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,
[tex]\dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2[/tex]
x is compression in spring
[tex]mv^2=kx^2\\\\x=\sqrt{\dfrac{mv^2}{k}} \\\\x=\sqrt{\dfrac{6251\times (27)^2}{48979 }}\\\\x=9.64\ m[/tex]
So, the compression in the spring is 9.64 meters.
