Work, Power and Energy

Basic Terms - Work

Work (in physics) is defined as a force acting over a distance.

W = F x d

Scalar Quantity:

Units:

Making the grade lab: Work done on an inclined plane.

Concept Question 1

Is it possible to do work on an object that remains at rest?

1) yes

2) no

Concept Question 1

If there is no displacement, there is no work done.If there is no displacement, there is no work done.

Work requires that there be a force acting over a

distance.

Is it possible to do work on an object that remains at rest?

1) yes

2) no

Concept Question 2

A box is being pulled A box is being pulled

across a rough floor across a rough floor

at a constant speed. at a constant speed.

What can you say What can you say

about the work done about the work done

by friction?by friction?

1) Friction does nowork at all

2) Friction doesnegative work

3) Friction does positive work

4) Work is not defined for friction as friction acts on the floor and the box

Concept Question 2

A box is being pulled A box is being pulled

across a rough floor across a rough floor

at a constant speed. at a constant speed.

What can you say What can you say

about the work done about the work done

by friction?by friction?

1) Friction does nowork at all

2) Friction doesnegative work

3) Friction does positive work

4) Work is not defined for friction as friction acts on the floor and the box

Work is defined for all forces. The friction acts opposite to the direction of displacement and is therefore negative here.

f

N

mg

displacement

Pull

Concept Question 3

Can friction ever do Can friction ever do

positive work?positive work?

1) yes

2) no

Concept Question 3

Can friction ever do Can friction ever do

positive work?positive work?

1) yes

2) no

Consider the book on your car seat. If you accelerate slowly the book does not slide on the seat but stays stationary with respect to the car. Friction is causing the book to move along with the car and hence force and displacement are in the same direction. Work is positive.

Power

Power is the rate at which work is done. It can be thought of as work per second.

Power = Work / sec.

Power = Work / time

P = W / t

Question: Can you name 2 units for power? Answer: Horsepower and

Watts.

Power

Power has the same trade-offs as work. A motor produces the same amount of power.

So, you can make a robot that’s fast, but weak.

Or you can make a robot that’s slow, but strong.

The total power in must equal the total power out (with an exception)...

Mechanical Energy

• Energy defined

Potential Energy

• Defined

• PE = mgh

Concept Question

Is it possible for the

gravitational potential

energy of an object to be

negative?

1) No.

2) Yes.

3) Maybe.

Concept Question

Is it possible for the

gravitational potential

energy of an object to be

negative?

1) No.

2) Yes.

3) Maybe.

Gravitational PE is Gravitational PE is mghmgh, where height height hh is measured is measured relative to some arbitrary reference level where PE = 0relative to some arbitrary reference level where PE = 0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero levelceiling is the zero level, then the book has negative PE on book has negative PE on the tablethe table. It is only differencesdifferences (or changes) in PE that have any physical meaning.

Kinetic Energy

• Defined

• KE = ½ mv2

Concept Question

Is it possible for the kinetic

energy of an object to be

negative?

1) No.

2) Yes.

3) Maybe.

Concept Question

Is it possible for the kinetic

energy of an object to be

negative?

1) No.

2) Yes.

3) Maybe.

In Newtonian mechanics, the answer is no. The kinetic energy is always positive since the velocity squared and the mass are always positive.

Curiously, in quantum mechanics and relativity there are no such constraints. We believe it to still be true, but we are open to the possibility that it may not.

Conservation of Energy

• Defined

Conservation of Energy

• Con. Dev. 8-1, Short Cut Lab, Ball Toss Lab

Concep Question 4

Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp?

1

4) same speed

for all balls

2 3

Concep Question 4

Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp?

1

4) same speed

for all balls

2 3

All of the balls have the same initial gravitational PEsame initial gravitational PE, since they are

all at the same heightsame height (PE = mgh). Thus, when they get to the

bottom, they all have the same final KEsame final KE, and hence the same speedsame speed

(KE = 1/2 mv2).

Follow-up: Which ball takes longest to get down the ramp?Follow-up: Which ball takes longest to get down the ramp?

The Rise of the Machines

• Okay, not these machines!

Simple Machines

• Define:

• Examples: lever, pulley, ramp, gears

Mechanical Advantage

Understanding the 2 components of Work is the key tounderstanding mechanical advantage.

Question: Where would you hold the wrench for it to be most effective?

Mechanical Advantage

If you hold the wrench here, you need a lot of force...

If you hold the wrench here, you don’t need as much force...

…but you don’t move very far. …but your hand

moves a long way.

Mechanical Advantage

It takes the same amount of work to turn the bolt.

You can opt for a lot of force and little distance.

W = F x d

Or you can choose a little force but a lot of distance.

W = f x DIn many of our machines, we want to increase our force, so we don’t mind going the extra distance.

Mechanical Advantage

Question: Which ramp would you prefer to use to move a heavy weight to the top of the box?

Mechanical Advantage

With our gear box, you were able to create a large torque here...

…but you had to turn this handle many times.Remember: W = x

Mechanical Advantage

• Tug-of-war demo.

• Concept Development 8-2

Efficiency

• Are machines 100% efficient? Why or why not?

• Efficiency = Useful work out / Total work in

Friction = Bad

Friction is caused by two surfaces rubbing together.

Friction in our gear box causes a loss in the input power. It is lost in the form of heat and sound energy.

Friction = Good

But friction is also what makes our robot move.

The turning wheel produces a frictional force against the ground, which causes the robot to move.

More fun chapter problems

• Chapter 8 # 1, 2, 3, 5, 6, 8, 9, 10, 14, 15, 16, 18, 22, 24, 25, 26, 27, 33, 34, 35 & 36.