Facts that Matter
If displacement is in the direction opposite to the force
W = − F × s
(Case II) If displacement is perpendicular to the force, work done is zero.
Unit of energy = Joules
1 kJ = 1000 J
Kinetic energy of body moving with a certain velocity = work done on it to make it acquire that velocity.
∴ ... (ii) and
F = ma ... (iii)
Substitute (ii) and (iii) in (i), we get W = F × s
if u = 0, (object starts at rest)
∴ W = (1/2) mv2
Work done = Change in kinetic energy
∴ Ek = (1/2)mv2
The energy possessed by such an object is called the gravitational potential energy.
∴ GPE = work done in raising a body from the ground to a point against gravity.
Consider a body with mass m, raised through a height h, from the ground, Force required to raise the object = weight of object mg.
Object gains energy equal to the work done on it.
∴ Work done on the object against gravity is W.
∴ W = force × displacement = mg × h
W = mgh
∴ PE = mgh
Work done in both the cases (i) and (ii) is same as a body is raised from position A to B, even if the path taken is different but the height attained is the same.
Potential energy + Kinetic energy = Constant (Mechanical energy)
A body of mass ‘m’ is raised to height ‘h’ at A its potential energy is maximum and kinetic energy is 0 as it is stationary.
When body falls at B, h is decreasing hence potential energy decreases and ‘v’ is increasing hence kinetic energy is increasing.
When the body is about to reach the ground level, h = 0, v will be maximum hence kinetic energy > potential energy
∴ Decrease in potential energy = Increase in kinetic energy
This shows the continual transformation of gravitational potential energy into kinetic energy.
1 kilowatt = 1000 watts
1 kilowatt = 1000 J/s
The energy used in one hour at the rate of 1kW is called 1kWh.