Question

An engine is attached to a wagon through a shock absorber of length $1.5m$ . The system with a total mass of $50,000kg$ is moving with a speed of $36km/h$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0m$. If $90\%$ of energy of the wagon is lost due to friction, calculate the spring constant.

Answer 1

Step:1 Calculate the kinetic energy of the system.

Given mass, $m=50,000kg$

Speed $v=36\times \frac{5}{18}m/s=10m/s$

Length of the shock absorber $x=1.5m$

$KE=\frac{1}{2}m{v}^2=\frac{1}{2}\times 5\times {10}^4\times {10}^{2}J$

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

Step: 2 Find spring constant.

$90\%$ of $KE$ of wagon lost due to friction and only $10\%$ of this is stored in the spring.

$\frac{1}{2}k{x}^2=2.5\times {10}^5=10\%of2.5\times {10}^{6}J$

Here, $x=1m$

$k=\frac{2\times 2.5\times {10}^5}{(1{)}^2}N/m$

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

Final Answer: $k=5.0\times {10}^{5}N/m$