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Work and Energy Conservation Law Work and Energy Work is a force applied to an object that causes the point of application of the force to move through some distance Energy is the capacity of an object to do work Unit: Joules Energy and work are scalar quantities Work Is work a dot product or a cross product? W Fd cos Example problem A man cleaning a floor pulls a vacuum cleaner with a force of magnitude F= 50.0 N at an angle of 30.0º with the horizontal. Calculate the work done by the force on the vacuum cleaner as the vacuum cleaner is displaced 3.00m to the right. Answer W=Fd cos θ W= 50.0 N (3.00m) cos 30º W = 130 J Work a Scalar Product Work is the dot product of Force and Displacement W F d Work Done by a Constant Force A particle moving in the xy plane undergoes a displacement as shown below in a constant force as given below acts on the particle. A) Calculate the magnitude of the displacement and that of the force. B) Calculate the work done on the object. d (2.0i 3.0 j )m F (5.0i 2.0 j ) N Answer d x2 y2 d (2.0) 2 (3.0) 2 d 3.6m F Fx2 Fy2 F (5.0) 2 (2.0) 2 F 5.4 N W F d W (5.0i 2.0 j ) (2.0i 3.0 j ) W (5.0i 2.0i) (5.0i 3.0 j ) (2.0 j 2.0i) (2.0 j 3.0 j ) W 10 0 0 6 16 J Work Done by a Varying Force Imagine a particle undergoes a very small displacement Δx The Fx is approximately constant over this small displacement. Work done can be expressed as W Fx x Graph of a Varying Force Force Force vs. displacement 6 5 4 3 2 1 0 Series1 1 2 3 4 Displacement 5 6 Work Done by a Varying Force W Fx x xf W lim Fx x x 0 xf W xi F dx x xi Work Integration Work Video Power Power is the rate of doing work or of transferring energy. dw P dt Power Units Power is measured in joules per second. 1 J/s = Watt 1 hp = 746 W 1 kWh = 3.6 x 106W Power and Force If force F causes a particle to undergo a displacement ds, the work done is dW=F•ds. Since ds/dt is v the power is given by the following formula: dW P dt F ds P dt P F v Problem Consider a car traveling at a steady speed of 60 km/h (16.7 m/s). It encounters a frictional force (rolling and air drag) of 520 N. At what power level does the engine deliver energy to the wheels? Answer P = Fv 8.68 kW 11.6 hp