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.