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
antiparallel to F
If a
variable force F produces a displacement in the direction of F, the work done is determined from the
area under Fx 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:
v^{2} = u^{2} +2as,
as = 12 (v^{2}  u^{2})
Since kinetic energy is equal to the work done on the mass to bring it from rest to a speed v,
The kinetic energy, E_{K}  = Work done by the force F = Fs = mas = ½ m (v^{2}  u^{2})  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 shortrange interatomic 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 h_{2}. 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. [/t] Useful Output Energy  x100% =  Useful Output Power  x100%  Input Energy  Input Power  Power {instantaneous} is defined as the work done per unit time. [/t] Total Work Done  =  W  Total Time  t  Since work done W = F x s, [/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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