Work, Power, & Efficiency

November 2015

Physics students know

the definition of w

ork!

Work

Work: The word looks the same, but it has different meaning in physics than the way it is normally used in the everyday language

Work W is done when a constant force F exerted on an object through distance d

work = force along distance × the distance moved

Only the component of force that acts in the same direction as the motion is doing work on the box.

Vertical component is just trying (unsuccessfully) to lift the object up.

d

F

θ Fd

F

θ Fd

dW = F d = Fd cosθwork = force × distance moved × cos of the angle between them

The SI unit for work is the newton–metre and is called the joule named after the 19th Century physicist James Prescott Joule.

1 J (Joule) = 1N x 1 m

Work is a scalar (add like ordinary numbers)

Units

According to the physics definition, you are NOT doing work if you are just holding the weight above your head

(no distance moved)

Work - like studying very hard, trying to lift up the car and get completely exausted, holding weights above head for half an hour is

no work worth mentioning in physics.

you are doing work only while you are lifting the weight above your head

(force in the direction of distance moved)

A force is applied. Question: Is the work done by that force?

Who’s doing the work around here?

NO WORK WORK

If I carry a box across the room I do not do work on it because the force is not in the direction of the motion (cos 900 = 0)

θ = 00 00< θ <900 θ = 900 900< θ <1800 θ = 1800

cos θ = 1 cos θ = + cos θ = 0 cos θ = – cos θ = –1

Work done by a force F is zero if:

F

motion

normal force

F

d d

F

force is exerted but no motion is involved:

no distance moved, no work

force is perpendicular to the direction of motion (cos 900 = 0)

gravitational force

tension in the string

when the force and direction of motion are generally in the same directions

when the force and direction of motion are generally in the opposite directions

00< θ < 900 → cos θ = + cos 00 = 1

Work done by force F is:

W = Fd

W = - Fd

(the work done by friction force is always negative)

positive

negative

900< θ < 1800 → cos θ = – cos 1800 = –1

We do:

1) Is work positive, negative, or zero? a) a book falls off a table

b) a rocket accelerates through space

2) Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 N directed at an angle of 41° below the horizontal direction. Calculate the work that Mike does on the mower in pushing it 9.1 m across the yard

We do:

1) Is work positive, negative, or zero? a) a book falls off a table

Postive! The force (gravity) is in the same direction as the motion.

b) a rocket accelerates through space Positive! The force (of expelled gasses on the rocket) are in the same direction as the motion.

We do:

2) Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 N directed at an angle of 41° below the horizontal direction. Calculate the work that Mike does on the mower in pushing it 9.1 m across the yard

d410

F

F = 45 N

d = 9.1 m

θ = 410

W = Fd cos θ = 310 J

You do:

1) Is work positive, negative, or zero? a) A waiter carries a tray full of meals above his head by

one arm straight across the room at constant speed.

b) friction slows a sliding hockey puck

2) Forward force is 200 N. Friction force is 200 N. The distance moved is 200 km. Find

a) the work done by forward force F on the car.b) the work done by friction force Ffr on the car.c) the net work done on the car.

You do:

1) Is work positive, negative, or zero? a) A waiter carries a tray full of meals above his head by

one arm straight across the room at constant speed.No work! The force is exerted upward, and the motion is horizontal.

b) friction slows a sliding hockey puckNegative work! The force is opposite the motion.

Forward force is 200 N. Friction force is 200 N. The distance moved is 200 km. Find a. the work done by forward force F on the car.b. the work done by friction force Ffr on the car.c. the net work done on the car.

F = 200 N

Ffr = 200 N

d = 2x105 m

a. WF = Fd cos 00 = 4x107 J

b. Wfr = Ffr d cos 1800 = - 4x107 J

c. the net work done on the car means the work done by net force on the car.

It can be found as:

W = WF + Wfr = 0

or

W = Fnet d cos θ = 0 (Fnet = 0)

Work done by a varying force - graphically

W = Fd cos θ applies only when the force is constant.

Force can vary in magnitude or direction during the action.

Examples: 1) rocket moving away from the Earth – force of gravity decreases 2.) varying force of the golf club on a golf ball, etc …

In these cases, work done is most easily determined graphically.

The lady from the first slide is pulling the car for 2 m with force of 160 N at the angle of 60o , then she gets tired and lowers her arms behind her at an angle of 45o pulling it now with 170 N for next 2 m. Finally seeing the end of the journey she pulls it horizontally with the force of 40 N for 1 m.

Work done by her on the car is:

W = (160 N)(cos 60o)(2m) +(170 N)(cos 45o)(2m) + (40 N)(cos 0o)(1m)

W = 80x2 + 120x2 + 40x1 = pink area + green area + blue area = 440 J

http://www.kcvs.ca/map/java/applets/workEnergy/applethelp/lesson/lesson.html#1

In general:

The area under a Force - distance graph equals the work done by that force

Graphical determination of work: You do

A man pushes a shopping cart 6 meters. What is the work done?

Find area: (1/2)(2)(1)+(2)(2)+(1/2)(2)(3) = 8 J

Power

Power is the work done in unit time or energy converted in unit time

measures how fast work is done or how quickly energy is converted.

◘

Units: 1J(joule)

1 W(Watt) = 1s

A 100 W light bulb converts electrical energy to heat and light at the rate of 100 J every second.

orW E

P = P = t t

Calculate the power of a worker in a supermarket who stacks shelves 1.5 m high with cartons of orange juice, each of mass 6.0 kg, at the rate of 30 cartons per minute.

Calculate the power of a worker in a supermarket who stacks shelves 1.5 m high with cartons of orange juice, each of mass 6.0 kg, at the rate of 30 cartons per minute.

0W Fdcos0 (30×60N)×1.5mP = = =

t t 60s P = 45 W

Efficiency

Efficiency is the ratio of how much work, energy or power we get out of a system compared to how much is put in.

◘

useful outputefficiency =

total input

No units◘

Efficiency can be expressed as percentage by multiplying by 100%.

◘

out out out

in in in

W E Peff = = =

W E P

No real machine can ever be 100% efficient, because there will always be some energy lost as heat

◘

A car engine has an efficiency of 20 % and produces an average of 25 kJ of useful work per second.How much energy is converted into heat per second.

A car engine has an efficiency of 20 % and produces an average of 25 kJ of useful work per second.How much energy is converted into heat per second.

out

in

Eeff =

E

in

25000J0.2 =

EEin = 125000 J

heat = 125 kJ – 25 kJ = 100 kJ

Quick Review (2 min)

With your table partner …

Person with longer hair:• Define power in your own words• State the equation and units for power.

Person with shorter hair:• Define efficiency in your own words• State the equation and units for efficiency

Power & Efficiency – You do An elevator lifts a total mass of 1.1X103

kg a distance of 40.0 m in 12.5 s. How much power does the elevator deliver?

What work is required to lift a 215 kg mass a distance of 5.65 m, using a machine that is 72.5% efficient?

P = W/t = Fd/t = mgd/t = 1100*9.8(40.0)/12.5 = 34,500 W

E = Wout / Win => Win = Wout / E

Win = 215*5.65*9.8 / .725 = 16, 400 J