Final answer:
The force constant of the quarter car representation can be found using Hooke's Law, which states that the restoring force of a spring is proportional to the displacement of the system from its equilibrium position. By rearranging the equation and plugging in the given values, we can determine the force constant to be 6.53 x 10^4 N/m.
Step-by-step explanation:
The force constant, or stiffness, of a quarter car representation can be found using Hooke's Law, which states that the restoring force of a spring is proportional to the displacement of the system from its equilibrium position. Hooke's Law can be written as F = -kx, where F is the restoring force, k is the force constant, and x is the displacement. To solve for k, we can rearrange the equation as k = -F/x.
In the given information, the car settles 1.20 cm, which is equal to -1.20 x 10^-2 m, and the restoring force is equal to the weight of the person, which is 784 N. Plugging these values into the equation, we find that k = -(784 N) / (-1.20 x 10^-2 m) = 6.53 x 10^4 N/m.