Question

A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is :

• A. $\frac{\pi F}{\sqrt{mk}}$
• B. $\frac{2F}{\sqrt{mk}}$
• C. $\frac{F}{\sqrt{mk}}$
• D. $\frac{F}{\pi \sqrt{mk}}$

Answer 1

Answer: (C)

$\frac{F}{\sqrt{mk}}$

Maximum speed is at mean position(equilibrium). $F=kx$
$x=\frac{F}{k}$
$W_F+W_{sp}=\Delta KE$
$F\left(x\right)-\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2-0$
$F\left(\frac{F}{k}\right)-\frac{1}{2}k{\left(\frac{F}{k}\right)}^2=\frac{1}{2}m{v}^2$
$\Rightarrow V_{max}=\frac{F}{\sqrt{mk}}$