1. Work The displacement of an object in a parallel direction to an applied force. F d W=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 kgm 2 /s 2 W=Fd Work is a scalar quantity. The force and displacement must be in parallel directions.

2. Vertical 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 hihi hfhf d

3. d F No work is accomplished by force F in this situation.

4. Work Also defined as a transfer of energy. Also defined as a transfer of energy. Whenever work is accomplished, energy of some type is transferred. Whenever work is accomplished, energy of some type is transferred.

5. Work by various components F f d W F =Fd Work accomplished by force, F moving a distance d W f = -fd Work accomplished by friction through a distance, d. Constant velocity Net work is zero Wnet=Fnet(d)=(F-f)d=Fd-fd=W F -W f =0 Acceleration Wnet=Fnet(d)=mad=(F-f)d=W F -W f

6. F d Work is positive when the force and displacement are in the same direction. F d Work is negative when the force and displacement are in opposite 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

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

8. Power 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  P= W/t Power =Work/time  P= W/t Power = (F)(d)/t = F(d/t) Power = (F)(d)/t = F(d/t) Power = Force x velocity  P=Fv Power = Force x velocity  P=Fv v = average velocity (v f +v i )/2 v = average velocity (v f +v i )/2 P  (N)(m)/s= (J)/(s)=(kgm 2 /s 3 ) = Watt P  (N)(m)/s= (J)/(s)=(kgm 2 /s 3 ) = Watt Power is measured in Watts, abbreviated W. Power is measured in Watts, abbreviated W. 1 horsepower = 746 Watts (1 hp =746 W) 1 horsepower = 746 Watts (1 hp =746 W)

9. Work in Various Directions d

10. Situation 1 d An object pulled at an angle on a level horizontal surface. F FxFx W=(Fcosθ)d W=F x d The applied force F and d are not in a parallel direction. F x =Fcosθ

11. Situation 2 x W h θ Given: W, x, θ h=xtanθ Work=Wh=Wxtanθ

12. Situation 3 x F d θ Given: F, x, θ d=x/cosθ W=Fd

13. Situation 4 F d θ Given: F, d, θ F !! =Fcosθ W=F || d=Fdcosθ or θ x x=dcosθ W=Fx W=Fdcosθ F ||