Work and Power

Work:

• In physics we say that work is done on an object if a force is applied to it and that force causes it to move a certain distance.

Work = W = Fd

N m

N•m = J = Joule

WORK IS ENERGY!!!

What is a Joule?

N • m

kg m • m s2

kg m2

s2

The energy required to lift a small apple one meter straight up.

Here’s the important thing about work…work is only done if the force has a component in the same direction as the

displacement.

m = 10 kg

F = 25N

d = 2m

Is this guy doing work on the box?

Yes. The force vector is in the same direction as the displacement.How much work is being done? W = Fd

W =25N(2m) W = 50 Nm = 50J

Is work done when pulling this dog?

Yes. The force vector has some component in the same direction as the displacement.

How much work is being done?

d = 10m

30°

F

Fx

Fy

30°

= 70NFx = cosΘ = A HFx = FcosΘ

Fx = 70Ncos30°

Fx = 61N

W = FdW =61N(10m) W =610J

Is work being done by this waiter?

No. He could carry around that tray all day and according to physics he wouldn’t be doing any work.

There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

• How much work is needed to lift at a constant speed a 15kg book 3m?

W = Fd

W = mgd

W = (15kg)(10m/s2)(3m)

W = 450 J

Which path (incline vs. ladder) requires more work to get the box to the top?

10 m5 m

30°

mbox = 10 kg

W = Fd

W = (50N)(10m)

W = 500 J

W = Fd

W = (100N)(5m)

W = 500 J

Same amount of work!

A particular task may require a certain amount of work but it might be done over different lengths of

time…

• This is known as Power (P). It measures the rate at which work is done.

P = W t

P = Fd t

d = vt

P = Fv

P = Fd t

J = watt = Ws

Who has more power?

• Dan Parker and Brad Bowen are in the weightlifting room. Dan lifts the 50 kg barbell over his head 10 times in one minute; Brad lifts the 50 kg barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power?

Brad is more "power-full" since he does the same work in less time. Power and time are inversely proportional.

Try this…• A crane lifts a load with a mass of 1000kg a vertical

distance of 25m in 9s at a constant velocity. How powerful is the crane?

P = W = Fd t t

= Fgd t= mgh t

= (1000kg)(10m/s2)(25m) 9s

= 27000 W

Try this…

• A 45 kg bicyclist climbs a hill at a constant speed of 3 m/s by applying an average force of 80 N. How much power does the bicyclist develop?

P = Fv

P = (80 N)(3 m/s)

P = 240 W

• Power is a rate (ENERGY PER SECOND).• Your electric bill (power bill) is based on your

rate of energy use.• A lightbulb with a 60 Watt power rating means

that the bulb uses 60 joules of energy per second.

W = ΔET

Work = a change in total energy