a car with bad shock absorbers bounces up and down with a period of 0.731s after hitting a bump. The car has a mass of 1850kg and is supported by four springs of equal force constant k.
Determine a value for k.
Answer in units of N/m.
if you can, could you explain how to get the answer.
thanks
To determine the value of the force constant k, we can use the formula for the period of oscillation of a mass-spring system:
T = 2π√(m/k)
Where:
T = Period of oscillation (0.731s in this case)
m = Mass of the car (1850kg)
Rearranging the formula, we can solve for k:
k = (4π²m) / T²
Plugging in the given values, we have:
k = (4π² * 1850kg) / (0.731s)²
First, let's calculate the value inside the parentheses:
(4π² * 1850kg) = 4 * 3.14² * 1850kg ≈ 36264.724 N
Next, let's calculate the denominator:
(0.731s)² = 0.533561s²
Now, we can substitute these values into the formula:
k ≈ 36264.724 N / 0.533561s²
Simplifying the expression, we have:
k ≈ 68000 N/m (rounded to the nearest whole number)
Therefore, the value of k, the force constant of each spring, is approximately 68000 N/m.