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Laws of Conservation

Problem 1.183

A flatcar of mass m0m_{0} starts moving to the right due to a constant horizontal force F (Fig. 1.46). Sand spills on the flatcar from a stationary hopper. The velocity of loading is constant and equal to μ\mu kg/s\mathrm{kg} / \mathrm{s}. Find the time dependence of the velocity and the acceleration of the flatcar in the process of loading. The friction is negligibly small.

Reveal Answer
v=Ft/m0(1+μt/m0),w=F/m0(1+μt/m0)2\mathbf{v}=\mathbf{F} t / m_{0}\left(1+\mu t / m_{0}\right), \mathbf{w}=\mathbf{F} / m_{0}\left(1+\mu t / m_{0}\right)^{2}
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