Answer to Question #105979 in Classical Mechanics for BestH

Question #105979
A spring is kept caught by a thread.In one moment we burn the thread and the object flies with the speed of V1=10m/s.If μ=0.01 find the distance of the road made by the carriage until it stops.Mass of the carriage=1kg,mass of the object=0.1kg.
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Expert's answer
2020-03-20T09:39:42-0400

Assume that the collision is absolutely inelastic. Applying momentum conservation, we have


mv=(m+M)u,u=mm+Mv1.mv=(m+M)u,\\ u=\frac{m}{m+M}v_1.

Applying Newton's second law, fond the deceleration:


ma=μ(M+m)g,a=μg(M+m)m.ma=\mu(M+m)g,\\a=\frac{\mu g(M+m)}{m}.


The distance covered upon such deceleration from initial velocity to rest will be


d=u22a=v12m32μg(m+M)3=0.38 m.d=\frac{u^2}{2a}=\frac{v_1^2m^3}{2\mu g(m+M)^3}=0.38\text{ m}.

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