Final answer:
The force constant of the rear suspension of a car when a 130-kg box is loaded is calculated using Hooke's Law (F=kx), resulting in a force constant of 6705 N/m.
Step-by-step explanation:
The question asks for the force constant of the rear suspension of a car when a 130-kg box is loaded into the trunk of a car, causing the height of the car's bumper to decrease by 19 cm. To determine the force constant, we must use Hooke's Law, which is represented by the formula F = kx, where F is the force applied by the weight of the box, k is the force constant, and x is the displacement caused by the load (x should be in meters).
The weight of the box is calculated by multiplying the mass of the box by the acceleration due to gravity (9.80 m/s2). For a 130 kg box, the weight F is 130 kg × 9.80 m/s2 = 1274 N.
To find k, we rearrange the formula to k = F/x. The displacement x is 19 cm, which is 0.19 meters. So, the force constant k is 1274 N / 0.19 m = 6705 N/m. Therefore, the rear suspension's force constant is 6705 N/m.