Physics - W.E.P. Question with Solution | TestHub

Mass of the system$\left(m\right)=50000\text{kg}$

Speed of the system$\left(v\right)=36\text{km/h}$

$=36\times \frac{5}{18}\text{m/s}\left(\because 1\text{km/h}=\frac{5}{18}\text{m/s}\right)$

$=10\text{m/s}$

Compression of the spring$\left(x\right)=1.0\text{m}$

$\text{KE of the system}=\frac{1}{2}{\text{mv}}^2$

$=\frac{1}{2}{\times 50000\times \left(10\right)}^2$

$=25000\times 100\text{J}$

$=2.5\times {10}^6\text{J}$

Since, 90% KE of the system is lost due to friction, therefore kinetic energy transferred to shock absorber,

$=10\%,K{E}_{total}=\frac{10}{100}\times 2.5\times {10}^6\text{J}=2.5\times {10}^5\text{J}$

This K.E. is converted in to spring energy

$2.5\times {10}^5=\frac{1}{2}k{x}^2$

$2.5\times {10}^5=\frac{1}{2}\times k\times 1^2$

$k=5.0\times {10}^5\text{N/m}$