Question

A car with bad shock absorbers bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1 500 kg and is supported by four springs of equal force constant k. Determine the value of k.

Answer 1

The value of the force constant k for the springs of a car can be found by rearranging the formula T = 2π√(m/k) and plugging in the mass of the car and the period of oscillation. The calculated value then needs to be divided by four to obtain the force constant for one spring.

Step-by-step explanation:

To determine the value of the force constant k for the springs of a car with a mass of 1500 kg and a bouncing period of 1.50 s after hitting a bump, we can apply the principles of a simple harmonic oscillator. The formula for the period T of a simple harmonic oscillator is given by T = 2π√(m/k), where m is the mass of the object and k is the force constant of the spring.

To solve for k, we rearrange the equation to get k = (4π²m)/T². Plugging in the values for m as 1500 kg and T as 1.50 s, we get k = (4π² × 1500 kg) / (1.50 s)². After calculating the value, we find the force constant k for one spring. Since the car is supported by four springs, the total force constant needs to be divided by four to find the force constant of one spring.

Answer 2

k = 6580 N/m

Step-by-step explanation:

Given: T = 1.5s, m = 1500kg

`T=(2\pi)/(\omega)\\\\\omega=(2\pi)/(T) \\\\ \omega=\sqrt{(4k)/(m)}\\\\k=(1)/(4)\omega^(2)m\\\\k=(1)/(4)((2\pi)/(T))^(2)(m)\\\\k=(1)/(4)((2\pi)/(1.5s))^(2)(1500kg)=6579.7 (N)/(m)`

4k because there are 4 wheels