Answer to Question #193994 in Mechanics | Relativity for firdevs Kizilbent

Question

Spiderman uses his spider webs to save a runaway train (see the figure). His web stretches a few city blocks before the 1.0×104 kgkg train comes to a stop.Part A Assuming the web acts like a spring, estimate the spring constant. Assume the train is moving 30 m/sm/s , and that the distance of "a few city blocks" is perhaps about 600 meters.

Answer 1

Explanations & Calculations

• I assume this would be the figure you are referring to

• And if we draw a schematic of the situation it would be something like follows

• Then using energy transformation between the masses & the web (kinetic energy to elastic energy), this sum could be solved.
• For that, we need to assume that the web-springs are almost parallel with the train's path of movement, not slanted as in the real situation.
• This is done to approximate that 500m is equal to the elongation of each web spring.
• Then,

$\qquad\qquad \begin{aligned} \small E_k&=\small E_e\\ \small \frac{mv^2}{2}&=\small \frac{kx^2}{2}\\ \small k&=\small \frac{mv^2}{x^2}\\ &=\small \frac{10^4kg\times(30ms^{-1})^2}{(600m)^2}\\ &=\small \bold{25\,Nm^{-1}} \end{aligned}$

• All the kinetic energy the train had is absorbed by the 2 web springs. Therefore, each bears only half of the initial energy.
• But we are asked to assume the entire web as a spring.