Question

(a) Take a dart, some sand or plasticine in a bag or a dartboard. Aim the dart at the sand bag with

1. little force (less velocity), and
2. full force (high velocity).

Record your observations. In which case does the dart penetrate more in the sandbag and why? Refer to Fig.

(b) Repeat the above activity by throwing two darts of unequal masses using full force. When do you do more work? Which dart possesses more kinetic energy and why?

It is seen that a fast-moving dart penetrates more in the sandbag. It does more work. So a fast-moving dart possesses more K.E. Also the heavier dart penetrates more in the sandbag. It does more work and, therefore, possesses more kinetic energy.

Answer 1

(a) The dart thrown with full force moves with greater speed and penetrates farther into the sandbag. Hence, it has greater kinetic energy and does more work against the sand.

(b) The heavier dart penetrates farther into the sandbag and does more work. If both darts move with the same speed, the heavier dart has greater kinetic energy because

 \[\mathrm{K.E.}=\frac{1}{2}mv^{2}\]

Thus, at the same speed, kinetic energy increases with mass.