laws of physics

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
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
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.
Useful Output
Energy x100%
Useful Output
Power x100%
Input Energy Input Power
Power {instantaneous} is defined as the work done
per unit time.
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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