Question

A 5.2 × 105 kg subway train is brought to a stop from a speed of 0.55 m/s in 0.51 m by a large spring bumper at the end of its track. What is the force constant k of the spring in N/m?

Answer 1

Given:

The mass of the subway train is,

`m=5.2*10^5\text{ kg}`

The initial speed of the train is,

`v=0.55\text{ m/s}`

The distance moved by train is,

`x=0.51\text{ m}`

To find:

the spring constant

Step-by-step explanation:

The kinetic energy of the train converts into the potential energy of the spring. So we can write,

`\begin{gathered} (1)/(2)kx^2=(1)/(2)mv^2 \\ k=(mv^2)/(x^2) \end{gathered}`

Substituting the values we get,

`\begin{gathered} k=(5.2*10^5*0.55^2)/(0.51^2) \\ =0.60*10^6\text{ N/m} \end{gathered}`

Hence, the spring constant is

`0.60*10^6\text{ N/m}`