Work Power Energy-jee-aipmt

**WORK**

◊ Whenever a force acting on a body is able to actually move it through some distance in the direction of force, the work is said to be done by the force.

◊ When a constant force acts on a particle while it moves through a displacement, the force is said to do work W on the particle given by

where is the smaller angle between and?

◊ If the force and displacement are in the same direction, = 0.

∴ W = Fs .

◊ If and are perpendicular to each other, then,

This means that if the displacement of the body is perpendicular to the force no work is done.

◊ If the force and displacement are variable quantities, then

= area under the force-displacement graph, added with proper sign

◊ Work is a scalar quantity.

◊ In SI system the absolute unit of work is joule, while in CGS system, the unit of work is erg.

◊ Dimensions of work are

◊ Work done by a constant force in moving from one point to other depends only on the initial and final positions and not on the actual path followed by two points.

◊ If the work done by a force during a round trip of a system is zero, the force is said to be conservative, otherwise, it is called non-conservative. The force of Friction is a non-conservative force.

◊ Work done in moving an object against gravity depends only on the initial and final positions of the object but not upon the path taken. This shows that gravitational force is a conservative force.

◊ All the central forces are conservative forces.

◊ The work done by the force of gravity during the motion of a particle through a height h is

W = mgh, where m is the mass of the particle.

◊ Work was done in compressing/stretching a spring, where k is spring constant and x is the displacement from the normal position of rest.

◊ When one end of a spring is attached to a fixed vertical support and a block attached to the free end moves on a horizontal table from x =x_{1} to x =x_{2}, then

◊ Work was done by the couple for an angular displacement of

Where is the torque of couple?

**POWER**

◊Power is the time rate of doing work. Thus,

Power =

◊ If a constant force F acts on a body for time t and if due to this the body moves a distance ‘s’ in the direction of the force, with uniform velocity v, then power P developed is given by

Here θ is the smaller angle between force and velocity of the body.

◊ Power is a scalar quantity. SI unit of power is watt where 1 watt = 1 joule/sec.

◊ The practical unit of power is horse power (*hp*), where 1 hp = 746 watts.

◊Dimensions of power are