Work & Power

Physics 2009

Work

• In Physics, Work is done when a force moves a body through a distance.

• WORK = Force x Displacement

Work Units

• Since, Force Newton (N)

displacement meter (m)

• DERIVED unit for work Newton meter (Nm).

• The FUNDAMENTAL unit for work is the Joule.

• Joule (J) = N m 1 JOULE = the ability to exert a force of 1 NEWTON over a distance of 1 METER.

Work

• Atlas bears the weight of the world on his shoulders.

• How much work is done?

• NONE…… the world did not move…The force must move the object.

Work or No Work

• Lifting your bookbag • Carrying your bookbag • A waitress carrying a tray around?

No work because the supporting force is perpendicular to the motion.

• Work is done on an object only if the object moves and only if the force and displacement are in the same direction.

• DIRECTION IS THE KEY TO WORK….

http://id.mind.net/~zona/mstm/physics/mechanics/energy/work/work2.gif

work

no work

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/wnot.gif

No work occurs when:

Work Problems

1. A force of 825 N is required to push a car across a lot. Two students push the car 35 m. How much work is done?

F= 825 N

d = 35 m

W = Fd

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

Work Problems

What work is done by a forklift that raises a 583-kg box 1.2m?

m = 583 kg

d = 1.2m

Work

• To move a refrigerator into the back of a moving van. Would you prefer to lift it straight up or walk it up a ramp?

• Which method required less work? • Equal amounts of work are done.• The ramp reduces the amount of

effort it takes to do work, but DOES NOT CHANGE the amount of work that is done.

Work

• To calculate the work done in moving the refrigerator into the truck, which displacement do we use? – The displacement from the start of the

ramp to the end, or the height of the ramp?

• Since a force is being applied to move the box upward, only movement in the direction of the force counts, so we use the height of the ramp.

Work Problems

• An airplane passenger carries a 215N suitcase up a flight of stairs a displacement of 4.2m vertically and 4.6m horizontally. How much work have they done?

Work

• Only force that is in the same direction of the motion counts.

• If you pull a wagon at an angle, only the horizontal part of motion counts – only the horizontal part of the pull does any work!

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

Work

• If the angle between force and displacement is θ then

Fx = F cos θ

• Then the work done is

W = Fx x d= F cos θ d

Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

W=Fd (cos θ)

Work

W = Fd cos θ

• If θ = 90o • W = Fd cos 90o

• So, W = 0

• Work is a scalar quantity.

• No direction is associated with work even though it depends on two vector quantities. C

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Work Direction

Positive and Negative Work

• When positive work is done on an object, its speed increases; when negative work is done, its speed decreases.

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Work Problems

• A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right. What is the net work done on the block?

• A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m to the right. What is the net work done on the block?

http://www.physicsclassroom.com/Class/energy/U5L1a.html

http://www.physicsclassroom.com/Class/energy/U5L1a.html

Work Problems

A physics student pulls a box of books as shown. The 455 N force is applied along the rope itself. How much work is done by the student on the books if the box is dragged 24.5 m.

http://k12.albemarle.org/Instruction/Physics/energy2/test1c.htm

Questionable Work

Which ramp requires more work to move the car up a set height?

a. 30°

b. 45 °

c. 60 °

d. work is equal http://www.physicsclassroom.com/mmedia/energy/au.html

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Work Done by a Variable Force

If the force changes with the displacement, W=Fd is no longer valid– Calculus is needed to calculate this directly

However, If force is plotted vs displacement the work can be graphically found as the area under the curve.

Constant Force Changing Force

Work Done by a Variable Force

Varying Force of a Spring

Recall the spring force is

Fs = kx

So, the work is

Calculate the work

Work Overview

http://hyperphysics.phy-astr.gsu.edu/hbase/wcon.html

Review

• Work is dependent on force and displacement.

The amount of work that is done in moving a 50N box a distance of 30 m is the ______ whether it takes 1 minute, 1 hour, or 1 day.

• Power is different. It takes ______ power to move that 50 N box 30 meters in 1 minute than it takes to move it the same distance in 1 hour.

• When you’re talking about power…

TIME MATTERS!

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Power

• Power is the rate at which work is done.

• Since work is equal to force x displacement:

Time

WorkPower

Time

ntDisplacemeForcePower

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Power Units

• Derived Units:

• Fundamental Units:

• 1 kilowatt = 1 kW = 1000 watts

• 1 kWh (kilowatt hour) = 3.60 x 106 J

• 1 horsepower (hp) = 745.7 W

s

J

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Power Derivation

t

WP

t

Fd

vt

d FvP

P=Fv

Power Problems

A small motor does 4000J of work in 20 seconds. What is the power of the motor in watts?

W = 4000 J

T = 20 s

P = ?

Power Problems

An electric motor lifts an elevator that weighs 1.2 x 104N a distance of 9.00 meters in 15.0 s. What is the power of the motor in kilowatts?

F = 1.2 x 104 N

d = 9.00 m

t = 15.0 s

P = ? (kW)

Power Problems

An electric motor develops 65 kW of power as it lifts a loaded elevator 17.5 meters in 35.0 s. How much force does the motor exert?

P = 65 kW = 65,000 W

d = 17.5 m

t = 35.0 s

F = ?