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

Answer 1

Answer: (C)

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} kx^{2} = \frac{1}{2} mv^{2} -0$
$ F\left(\frac{F}{k}\right)- \frac{1}{2} k \left(\frac{F}{k}\right)^{2} = \frac{1}{2} mv^{2} $
$ \Rightarrow v_{max } = \frac{F}{\sqrt{mk}}$