A trolley of initial mass rolls on a smooth horizontal track while rain falls…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum
Problem
A trolley of initial mass m0 rolls on a smooth horizontal track while rain falls vertically into it. Due to the collected water, its mass at any instant is m(t)=m0+βt, where β is a constant rate of mass accumulation. A constant horizontal force F0 acts on the trolley in the forward direction.
(i) Write an expression for the instantaneous linear momentum of the trolley at time t.
(ii) By integrating the appropriate relation between force and momentum, obtain an expression for the impulse delivered to the trolley in the time interval from t1 to t2.
(iii) Show explicitly how the variable mass term appears in your final result and comment on whether the impulse–momentum theorem remains formally unchanged despite the mass variation.