Mechanics

Topic 2.3 Work, Energy and Power

Work

A simple definition of work is the force multiplied by the distance movedHowever this does not take in to account of the case when the force applied is not in the direction of the motionHere we have to calculate the component of the force doing the work in the direction movedi.e. Work is equal to the magnitude of the component of the force in the direction moved multiplied by the distance moved

Work = Fs = Fs cosWhere F is the force s is the displacement is the angle between the force and

the direction

F

s

The SI unit of work is the newton-metre (Nm) and it is called the joule (J)

Work is a scalar quantity

Force-displacement Graphs

The area under any force-displacement graph is the work doneforce

displacement

Area = work done

Energy and Power

Kinetic Energy This is the energy that a body

possesses by virtue of its motion If the mass of a body is m and its

velocity is v then its kinetic energy, Ek

= ½ m v2

Energy and Power

Gravitational Potential Energy This is the energy that a body

possesses by virtue of its position in the gravitational field

If the mass of a body is m and its height above a fixed position is h then its change in gravitational potential energy, Ep = mgh

where g = the acceleration due to gravity

The Principle of Conservation of Energy

Energy can be transformed from one form to another, but it cannot be created nor destroyed, i.e. the total energy of a system is constantEnergy is measured in joules and it is a scalar quantity

KineticGravitational PotentialElasticHeat (often refered to as internal)LightSoundElectricalChemicalNuclear

Types of Energy

Energy and Power

Elastic Potential Energy This is the energy that a body

possesses by virtue of its position from the equilibrium condition of the spring

If the mass of a body is m and its displacement from the equilibrium position is s then its elastic potential energy, E elas = ½ k s2

where k = the spring constant

In Mechanical Situations

Falling objects and roller coaster rides are situations where Ep + Ek = constant if we ignore the effects of air resistance and friction.Inclined planes and falling objects can often be solved more simply using this principle rather than the kinematics equations

In all collisions and explosions momentum is conserved, but generally there is a loss of kinetic energy, usually to internal energy (heat) and to a small extent to soundIn an inelastic collision there is a loss of kinetic energy (momentum is still conserved)In an elastic collision the kinetic energy is conserved (as well as momentum)

Power

Power is the rate of workingPower = work

timeP = W

tThe unit of power is the joule per second (Js-1) which is called the watt (W)

Power and Velocity

Since W = FsAnd power developed P = W

t Then P = Fs

tBut s = velocity

tTherefore P = Fv

Efficiency

Efficiency is defined as the ratio of the useful output to the total inputThis can be calculated using energy or power values as long as you are consistentEfficiency is normally expressed as a percentage