Answer to Question #105979 in Classical Mechanics for BestH

Question

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.

Answer 1

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

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

Applying Newton's second law, fond the deceleration:

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

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

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