Jumping off tracks

Classical Mechanics Level 2

The figure shows a small block of mass m m which started with a speed v v on the horizontal part of the bigger block ( ( of mass M M placed on a horizontal floor ) ) towards its semicircular, curved part. All the surfaces are frictionless.

Find the speed of the bigger block when the smaller block reaches point A A (i.e. the point it reaches after traveling half of the length of the semicircular arc).

m v M + m \frac{mv}{M+m} M v M + m \frac{Mv}{M+m} 2 m v M + m \frac{2mv}{M+m} 2 M v M + m \frac{2Mv}{M+m}

Abha Vishwakarma by Abha Vishwakarma , 20, India

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1 solution

Parth Sankhe
Nov 1, 2018

The small block will be moving vertically upwards at A, thus it's horizontal speed (w.r.t wedge) = 0. However, it's speed w.r.t to the ground frame will be same as that of the wedge, as they are in contact. Let that speed be x x .

Conserving linear momentum (along the horizontal),

m v = ( M + m ) x mv=(M+m)x

x = m v M + m x=\frac {mv}{M+m}

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