Beach on the highway

Classical Mechanics Level 4

A cart loaded with sand moves along a flat, straight track due to a constant force $F$ parallel to the cart's velocity vector. The sand spills through a hole in the bottom at a constant rate $z$ kg/s .

Find the time when the velocity of the cart will be $\frac{F}{z}$ given that velocity of cart at $t=0$ is zero, and the initial mass of the cart $t=0$ is $M$ .

\frac{M((e)^{2}-1)}{ze}

\frac{M(e-1)}{ze}

\frac{M(e-1)}{z}

\frac{Mz(e-1)}{e}

\frac{M(e-2)}{ze}

1 solution

Rohan Gupta
Oct 28, 2015

a=F/(M-zt)=dv/dt integrating this equation with v=0 to F/z and t=0 to t we get the answer

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Beach on the highway

1 solution

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