All Problems

Laws of Conservation

Problem 1.182

A cart loaded with sand moves along a horizontal plane due to a constant force F coinciding in direction with the cart's velocity vector. In the process, sand spills through a hole in the bottom with a constant velocity \(\mu \mathrm{kg} / \mathrm{s}\). Find the acceleration and the velocity of the cart at the moment \(t,\) if at the initial moment \(t=0\) the cart with loaded sand had the mass \(m_{0}\) and its velocity was equal to zero. The friction is to be neglected.

Reveal Answer
v=Fμ‾ln⁡m0m0−μt,w=Fm0−μ‾t\mathbf{v}=\frac{\mathbf{F}}{\underline{\mu}} \ln \frac{m_{0}}{m_{0}-\mu t}, \quad \mathbf{w}=\frac{\mathbf{F}}{m_{0}-\underline{\mu} t}
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