Work, Energy and Power

(A) Work and energy

In physics, work is done when a force exerts on an object over a displacement. It is defined in the following way:

Work = Force in the direction of displacement ×Displacement

W = F//×s

The Sl unit of work is J (joule) or N m.

1 J of work is done whenever a force of 1 N moves a displacement of 1 m in the direction of the force.

Work done by a force = energy transferred

The following shows how to calculate the work done by a force in different cases.

Case / Work done by the force
/ W = Fs
/ W = (F cos θ)(s) = Fs cosθ
/ W = (0)(s) = 0
/ W = (-F)s = -Fs
/ W = (- F cos )(s) = (F cos θ)(s)= Fs cosθ

Energy exists in different forms. In mechanics, mechanical energy is involved.

Mechanical energy includes:

(a)Kinetic energy (KE) - energy possessed by a moving object.

(b)Gravitational potential energy (PE) - the work done by a force to raise an object from the ground at a constant speed.

(c)Elastic potential energy - energy possessed by an elastic object when it is stretched, compressed or twisted.

(B) Kinetic Energy and Gravitational potential energy

Kinetic energy is the energy possessed by a moving object. For an object with mass m and speed v, its kinetic energy Ekis defined as

Ek =

Gravitational potential energy of an object (with respect to the ground)is the work done by a force to raise this object from the ground to a height at a constant speed. For an object with mass m at a height h above the ground, its gravitational potential energy Ep with respect to the ground is given by

Ep= mgh,

where g is the acceleration due to gravity.

The Sl unit of energy is J (joule) or N m.

(C) Energy changes

The principle of conservation of energy states that energy can be changed from one form to another but it cannot be created or destroyed.

(D) Power

Power is the rate at which energy is transferred or work is done.

The SI unit of power is W (watt) or J s-1

For an object moving at a constant velocity, ‘F’ is the applied force that opposes resisting force acting on the object moving at a constant velocity, we have

power P by the force = force x velocity, i.e.

P = Fv

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