Question

During a hailstorm, it is wiser to park a car inside. Otherwise, the car might get damaged. Both rain and hail are precipitation. However, when a rain droplet hits a car's roof, it sticks to the roof (makes the roof wet, inelastic collision). When a hail pebble hits a car's roof, it typically bounces off (elastic collision).

For simplicity, if considering a droplet and a pebble of the same mass, the impulse of the hail pebble is up to twice the impulse of the rain droplet. Is this true?

Answer 1

The statement is TRUE.

Impulse is defined as the change in momentum.

When rain drops hit a car it sticks to the surface of the car i.e., final velocity is zero. Hence, if mass of the droplet be m and it strike the surface of the car with a velocity v then impulse is

For a pebble with a same mass and the velocity that it bounces off with is the same velocity of striking we have

- sign indicates the direction of velocity is opposite to the direction of striking.

We see that

So, the impulse imparted by the hail pebble is twice the impulse of the rain droplet.