A construction vehicle of mass 30 Mg is used to unload sand

A construction vehicle of mass 30 Mg is used to unload sand in a horizontal line through a port on the bottom of the vehicle. It initially carries 7600 kg of sand and dumps it at a rate of 900 kg/s relative to the vehicle port. If the velocity of the vehicle increases by 0.12 every second, determine the resulting force created by the vehicle and exiting sand if the sand exits at a velocity of 0.26 m/s relative to the vehicle. Assume that the vehicle is free to roll and friction is negligible.

Solution

the resulting force is calculated as follows:

F = d(mv)/dt

                     = (dm/dt)v + m(dv/dt)

                     = (900)(0.26) + (30000 + 7600)(0.12)

                     = 4746 N