Final answer:
To calculate the spring constant, we apply Hooke's law using the driver's weight as the force and the car's compression as the displacement. The spring constant k is found to be approximately 21476 N/m after converting units and solving the equation.
Step-by-step explanation:
The question is asking to find the spring constant k for the car's suspension system. According to Hooke's law, F = -kx, where F is the force applied to the spring, x is the displacement caused by the force, and k is the spring constant. The negative sign indicates the restoring force the spring exerts in opposition to the applied force.
First, we convert the driver's weight to a force. Since the driver's mass is 81 kg, we calculate the gravitational force (weight) as F = mg. Using g = 9.81 m/s² (acceleration due to gravity), we have F = 81 kg × 9.81 m/s² = 794.61 N. While the displacement x provided is 37 mm, we need to convert this to meters: x = 37 mm × 10⁻³ m/mm = 0.037 m.
By using the force and displacement in Hooke's law, we can solve for the spring constant k:
k = F/x which gives us k = 794.61 N / 0.037 m ≈ 21476 N/m.
When we round to the nearest whole number, the spring constant k is approximately 21476 N/m.