When four people weighing 70 kg each get into the car, the car’s shock absorber spring is compressed by 2.5 cm.

When four people weighing 70 kg each get into the car, the car’s shock absorber spring is compressed by 2.5 cm. Find the stiffness of one spring if there are four springs in total.

Given:
m1 = m2 = m3 = m4 = 70 kilograms – the mass of people in the car;
g = 10 N / kg – acceleration of gravity;
n = 4 – the number of shock absorber springs;
xd1 = xd2 = xd3 = xd4 = 2.5 centimeters = 0.025 meters – the amount of compression of the shock absorber springs.
It is required to determine the stiffness of the shock absorber spring k.
People sitting in a car act on the shock absorber springs with a gravity equal to:
F = F1 + F2 + F3 + F4 = m1 * g + m2 * g + m3 * g + m4 * g = 4 * m * g = 4 * 70 * 10 = 2800 Newtons.
We will assume that the load on all springs is distributed evenly, then a force acts on each spring:
F1 = F / n = 2800/4 = 700 Newtons.
Then the stiffness of the spring is:
k = F / dx = 700 / 0.025 = 28,000 N / kg.
Answer: The stiffness of the shock absorber spring is 28,000 N / kg.