Initially spring is compressed x, and the masses are at rest. Find v1 and v2 whe
ID: 1817925 • Letter: I
Question
Initially spring is compressed x, and the masses are at rest. Find v1 and v2 when the spring is not compressed anymore.
Explanation / Answer
consider the system as both the blocks and the spring so that the spring force is internal force in the system now there are no horizontal forces external to the system (assuming there is no friction) so we can conserve momentum in the horizontal direction or let us say it as x-direction p,initial = 0 since both thee blocks are at rest assuming velocity of m2 is v2 towards right and velocity of m1 is v1 towards left and taking positive direction towards right then p,final = (m2)*(v2)-(m1)*(v1) p,initial = p,final so m2*v2 = m1*v1 ----------------> Eq(1) now there are now dissipative forces acting on the system so we can apply conservation of energy E,initial = potential enrgy stored in the spring = (1/2)*(k)*(x^2) E,final = kinetic energy of blocks = (1/2)*(m1)*(v1^2)+(1/2)*(m2)*(v2*2) E,initial = E,final (1/2)*(k)*(x^2)=(1/2)*(m1)*)(v1*2)+(1/2)*(m2)*(v2^2) ------------>Eq(2) soving Eq(1) and Eq(2) we get answer v1= {sqrt (m2*k/((m1^2)+m1*m2))}*x v2 = {sqrt(m1*k/((m2^2)+m1*m2))}*x Check the equations solving part Hope this is helpful