WorkWorkThe displacement of an object in a The displacement of an object in a

parallel direction to an applied force.parallel direction to an applied force.

F

dW=Force x displacement

Work is measured in Joules (J) which comes from a Newton-meter (Nm).The fundamental units that make up a Joule are kgm2/s2

W=Fd

Work is a scalar quantity.

The force and displacement must be in parallel directions.

Vertical WorkVertical Work

F

W

F=W for a mass lifted at constant velocity

Vertical Work:Work=(weight)(Δh)

d=change in height=final height –initial height

hi

hf

d

d

F

No work is accomplished by force F in this situation.

WorkWork Also defined as a transfer of Also defined as a transfer of

energy.energy. Whenever work is accomplished, Whenever work is accomplished,

energy of some type is energy of some type is transferred.transferred.

Work by various Work by various componentscomponents

Ff

d

WF=Fd Work accomplished by force, F moving a distance dWf = -fd Work accomplished by friction through a distance, d.

Constant velocityNet work is zeroWnet=Fnet(d)=(F-f)d=Fd-fd=WF-Wf=0

AccelerationWnet=Fnet(d)=mad=(F-f)d=WF-Wf

F

d

Work is positivewhen the forceand displacementare in the samedirection.

F

d

Work is negative when the force anddisplacement are inopposite directions.

Positive work: • Work is accomplished by the force.

• Energy in transferred into the system

Negative work: •Work is accomplished on the force.

•Energy is transferred out of the system

Work is the area under a force-Work is the area under a force-displacement graph.displacement graph.

PowerPower Power is the rate of doing work.Power is the rate of doing work. Power is the rate of energy transfer.Power is the rate of energy transfer. Power =Work/time Power =Work/time P= W/tP= W/t Power = (F)(d)/t = F(d/t)Power = (F)(d)/t = F(d/t) Power = Force x velocity Power = Force x velocity P=FvP=Fv v = average velocity (vv = average velocity (vff+v+vii)/2)/2 P P (N)(m)/s= (J)/(s)=(kgm (N)(m)/s= (J)/(s)=(kgm22/s/s33) = Watt) = Watt Power is measured in Power is measured in WattsWatts, abbreviated W., abbreviated W. 1 horsepower = 746 Watts (1 hp =746 W)1 horsepower = 746 Watts (1 hp =746 W)

Work in Various Work in Various DirectionsDirections

d

Situation 1Situation 1

d

An object pulled at an angle on a level horizontal surface.

F

Fx

W=(Fcosθ)d

W=Fxd

The applied force F and d are not in a parallel direction.

Fx=Fcosθ

Situation 2Situation 2

x

W

h

θ

Given: W, x, θ

h=xtanθ

Work=Wh=Wxtanθ

Situation 3 Situation 3

x

Fd

θ

Given: F, x, θ

d=x/cosθ

W=Fd

Situation 4Situation 4

Fd

θ

Given: F, d, θ

F!!=Fcosθ

W=F||d=Fdcosθ

or

θ

x

x=dcosθ

W=FxW=Fdcosθ

F||