A flat car of mass mo starts moving to the right due to a constant horizontal force F . Sand spills on the flat car from a stationary hooper . the rate of loading is constant and equals u kg/s . find the time dependence of the velocity and the acceleration of flat car in the process of loading . neglect friction.
can anybody tell me the general method to solve the questions of the variable mass ?
There is no hard and fast rule to do such problems but the way I do them and find them easy is:
Consider a instant t time later.
Mass of the car will be : m + ut
Force is constant thus : acc = F/(m+ut)
Force can be written as a = dv/dt thus solving this differential equation we can get by integrating it from time 0 to t and velocity v' to v where v' is initial velocity.
Solve it to get : v = v' + F/r log (m+ut) where v' = F/m
Accelaration can be given by equation (1) : a = F/(m+ut).
I hope this solution is correct and is you find anything wrong please let me know about it.