Mechanics (momentum)

Classical Mechanics Level 5

A flatcar of mass M M starts moving to the right due to a constant force F F . Sand spills on the car from a stationary hopper. The velocity of loading is constant and equal to n n . Find the velocity at time t t .

Details and Assumptions:

  • n = 5 k g s − 1 n=5kgs^{-1}
  • t = 2 s t=2s
  • F = 10 N F=10N
  • M = 2 k g M=2kg
5.33 m s − 1 5.33ms^{-1} 1.98 m s − 1 1.98ms^{-1} 2.667 m s − 1 2.667ms^{-1} 1.667 m s − 1 1.667ms^{-1}

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Ayush Shridhar by Ayush Shridhar , 22, India

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2 solutions

Mark Hennings
Apr 27, 2017

The momentum of the system at time t t is p = ( M + n t ) v p=(M+nt)v , and the only external force acting is F F , so that p ˙ = F \dot{p} = F . Since the system starts at rest, we have p = F t p = Ft , and hence v = F t M + n t v \; = \; \frac{Ft}{M + nt} making the correct answer 5 3 \boxed{\tfrac53} .

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