1. V P Power, force and velocity Power is the rate at which a force does work. The SI unit of power is the watt (W) 1 W is the rate f working of 1 J s -1. If an engine drives an object at velocity v by means of a force F in the direction of motion, the power developed by the engine Fv.

2. V P Power, force and velocity Example 1 A crane lifts a load of 60 kg to a height of 15 m at a steady speed of 0.5 ms -1. Find the power required. Time taken to lift load = 15  0.5 = 30 s Work done against gravity = 60g  15 = 8828 J Power P = 8828  30 = 294 W. Or Power P = F  v = 60g  0.5 = 294 W

3. V P Power, force and velocity Example 2 A car of mass 800 kg moves at a steady speed of 12 ms -1 up a slope inclined to the horizontal at an angle 10 . resistance forces total 600 N. Find the power output of the engine. Work done in one second = P = 1961  12 = 23.5 kW DF – 800g  sin10 – 600 = 0 DF = 1961

4. V P Power, force and velocity Example 3 A pump raises water from a tank through a height of 2 m and outputs through a circular nozzle of radius 2 cm at 5 ms -1. Find the rate at which the pump is working. Volume of water =   0.02 2  5 = 0.0062832 m 3 Mass of water = 0.0062832  1000 = 6.283 kg KE = ½ mv 2 = ½  6.283  5 2 = 78.5375 J PE = mgh = 6.283  9.8  2 = 123.1468 J Total work done in one second = 202 J Rate of working = P = 202 W.