As illustrated in the figure, 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. Determine the compression of the spring when the system is in its equilibrium position.

Step-by-step solution

Consider the blocks m₁ and m₂ as a single system of mass (m₁ + m₂) . In the equilibrium position, the net force acting on the system along the inclined plane is zero. The downward force along the incline due to gravity is (m₁ + m₂)g . The upward force along the incline due to the compressed spring is kx , where x is the compression of the spring. Equating these forces: kx = (m₁ + m₂)g x = (m₁ + m₂)g k