5-Work Energy Power notes

Work, Energy, Power

Work – is the product of the force and the distance moved in the direction of the force.

Energy – is the capacity to do work.

Conservation of Energy - the total energy for an isolated system remains constant.
Potential energy - the energy possessed by a system by virtue of the relative positions of its component parts.
Derive from W = Fs , Ep = mgh



Consider an object m being lifted vertically without acceleration with force F=its weight=mg:
Gain in GPE = work done by force F against gravity = F h cos 0° = mgh
If PE at ground is taken to be zero, PE at height h above ground = mgh

Kinetic energy – the energy a body has because of its motion.

Strain energy – the energy a body has because of extension/compression of spring from it’s natural length

Strain Energy = 1/2 Fe = 1/2 ke2



(area under F-e graph)
Derive from equation of motion Ek = 1/2mv 2
Suppose an object m is acted on by a constant net force F from rest to final velocity v through a distance s in the direction of the force.



By Newton’s 2nd Law, F=ma, since F is constant, object has constant acceleration. Now v2 – u2 = 2as ; a = v2 / 2s
K.E of object = work done by force on object = F s cos 00 = F s = (ma) s = m (v2 / 2s) s = 1/2 m v2
Principal of Conservation of Energy – Total energy in a given system is always constant It can be transformed from one form to another but cannot be destroyed or created.

Work-energy theorem (COE)



Fs = 1/2m(v2-u2)
i.e. Work done on object = increase in KE
Note: work-energy theorem applies for cases where work done causes changes i k l
Power - the work done per unit time. (Or more generally, the rate of transfer of energy.)
Average power =

= Total work done / total time taken = ΔW/Δt = ΔEnergy/Δt
Derive power as the product of force and velocity
Instantaneous power = P instantaneous = dW/dt = F(ds/dt) = Fv
Efficiency – the ratio of the useful work output to the energy put in.
η = (output / input) x 100%