Question

What is the maximum compression of the spring with spring constant $50N/m$ if a ball of mass $0.5kg$ moving with a speed of $1.5m/s$ on a horizontal smooth surface, collides with it.

• A. $0.12m$
• B. $1.5m$
• C. $0.5m$
• D. $0.15m$

Answer 1

Answer: (D)

By the law of energy conservation,
The maximum compression in the spring occurs when the kinetic energy of the mass is fully converted to the elastic potential energy of the spring.
loss in $K.E$ of the mass = $\frac{1}{2}mv^{2}$
gain in $P.E$ of the spring = $\frac{1}{2}kx^{2}$
$\Delta U_{s p r i n g}=-\Delta KE_{b l o c k}$
$\Rightarrow \frac{1}{2}mv^{2}=\frac{1}{2}kx^{2}$
$\Rightarrow mv^{2}=kx^{2}$
$\Rightarrow x^{2}=\frac{m v^{2}}{k}$
$\Rightarrow x=v\sqrt{\frac{m}{k}}$
$\Rightarrow x=1.5\sqrt{\frac{0 . 5}{50}}$
$=0.15m$