Question

A slab $S$ of mass $m$ is released from a height $h_0$ to the top of a spring of force constant $k$. The maximum compression $x$ of the spring is given by the equation

• A. $mg{h}_0=\frac{1}{2}k{x}^2$
• B. $mg\left(h_0-x\right)=\frac{1}{2}k{x}^2$
• C. $mg{h}_0=\frac{1}{2}k{\left(h_0+x\right)}^2$
• D. $mg\left(h_0+x\right)=\frac{1}{2}k{x}^2$

Answer 1

Answer: (D)

$\Delta U+\Delta K=0$
$\Rightarrow \Delta U_g+\Delta U_s+0=0$
$\Rightarrow -[\left(mg\left(h_0+x\right)\right]+\left(\frac{1}{2}k{x}^2-0\right)=$
$\Rightarrow mg\left(h_0+x\right)=\frac{1}{2}k{x}^2$