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. The blocks are pushed from equilibrium by a further distance of (2/k)(m₁ + m₂) g against the spring and released. What is the common speed of the blocks at the moment they separate?

Step-by-step solution

Let the compression of the spring be x . The equilibrium position of the system of two blocks is given by balancing the forces along the incline: k x_ eq = (m₁ + m₂) g x_ eq = (m₁ + m₂) g k The blocks are pushed a further distance A from equilibrium, which becomes the amplitude of their simple harmonic motion: A = 2(m₁ + m₂) g k The blocks move together up the incline. Let N be the normal force between the blocks. The equation of motion for block m₂ is: N - m₂ g = m₂ a The blocks separate when the normal force beco