As shown in the figure, two blocks A and B , each having a mass of 320 g , are connected by a light string passing over a smooth light pulley. The horizontal surface on which block A can slide is smooth. Block A is attached to a spring of spring constant 40 N/m whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the system is released to move from rest with the spring vertical and uns

Step-by-step solution

Let x be the horizontal displacement of block A when it breaks off the surface. The length of the spring at this instant is L = h^2 + x^2 , where h = 0.4 m is the initial height of the spring. The extension in the spring is L = L - h . The spring force is F_s = k(L - h) . The vertical component of the spring force is F_y = F_s = k(L - h) h L = kh (1 - h L ) . Block A breaks off the surface when the normal reaction N becomes zero. At this instant, the vertical component of the spring force balances the weight of blo