Question

Two people with a combined mass of 139 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 9.20 cm . When the car hits a bump in the road, it oscillates up and down with a period of 1.73 s .

A) Find the total load supported by the springs.

B) Find the mass of the car.

Answer 1

Weight of the two people = 139 x 9.8 = 1362.2 N

Compression because of this weight = 9.20 cm = 0.092 m

we know, F=Kx

here, F = Weight of 2 people , K = Spring constant and x = compression length.

Therefore

spring constant k = 1362.2/0.092 = 14806.52 N/m

a)Time period T = 1.73 s

Let M = total load supported by the springs.

we know,

$T = 2 \pi \sqrt{\dfrac{total\ mass}{k}}$

or, $\frac{T}{2\pi }=\sqrt{\frac{M}{K}}$

$(\frac{T}{2\pi } )^{2}={\frac{M}{K}}$

120) = W

Or M = 1137.9  kg

= 1138 kg

Ans: 1138 kg

b) Mass of the car = total load - mass of the two people

= 1138 - 139

= 999 kg

Ans: 999 kg (Approx)

Thank you.