Question

(a) Allow two nails of unequal mass to fall through the same height on to a heap of sand [Fig. (a)]. Which nail penetrates more into the sand and why?

(b) Allow a nail to fall through different heights alternately on a sandbag. When does the nail penetrate more into the sand? Why? [Fig. (b)]

The nail falling from a greater height penetrates more into the sand. More work is done to penetrate more. This work changes to energy known as potential energy (P.E.). It means a high-lying object possesses more P.E. than a low-lying object of the same mass. Similarly, a nail with high mass possesses more P.E. Thus, a massive high-lying body possesses more P.E. than a light, low-lying body.

Answer 1

(a) The heavier nail penetrates more into the sand. Both nails fall from the same height, but the heavier nail has greater potential energy because

P.E. = mgh

Hence, it can do more work on the sand and penetrates deeper.

(b) The nail dropped from the greater height penetrates more into the sand. For the same mass, potential energy increases with height. Therefore, the nail falling from a greater height has more potential energy and does more work on the sand.

Thus, potential energy depends on both the mass of the body and its height above the ground.

Answer 2

(a) The heavier nail penetrates more into the sand. Both nails fall from the same height, but the heavier nail has greater potential energy because

P.E. = mgh

Hence, it can do more work on the sand and penetrates deeper.

(b) The nail dropped from the greater height penetrates more into the sand. For the same mass, potential energy increases with height. Therefore, the nail falling from a greater height has more potential energy and does more work on the sand.

Thus, potential energy depends on both the mass of the body and its height above the ground.