Olympiad problems

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Found problems: 2

2017 F = ma, 7

Tags: kinetic energy

7) A train, originally of mass $M$, is traveling on a frictionless straight horizontal track with constant speed $v$. Snow starts to fall vertically and sticks to the train at a rate of $\rho$, where $\rho$ has units of kilograms per second. The train's engine keeps the train moving at constant speed $v$ as snow accumulates on the train. What is the rate at which the kinetic energy of the train and snow increases? A) $0$ B) $Mgv$ C) $\frac{1}{2}Mv^2$ D) $\frac{1}{2}pv^2$ E) $\rho v^2$

2017 F = ma, 22

Tags: kinetic energy

22) A particle of mass m moving at speed $v_0$ collides with a particle of mass $M$ which is originally at rest. The fractional momentum transfer $f$ is the absolute value of the final momentum of $M$ divided by the initial momentum of $m$. The fractional energy transfer is the absolute value of the final kinetic energy of $M$ divided by the initial kinetic energy of $m$. If the collision is perfectly elastic, under what condition will the fractional energy transfer between the two objects be a maximum? A) $\frac{m}{M} \ll 1$ B) $0.5 < \frac{m}{M} < 1$ C) $m = M$ D) $1 < \frac{m}{M} < 2$ E) $\frac{m}{M} \gg 1$