A car with bad shocks bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1250 kg and is supported by four springs of force constant k. What is k for each spring?
To solve this problem, we can use the formula for the period of a mass-spring system:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the force constant of the spring.
Given that the period is 1.50 s and the mass is 1250 kg, we can rearrange the formula to solve for k:
k = (4π²m) / T²
Plugging in the given values:
k = (4π² * 1250 kg) / (1.50 s)²
k = 4π²(1250 kg) / 2.25 s²
k ≈ 4 * (3.1416)² * (1250 kg) / 2.25
k ≈ 4 * 9.87 * 1250 kg / 2.25
k ≈ 1957.6 N/m
Therefore, the force constant for each spring is approximately 1957.6 N/m.