The effective spring constant = 13.7 N/m
Explanations:Mass of the train, m = 10⁴ kg
The speed of the train, v = 80 km/h = 80 x 1000/3600
v = 22.22 m/s
The Kinetic Energy of the train (KE) is given as:
[tex]KE\text{ = }\frac{1}{2}mv^2[/tex]The distance moved by the spiderman's web, x = 600 m
Since the web acts like a spring, the Spring Energy (SE) is given by the formula:
[tex]SE\text{ = }\frac{1}{2}kx^2[/tex]where k represents the spring constant
According to the law of energy conservation:
The Kinetic Energy = The Spring Energy
[tex]\begin{gathered} \frac{1}{2}mv^2=\frac{1}{2}kx^2 \\ \frac{1}{2}\times10^4\times22.22^2=\text{ }\frac{1}{2}\times k\times600^2 \\ 2468642=180000k \\ k\text{ = }\frac{2468642}{180000} \\ k\text{ = }13.7\text{ N/m} \end{gathered}[/tex]The effective spring constant = 13.7 N/m
