A disc of mass 200 g is kept floating horizontally by throwing 40 pebb

1.	A disc of mass 200 g is kept floating horizontally by throwing 40 pebbles per second against it from below. If the mass of each pebble is 2g, calculate the velocity with which the pebbles are striking the disc. Assume the pebbles strike the disc normally and rebound with the same speed.
Answer» Mass of the disc M = 200 g = 0.2 kg Total downward force F = Mg = 0.2 × 9.8 =1.96 N Mass of one pebble m = 2 g = 2 × 10^-3 kg Let v be the velocity with which the pebbles strike the disc. Momentum given by one pebble = mv The pebbles rebound downward and strike from below. ∴ net momentum given to the disc in the upward direction = change in velocity of the pebble × m = (2v) m Total momentum given in one second =40 × m × 2v = 80 mv The disc remains horizontal if this is equal to the weight of the disc, Mg ∴ 80 mv = Mg 80 × 2 × 10^-3× v = 1.96 v = 12.25 ms^-1.

A disc of mass 200 g is kept floating horizontally by throwing 40 pebbles per second against it from below. If the mass of each pebble is 2g, calculate the velocity with which the pebbles are striking the disc. Assume the pebbles strike the disc normally and rebound with the same speed.

Answer»

Mass of the disc M = 200 g

= 0.2 kg

Total downward force

F = Mg

= 0.2 × 9.8 =1.96 N

Mass of one pebble m = 2 g = 2 × 10^-3 kg

Let v be the velocity with which the pebbles strike the disc. Momentum given by one pebble = mv The pebbles rebound downward and strike from below.

∴ net momentum given to the disc in the upward direction

= change in velocity of the pebble × m = (2v) m

Total momentum given in one second

=40 × m × 2v

= 80 mv

The disc remains horizontal if this is equal to the weight of the disc, Mg

∴ 80 mv = Mg

80 × 2 × 10^-3× v = 1.96

v = 12.25 ms^-1.