Work, Power & Energy

Work, Power & Energy :

Work is said to be done by a force if the point of application of force undergoes displacement either in the direction of force or in the direction of component of

force.

Amount of work done is equal to the dot product of force and displacement. If is the force acting on a body and is displacement, work done by that force is



Work done by a force can be positive or negative or zero

(a) If the displacement is in the direction of force or in the direction of component of force, work done is positive

(b) If the displacement is in a direction opposite to that of force or component of force, work done is negative

When a body of mass m is lifted to a height h above the ground without any acceleration,

a) work done by the applied force = mgh

b) work done by the gravitational

force = - mgh

c) work done by the resultant force = O

A block of mass m is suspended vertically using a rope of negligible mass. If the rope is used to lift the block vertically up with uniform acceleration a, work done

by the tension in the rope is

W = m (g + a) h

(h is distance through which it is lifted up)

Note: In the above case if the block is lowered with acceleration a W = - m (g - a) h

Energy : The capacity to do work is known as energy. It is a scalar quantity.

The energy possessed by a body by virtue of its state or position is known as potential energy.

e.g : Water on hill top and stretched or compressed spring possess potential energy.

The energy possessed by a body by virtue of its motion is called kinetic energy. Any body in motion possesses kinetic energy.

Gravitational potential energy of a body which is at a height 'h' above the ground is mgh (h is small so that g remains same almost)

Here surface of the earth is taken as reference.

Kinetic energy of a body = (m is mass, v is velocity)

Work done by an in balanced or resultant force on a body is equal to change in its kinetic energy. This is known as work-energy theorem.



According to the law of conservation of energy, the total energy of a closed system remains constant. Energy can neither be created nor destroyed but it can be

transformed from one form to another form without any loss or gain.
If p is linear momentum of a body moving with kinetic energy E, we can write

(m is mass of the body)



for a given body

A body can have energy without momentum. But it can not have momentum without energy.

A bullet of mass m moving with velocity v stops in wooden block after penetrating through a distance x. If F is resistance offered by the block to the bullet,





A sphere of mass m is dropped from a height 'h' above the ground. On reaching the ground, it pierces through a distance S and then stops finally. Resistance

offered by the ground is R. Then

mgh = (R - mg) S



Note: Here time of penetration is given by



A bullet of mass m is fired horizontally wiht a velocity V which strikes a wooden block of mass M suspended vertically. After striking the block, the bullet stops

in the block by piercing. If the combined system rises to a height 'h' above the initial position,



The rate of doing work by a force is called power



power is a scalar quantity.

Units of power : erg /s (CGS system)

Js^-1or watt (S I)

Horse power or HP (FPS)

1 H.P = 746 W
If a machine gun fires n bullets per second such that mass of each bullet is m and coming out with velocity v, power of that machine gun