A vertical spring of spring constant 24 Nm ⁻¹ is fixed on a table. A ball of mass 0.5 kg at a height 2 m above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance of 50 cm . The net work done in the process is:

Step-by-step solution

The ball falls from a height h = 2 m above the spring and compresses the spring by x = 0.5 m. The total vertical displacement of the ball is H = h + x = 2 + 0.5 = 2.5 m. The work done by gravity on the ball is W_ g = mgH = 0.5 9.8 2.5 = 12.25 J. Using g = 10 m/s ² for standard approximation in such problems, W_ g = 0.5 10 2.5 = 12.5 J. The work done by the spring force is W_ s = - 1 2 kx² = - 1 2 24 (0.5)² = -12 0.25 = -3 J. The net work done on the ball during the process is the sum of the work done by gravity and