A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a dist

Question

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance h 2 . The spring constant is _____ N m - 1 (Use g = 10 m s - 2 )

TestHub · Accepted Answer

Loss in the gravitational potential energy of the ball= gain in the potential energy by the spring

$- ∆ P E_{gravitational} = ∆ P E_{spring}$

$m g (h + \frac{h}{2}) = \frac{1}{2} k {(\frac{h}{2})}^{2}$ $\Rightarrow$ $m g \frac{3 h}{2} = \frac{k h^{2}}{8}$

$\Rightarrow k = \frac{12 m g}{h} = \frac{12 \times 0.1 \times 10}{0.1} = 120 N m^{- 1}$

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