Final answer:
To find the force constant k of the spring, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Step-by-step explanation:
To find the force constant k of the spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is given as:
F = -kx
Where F is the force exerted by the spring, k is the force constant, and x is the displacement from the equilibrium position. Rearranging the formula, we get:
k = -F/x
In this case, the force exerted by the spring is equal to the force required to stop the subway train. We can calculate the force using Newton's second law:
F = ma
where m is the mass of the subway train and a is the acceleration, which can be calculated using the formula:
a = (v² - u²) / (2s)
Where v is the final velocity (which is 0 m/s in this case), u is the initial velocity (0.500 m/s), and s is the displacement (0.900 m).
Substituting these values into the formula, we can solve for a. Then, we can substitute the values of F and x into Hooke's Law formula to calculate the force constant k.