Two blocks of masses m 1 and m 2 are connected by a spring of spring constant k (figure 9-E15). The block of mass m 2 is given a sharp impulse so that it acquires a velocity u 0 towards right. Find (a) the velocity of the center of mass, (b) the maximum elongation that the spring will suffer.

Question

Philoid · Accepted Answer

Given that there are two blocks of mass m₁ and m₂ respectively,

Block of mass m₂ is moving with velocity v₀ while m₁ is at rest initially.

K is the spring constant.

{a} Velocity of center of mass will be:

{b} The spring will attain maximum elongation when both the blocks will attain the velocity of centre of mass,

Let x be the maximum elongation of spring

Then, by energy conservation law

Change in kinetic energy = potential energy stored in spring

Two blocks of masses m1 and m2 are connected by a spring of spring constant k (figure 9-E15). The block of mass m2 is given a sharp impulse so that it acquires a velocity u0 towards right. Find (a) the velocity of the center of mass, (b) the maximum elongation that the spring will suffer.

Two blocks of masses m₁ and m₂ are connected by a spring of spring constant k (figure 9-E15). The block of mass m₂ is given a sharp impulse so that it acquires a velocity u₀ towards right. Find (a) the velocity of the center of mass, (b) the maximum elongation that the spring will suffer.