Question

Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls ? Here r is the distance between centres of the balls.

Answer 1

Given that V( r ) is the potential energy function, r is the distance between the balls and R is the radius of the two billiard balls.

For the case of elastic collision of two billiard balls, the potential energy is inversely dependent on the distance between them. Thus, when the balls are moved apart, the potential energy increases and when it is moved close to each other, the potential energy decreases.

The value of potential energy will become 0 in case the distance between the balls is 2R i.e., when the balls touch each other.

In graph (i), the value of V( r ) is not 0 at r=2R, hence it cannot possibly describe the elastic collision.

In graph (ii), the value of V( r ) is not 0 at r=2R, hence it cannot possibly describe the elastic collision.

In graph (iii), the value of V( r ) does not decrease on increasing the value of r, hence it cannot possibly describe the elastic collision.

Graph (iv) shows negative potential energy after r=2R which is not possible, hence it cannot possibly describe the elastic collision.

Graph (v) satisfies both the given conditions for the case of elastic collision.

In graph (v), the value of V( r ) is not 0 at r=2R, hence it cannot possibly describe the elastic collision.

Hence, potential energy curves (i), (ii), (iii), (iv) and (vi) cannot possibly describe the elastic collision of two billiard balls.