Question

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

• A. $mg(h+d)-\frac{1}{2}{kd}^2$
• B. $mg(h-d)-\frac{1}{2}{kd}^2$
• C. $mg(h-d)+\frac{1}{2}{kd}^2$
• D. $mg(h+d)+\frac{1}{2}{kd}^2$

Answer 1

The correct option is A $mg(h+d)-\frac{1}{2}{kd}^2$

Work done BY gravitational force = mg(h+d)

Work done ON spring = $0.5k{d}^2$

Total work done on the ball = $W_g+W_{byspring}=mg(h+d)-0.5k{d}^2$