Physics

Example : 21
A truck of mass 2500 kg is stopped by a force of 1000 N. It stops at a distance of 320 m. What is the amount of work done ? Is the work done by the force or against the force?
Solution. Here the force, F = 1000 N
Displacement, s = 320 m
∴ Work done, W = F . s
= (1000N) . (320 m)
= 320000 J
In this case, the force acts opposite to the direction of displacement. So the work is done against the force.

Example : 22
Two bodies of equal masses move with uniform velocity v and 3v respectively. Find the ratio of their kinetic energies.
Solution. In this problem, the masses of the bodies are equal, so let the mass of each body be m. We will now write down the expression for the kinetic energies of both the bodies separately.
(i) Mass of first body = m
Velocity of first body = v
So,K.E. of first body = mv² ...(1)
(ii) Mass of second body = m
Velocity of second body = 3v
So, K.E. of second body = m(3v)²
= m × 9v²
= × 9mv² ...(2)
Now, to find out the ratio of kinetic energies of the two bodies, we should divide equation (1) by equation (2), so that :
=
or …. (3)
Thus, the ratio of the kinetic energies is 1 : 9. We can also write down the equation (3) as follows:
K.E. of second body = 9 × K.E. of first body
That is, the kinetic energy of second body is 9 times the kinetic energy of the first body. It is clear from this example that when the velocity (or speed) of a body is "tripled" (from v to 3v), then its kinetic energy becomes "nine times".