Question

A block whose mass is $1kg$ is fastened to a spring. The spring has a spring constant of $100N{m}^{-1}$. The block is pulled to a distance $x=10cm$ from its equilibrium position at $x=0$ on a frictionless surface from rest at $t=0$. The kinetic energy and potential energy of the block when it is $5cm$ away from the mean position is

• A. $0.0375J,0.125J$
• B. $0.125J,0.375J$
• C. $0.125J,0.125J$
• D. $0.0375J,0.375J$

Answer 1

Answer: (A)

Here, $m=1kg,k=100N{m}^{-1}$
$A=10cm=0.1m$
The block executes $SHM$, its angular frequency is given by
$\omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{100N{m}^{-1}}{1kg}}=10rad{s}^{-1}$
Velocity of the block at $x=5cm=0.05m$ is
$v=\omega \sqrt{A^2-x^2}$
$=10\sqrt{{\left(0.1\right)}^2-{\left(0.05\right)}^2}$
$=10\sqrt{7.5\times 10^{-3}}m{s}^{-1}$
Kinetic energy of the block,
$K=\frac{1}{2}m{v}^2$
$=\frac{1}{2}\times 1\times 0.75$
$=0.0375J$
Potential energy of the block,
$U=\frac{1}{2}k{x}^2$
$=\frac{1}{2}\times 100\times {\left(0.05\right)}^2=0.125J$