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

Total load = 2999.126 kg

Step-by-step 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{(m)/(k) }`

`(m)/(k) = (T^(2) )/(4\pi ^(2) )`

thus,

`m = k(T^(2) )/(4\pi ^(2))`

T = 1.66s

substituting these values in the equation,

`m =13,676.923(1.66^(2) )/(4\pi ^(2)  )`

m = 2999.126 kg