Question

Define kinetic energy. Write the equation for kinetic energy. Two bodies of equal masses move with uniform velocities v and 3v respectively. Find the ratio of their kinetic energies. [5 MARKS]

Answer 1

Definition: 1 Mark
Equation: 1 Mark
Problem: 3 Mark

1. Energy which a body possesses by virtue of being in motion
2. Kinetic energy $=\frac{1}{2}m{v}^2$
3. In this problem, the masses of the two bodies are equal, so let the mass of each body be m. We will now write down the expressions 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 $=\frac{1}{2}m{v}^2$

(ii) Mass of second body = m
Velocity of second body = 3v

So, K.E of second body $=\frac{1}{2}m(3v{)}^2$

$\frac{1}{2}m\times 9v^2$

$\frac{9}{2}m{v}^2$

Now, to find out the ratio of kinetic energies of the two bodies, we should divide equation (1) by equation (2), so that:

$\frac{K.Eoffirstbody}{K.Eofsecondbody}=\frac{\frac{1}{2}m{v}^2}{\frac{9}{2}m{v}^2}$

or $\frac{K.Eoffirstbody}{K.Eofsecondbody}=\frac{1}{9}$

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 $=9\times K.Eoffirstbody$

That is, the kinetic energy of second body is 9 times the kinetic energy fo 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".