Discussion on BITSAT

 A mass M slides across a frictionless horizontal table with constant speed V_0_. It collides with a spring of spring constant k, compressing it. The mass-spring system then rebounds. Take the position of the mass when it first hits the spring to be x=0.

a) Suppose that the mass comes to a momentary stop after compressing the spring a distance L. What is the spring constant k in terms of V_0_, M, and L?

b) The spring reexpands, pushing the mass back. What is the speed of the mass M when it passes through x=0?

2. Relevant equations
F_spring_ = k*d;
E_stored in spring_ = 1/2(k*d^2^)

3. The attempt at a solution

a) E_i_ = E_f_
1/2mv^2^ = 1/2kx^2;
mv^2^ = kL^2
(mV_0_^2)/L^2 = k;