Question

A block mass $8kg$ is released from the top of an inclined smooth surface as shown in figure, If spring constant of spring is $200N/m$ and block comes to rest after compressing spring by $1m$ then find the distance travelled by block before it comes to rest:

Answer 1

Given:
Mass $=8kg$
K $=2000N/m$
$h=(s+1)\sin {30}^o$
$h=(s+1)\times \frac{1}{2}$
Lost in PE of block $=$ Gain in PE of spring
$\Rightarrow mgh=\frac{1}{2}k{x}^2$
$\Rightarrow 8\times 10\times \left(\frac{s+1}{2}\right)=\frac{1}{2}\times 2000\times 1$
$\Rightarrow s=24m$
Total distance travelled before coming to rest $=s+1=25m$