# Work Energy Power Part 8

Power: power is defined as the time rate of doing work. P =  = = = Fvcos.

SI unit of power is watt = Nms-1 Dimension [P] =  =  = [ML2T-3].

1 horse power (H.P.) = The amount of power is required to hold a mass of 550 lb for 1 second at a height  1 ft from the surface of earth against the gravitational attraction of earth.

Example: 1. A car of mass m is moved upward on a rough inclined road of inclination . The coefficient of friction between wheel of the car and inclined road is . Find the power delivered by the car to move upward with constant speed v.

The net downward force acting on the car along the inclination is

F = component of weight of the car along the inclination + frictional force

Or, F = mgsin + mgcos = mg(sin + cos).

As the car is moving upward with constant speed v, then the power delivered by the car is P = Fv = mgv(sin + cos).

2. An electric pump can lift a liter of water per second to a reservoir at a height h meter from ground. If the radius of the pipe through which the water is moved is b meter then calculate the velocity of water. Find the power delivered by the pump. [Neglect all resistive forces]

If the velocity of water is v then, volume of water is moved per second = area of pipe distance travelled by water per second

Or,

v =  ms-1.

The pump can lift the volume of water per second is a liter = cm3.

Mass of the water is lifted per second is m = gram = a kg [density of water = 1 gcm-3].

The potential energy per second of water due to move at a height h is EP = mgh = agh joule.

The kinetic energy of water per second is EK =  =  =  joule.

Therefore the total energy of water per second is E = agh +  joule.

Therefore power delivered by the pump is P =  =  = agh +  watt.