Work, Energy and Power

Work Done by a force is defined as the product of

the force and displacement (of its point of

application) in the direction of the force

W = F s cos θ

Negative work is said to be done by F if x or its

compo. is anti-parallel to F

If a variable force F produces a displacement in the

direction of F, the work done is determined from the

area under F-x graph. {May need to find area by

“counting the squares”. }

By Principle of Conservation of Energy,

Work Done on a system = KE gain + GPE gain +

Work done against friction}

Consider a rigid object of mass m that is initially at

rest. To accelerate it uniformly to a speed v, a

constant net force F is exerted on it, parallel to its

motion over a displacement s.

Since F is constant, acceleration is constant,

Therefore, using the equation:

v2 = u2 +2as,

as = 12 (v2 – u2)

Since kinetic energy is equal to the work done on the

mass to bring it from rest to a speed v,

The kinetic energy, EK = Work done by the force F

= Fs

= mas

= ½ m (v2 – u2)

Gravitational potential energy: this arises in a

system of masses where there are attractive

gravitational forces between them. The gravitational

potential energy of an object is the energy it

possesses by virtue of its position in a gravitational

field.

Elastic potential energy: this arises in a system of

atoms where there are either attractive or repulsive

short-range inter-atomic forces between them.

Electric potential energy: this arises in a system of

charges where there are either attractive or repulsive

electric forces between them.

The potential energy, U, of a body in a force field

{whether gravitational or electric field} is related to

the force F it experiences by:

F = – dU / dx.

Consider an object of mass m being lifted vertically

by a force F, without acceleration, from a certain

height h 1 to a height h2. Since the object moves up

at

a constant speed, F is equal to mg.

The change in potential energy of the mass = Work

done by the force F

= F s

= F h

= m g h

Efficiency: The ratio of (useful) output energy of a

machine to the input energy.

ie

=

Useful Output

Energy x100%

=

Useful Output

Power x100%

Input Energy Input Power

Power {instantaneous} is defined as the work done

per unit time.

P

=

Total Work

Done =W

Total Time t

Since work done W = F x s,

P = F x s = Fv t

for object moving at const speed: F = Total resistive

force {equilibrium condition}

for object beginning to accelerate: F = Total resistive

force + ma

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