Question

Spiderman uses his spider webs to save a runaway trainmoving about. His web stretches a fewcity blocks (500 m) before the train (10^4kg) comes to a stop.Assuming the web acts like a spring, estimate the effectivespring constant.

Answer 1

Given:

the mass of the train is

$m=10^4\text{ kg}$

The webs of the spider stretched by

$x=500\text{ m}$

Required: effective spring constant of the web

Explanation:

to solve this problem we use energy conservation.

when the train is moving with velocity v it has kinetic energy and when the spider tries to stop the train then it will gain potential energy in its webs.

then we have

$\begin{gathered} P.E=K.E \\ \frac{1}{2}kx^2=\frac{1}{2}mv^2 \end{gathered}$

we assume that train is moving with some velocity say 90 km/h.

change it in m/s.

we get

$\begin{gathered} v=\frac{90\times1000\text{ m}}{3600\text{ s}} \\ v=25\text{ m/s} \end{gathered}$

plugging all the values in the above equation, we get

$\begin{gathered} \frac{1}{2}k\times(500\text{ m})^2=\frac{1}{2}\times10^4\text{ kg}\times(25\text{ m/s})^2 \\ k=\frac{10^4\text{ }\times625\text{ }}{25\times10^4} \\ k=25\text{ N/m} \end{gathered}$

Thus, the effective spring constant is 25 N/m.