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?

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

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.

Answer

Work Done by a Varying Force Imagine a particle undergoes a very small displacement Δx The F x is approximately constant over this small displacement. Work done can be expressed as

Graph of a Varying Force

Work Done by a Varying Force

Work

Integration

Work Video

Power Power is the rate of doing work or of transferring energy.

Power Units Power is measured in joules per second. 1 J/s = Watt 1 hp = 746 W 1 kWh = 3.6 x 10 6 W

Power and Force If force F causes a particle to undergo a displacement ds, the work done is dW=Fds. Since ds/dt is v the power is given by the following formula:

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