We know from the principle of work and energy that the total change in mechanical energy of a body is equal to the work done on the body. It follows directly that:
If the total work done by the external forces acting on a body is zero there is no change in the total mechanical energy of the body, i.e. energy is conserved.
This is the principle of conservation of mechanical energy.
Remember that the weight of a body is not an external force in this context as work done by the weight is already included as potential energy.
At present we are concerned with only two types of mechanical energy, so working out the loss in KE, say, and equating it to the gain in PE can solve problem. (However, for those readers intending to carry on studying mechanics and who will meet problems which also include the third type of mechanical energy we recommend the method of equating the total mechanical energy in two positions.)
Question
A particle is projected vertically with speed 8 in s. Find its speed after it has moved a vertical distance of 2 m (a) upwards (h) downwards. Take g as 9.8 and give answers corrected (2 significant figures)
