A trolley with sand is moving on a smooth horizontal surface. a weight released from a certain height without

A trolley with sand is moving on a smooth horizontal surface. a weight released from a certain height without initial velocity falls into the sand. Will the speed of the trolley change after the weight hits it?

Let M be the mass of the cart and V be its speed before the weight falls. And let m be the mass of the weight. The horizontal component of the weight’s velocity is 0, since the weight was falling vertically.

The amount of movement of the cart and weights before falling

MV + m * 0 = MV.

Let v be the speed of the cart after the fall. The mass of the cart with a weight M + m. The number of movements of the trolley with a weight

(M + m) v.

According to the law of conservation of momentum

(M + m) v = MV, whence

v = V * (M / (M + m)) <V.

Answer: The speed of the cart will decrease.