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 force constant k of the spring?

A. 1.25 × 10⁵ , {N/m}
B. 2.50 × 10⁵ , {N/m}
C. 5.00 × 10⁵ , {N/m}
D. 1.00 × 10⁶ , {N/m}

Answer 1

The force constant of the spring is 1.25 x 10^5 N/m.

Step-by-step explanation:

To find the force constant of the spring, we can use the equation:

k = (1/2)mv^2 / x^2

where k is the force constant, m is the mass of the subway train, v is the initial velocity, and x is the distance over which the train is brought to a stop.

Plugging in the values given in the question, we get:

k = (1/2)(5.00 x 10^5 kg)(0.500 m/s)^2 / (0.400 m)^2 = 1.25 x 10^5 N/m.

Therefore, the force constant of the spring is 1.25 x 10^5 N/m.