Question

A runaway train with a mass of 6,251 kg is approaching the end of the line at a speed of 27 m/s. The end of the line has a massive spring with a spring constant of 48,979 Nm. How far will the spring be compressed (in meters) when the train comes to rest

Answer 1

Answer:

The compression in the spring is 9.64 meters.

Explanation:

Given that,

Mass of the train, m = 6251 kg

Speed of the train, v = 27 m/s

Spring constant of the spring, k = 48979 N/m

We need to find the compression in the spring when it comes to rest. It is a case of conservation of energy. The kinetic energy of the train is converted to elastic potential energy. So,

$\dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2$

x is compression in spring

$mv^2=kx^2\\\\x=\sqrt{\dfrac{mv^2}{k}} \\\\x=\sqrt{\dfrac{6251\times (27)^2}{48979 }}\\\\x=9.64\ m$

So, the compression in the spring is 9.64 meters.