A block of mass m₁ is fastened to a spring on an incline of angle , and a block of mass m₂ is placed against it. From the equilibrium position, the blocks are pushed a further distance of (2/k)(m₁ + m₂) g against the spring and then released. Identify the position where the two blocks separate.

Step-by-step solution

Let x be the compression of the spring at any instant. The equation of motion for the combined system of mass (m₁ + m₂) is: kx - (m₁ + m₂)g = (m₁ + m₂)a where a is the acceleration of the blocks up the incline. The acceleration is: a = kx m₁ + m₂ - g For block m₂ , the forces acting along the incline are the normal force N exerted by m₁ and the component of gravity m₂ g . The equation of motion for m₂ is: N - m₂ g = m₂ a Substituting the value of a : N = m₂ (a + g ) = m₂ ( kx m₁ + m₂ - g + g ) = m₂ kx m₁ + m₂ The b