Question

Two people with a combined mass of 127 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 9.10 cm. When the car hits a bump in the road, it oscillates up and down with a period of 1.66 s. Find the total load supported by the springs.

Answer 1

Answer:

Total load = 2999.126 kg

Explanation:

Let the spring constant of the shock absorber be k.

We know that the force applied on a spring is directly proportional to elongated length and the constant of proportionality is called spring constant.

Thus

Force, F = kx

where,

x = elongation = 9.1 cm 0.091 m

mass of the people, m = 127 kg

F = weight of the people = mg = 127 x 9.8 = 1244.6 N

substituting these values in the first equation,

1244.6 = k x 0.091

thus, k = 13,676.923 N/m

Now we know that the time period, T of an oscillating spring with a load of mass m is

$T = 2\pi \sqrt{\frac{m}{k} }$

$\frac{m}{k} = \frac{T^{2} }{4\pi ^{2} }$

thus,

$m = k\frac{T^{2} }{4\pi ^{2}}$

T = 1.66s

substituting these values in the equation,

$m =13,676.923\frac{1.66^{2} }{4\pi ^{2} }$

m = 2999.126 kg