Work, Power, and the Basics of Energy. Work Work – Exerting force in a way that makes a change in the world. Throwing a rock is work: you’re exerting.

Work, Power, and the Basics of Energy

Work

Work – Exerting force in a way that makes a change in the world. Throwing a rock is work: you’re exerting a

force, and the rock’s location changes (i.e. “the world has been changed”)

Pushing on a brick wall is not work: you’re exerting a force, but the wall’s position doesn’t change.

Work So exerting force alone isn’t enough. You

have to both exert a force, and make a change.

If you’re not exerting a force, you’re not doing work.

Example: Throwing a ball. While you are “throwing the ball” (as opposed to just

holding it) you are exerting a force on the ball. And the ball is moving. So you’re doing work.

After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but you’re no longer doing work.

Who is doing work?

What must you ask to determine if work is being done?

By carrying the box up the stairs, force and distance is in the same direction

Work

Work

Work So, mathematically, we define work as “exerting a force over a

distance”:

(Work) = (Force exerted)(Distance over which force is exerted)

or

W = FdW = Work done F = Force exerted on objectD = Distance over which force is exerted.

Impulse looked at how long a force was applied (force x time); work considers at what distance it was applied.

Example of Work

You are pushing a very heavy stone block (200 kg) across the floor. You are exerting 620 N of force on the stone, and push it a total distance of 20 m before you get tired and stop.

How much work did you just do?W = (620 N)(20 m) = 12,400 Nm

New Unit! The units for work are Nm (Newtons × meters).

As we did with Newtons (which are kg m/s2), we will “define” the Newton-meter to be a new unit. We’ll call this unit the Joule.

Abbreviation for Joule: J So, 1 Nm = 1 J

(So in the previous example, we did 12,400 J of work)

Thinking about work…

A person carrying a backpack up four flights of stairs does ___________ the work as a person climbing two flights of stairs

a) half

b) twice

c) four times

d) the same

Thinking about work…

A person carrying a backpack up four flights of stairs does ___________ the work as a person climbing two flights of stairs

a) half

b) twice

c) four times

d) the same

Since W = F d, if youDOUBLE the distance,you DOUBLE the work

Thinking about work…

A weightlifter holding 500lbs over his head is doing no work.

True or False?

True! The weightlifter is notmoving the barbell overany distance. Therefore he is not doing any work.

Work Done By “Lifting” Something Notice that when we were pushing something along the

ground, the work done didn’t depend on the mass. Lifting up something does do work that depends on

mass. Because of gravity:

Gravity always pulls down with a force equal to mg, where m is the mass, and g = 10 m/s2.

So we must exert at least that much force to lift something. The more mass something has, the more work required to lift

it. So, work = force of gravity x distance

• = (mass x acceleration of gravity) x distance

Work Done By “Lifting” Something

Example: A weightlifter lifts a barbell with a mass of 280 kg a total of 2 meters off the floor. What is the minimum amount of work the weightlifter did? The barbell is “pulled” down by gravity

with a force of (280 kg)(10 m/s2) = 2,800 N

So the weightlifter must exert at least 2,800 N of force to lift the barbell at all.

If that minimum force is used, the work done will be:

W = (2,800 N)(2 m) = 5,600 J

Working at an advantageOften we’re limited by the amount of force we can

apply.

Simple Machines such as ramps, levers, pulleys, etc all allow you to do the same amount of work, but by applying a smaller force over a larger distance

Work = Force x Distance

= Force x Distance

Ramps: AKA Inclined Planes

Ramps allow the exertion of a smaller force over a longer distance to achieve the same change in gravitational potential energy (the same amount of work)

M

How “Hard” Are You Working? The rate at which work is done is called

power:(Power) = (Work Done) / (Time Spent Working)

P = W / t Power is “how hard” something is

working.

Power Example: Let’s say that it took us 40 s to move

that 200 kg block the 20 m. Remember that we did 12,400 J of work on stone the

block.(See earlier slide)

Since it took us 40 s to move the block, we were doing 12,400 J / 40 s = 310 J of work per second (so the units are J/s).

We will define a new unit:• Joules per second = Watts• 1 J/s = 1 W

So our power output was 310 W.

Power

What about the weightlifter? Pretend it takes the weightlifter a full 2

seconds to lift the weight: P = 5,600 J / 2 s = 2,800 J/s = 2,800 W We say 1,000 watts = 1 kilowatt So the weightlifter’s power was 2.8 kW

Kilowatts and Horsepower

Another common unit of power (not used in science, but used in everyday life) is the “horsepower” – basically the rate at which a (very powerful, very healthy) horse can do work over a 10 hour “work day.”

1 horsepower (hp) = 746 W or 0.746 kW.

How fast can your car do work? A compact car may have a 120 hp

engine. That means the car’s power is (120 hp)

(746 W/hp) = 89,520 W So a typical compact car can do 89,520 J

worth of work each second.

Fast work isn’t more work

Go back to our 200 kg block example. Remember that when it took us 40 s to push the block the 20 m, that implied that we had a power output of 310 W.

If we exerted the same force (620 N) and pushed the block the same distance (20 m), but took half as long to do so (20 s), our power output would double to 620 W.

Fast work isn’t more work

*But* Notice that the total work done doesn’t change – we still exerted 620 N of force over a distance of 20 m.

So increasing power output doesn’t mean you’re doing more work, it means you’re doing the work faster.

Work and Energy

Energy – The ability to do work.