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

Step-by-step 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 \\ (1)/(2)kx^2=(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*1000\text{ m}}{3600\text{ s}} \\ v=25\text{ m/s} \end{gathered}`

plugging all the values in the above equation, we get

`\begin{gathered} (1)/(2)k*(500\text{ m})^2=(1)/(2)*10^4\text{ kg}*(25\text{ m/s})^2 \\ k=\frac{10^4\text{ }*625\text{ }}{25*10^4} \\ k=25\text{ N/m} \end{gathered}`

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