Pain and CollisionsMomentum, Impulse, and Pressure

“It isn't the mountains ahead to climb that wear you out; it's the pebble in your shoe.”- Muhammad Ali

Today

Momentum ( p ).(mass times velocity)

Impulse ( I ).(change in momentum)

Pressure ( P ).(force over some area of space)

Today we’re introducing three simple and effective concepts that are usually used to assess damage, pain, and collisions, in addition to other things.

Momentum

Think of a time when you’ve heard this term.

It’s often used metaphorically - always at a time when it would take a lot of metaphorical force to stop it.

Direction of momentum is same as direction of velocity!

(Linear) Momentum

kg m sSI units:p = mv

Mass times Velocity.

Momentum is a vector so it gets broken down into components.

(Linear) Momentum

kg m sSI units:p = mv

|p| = 0 kg m/s

Mass times Velocity.

|p| = 12 kg m/s

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Don’t confuse momentum with inertia!inertia has to do with MASS.momentum is MASS times VELOCITY.

Let’s try itA pitcher claims he can throw a 0.145 kg

baseball with as much momentum as a 3.00 g bullet moving with a speed of 1500 m/s! What must the baseball’s speed be if the

pitcher’s claim is valid?

p = mv

Q51

A. the ball B. the bulletC. they are the same

KE = mv21 2

Which has greater kinetic energy?

Answer: B

Impulse

I = Δp = mvf ⎻ mvi

Change in Momentum.

kg m sSI units:

mass times final velocity minus mass times initial velocity.units: mass units (kg) times velocity units (kg)

Impulse

Are impulses bad if acted on too quickly?

(Usually…!)

In my experience, the answer to this question is YES!

Newton’s Second Law Revisited

Fnet = Δp Δt

Fnet = ma

This is the general form of Newton’s 2nd Law.

Impulse

Fnet Δt = mvf ⎻ mvi

Time is the collision time (start to end of impact).

Direction of impulse is the same as the direction of the force acting on an object (note: impulse only

happens if there’s a force!).

Can also be written as average/constant force (F) on an object times the duration of that force, Δt

Time is collision time or impact time or contact time… if the thing comes to rest its contact time is start of impact to time coming to rest. IF it bounces off it’s the total contact time with the impact surface (wall).

Impulse

Fnet Δt = mvf ⎻ mvi

Impulses hurt if acted on too quickly!

I

Remember “child falling out of bed”

example!

It hurts more to have your head hit a hardwood floor than a carpet because the force to stop your head acts for a shorter period of time for the hardwood floor! For a carpet you’re stopping over a slightly longer period of time because it’s squishy.

Impulse

Fnet Δt = mvf ⎻ mvi

Impulses hurt if acted on too quickly!

FΔt FΔt“Rolling with the punches”

Boxers opt for more Δt rather than more force!Another example.

Food generates the lady’s impulse.

The wall generates the car’s impulse.

I

I

Think about the DIRECTION of impulses. The direction is the external force acting on the object.

A 100-g lump of clay hits a wall at 70 cm/s and sticks. A 100-g rubber ball hits the same wall at 60 cm/s and

rebounds with a speed of 30 cm/s.

Which object has a larger impulse magnitude delivered by the wall during the collision?

Q52

A. The clayB. The ballC.Both impulses are the same.D.Cannot be determined.

Answer: B

Impulse and Average ForceWhat if the force isn’t constant?

High chance of death above this line

Force vs time in a car crash

Q53

Where is the biggest impulse?

A. Between 70 and 80 msB. Between 10 and 20 msC. Between 100 and 110 msD. Before the collision

Answer: AWe can model complex systems by using the AVERAGE force of a collision.Average force will deliver the same net impulse to an object over time delta t. If you were in a car crash you don’t want to experience the maximum force possible. Instead you want to experience an average force.

Impulse and Average Force

High chance of death above

this line

A car is travelling at 27 m/s (60 mph) and crashes into a pole, coming to rest in time 150ms. What is the average force exerted

on a 100kg person strapped into the car in this collision?

Favg Δt = mvf ⎻ mvi

Always wear seatbelts!

DO ON LIGHT BOARD.This person experienced much less Δt (hence more force!)

Pressure

Which hurts more?

Damage depends more on pressure than force!

Force over Area.

Have you ever stepped on a lego? It hurts a lot!

Pressure

Pressure (mainly for liquids and gases) or Stress (for solids) tells you over what area

the force is spread.

Force over Area.

Pressure or Stress = F / A

N m2SI units: Pascal (Pa)

A man sits on a four-legged chair with his feet off the floor. The combined mass of the man and chair is 95 kg. If the chair legs are circular and have a radius of 0.50 cm at the bottom, what pressure does each leg exert

on the floor?

Man on a Chair

What could you do to reduce pressure and

chance of scratching?

Do I apply the most pressure to the floor if I stand normally or on my toes? Same amount, but over smaller space.

Car Tires

0.024 m2

The four tires of an automobile are inflated to a gauge pressure of 2.0 x 105 Pa. Each tire has an area of

0.024 m2 in contact with the ground. Determine the weight of the automobile.

P = F / A

Momentum ( p ).(mass times velocity)

Impulse ( I ).(change in momentum)

Pressure ( P ).(force over some area of space)

Pressure or Stress = F / A

I = Fnet Δt = mvf ⎻ mvi

p = mv