Question

A 5.00×105-kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the spring constant k of the spring?

a) 3.13×106 N/m
b) 6.25×105 N/m
c) 1.25×105 N/m
d) 1.56×106 N/m

Answer 1

To find the spring constant k of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. We can calculate the force needed to stop the subway train using the equation F = ma. Then, we can calculate the spring constant k using Hooke's Law.

Step-by-step explanation:

To find the spring constant k of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position.

1. First, let's calculate the force needed to stop the subway train using the equation F = ma, where F is force, m is mass, and a is acceleration.
2. Next, we can calculate the spring constant k using Hooke's Law, which states that F = -kx, where F is force, k is the spring constant, and x is the displacement from the equilibrium position.

Using the calculations, the spring constant k of the spring is 1.56 × 10^6 N/m (option d).