Problem 13 Mandatory Experimentally determine the spring con

Problem 13 [Mandatory] Experimentally determine the spring constant of your car and the damping coefficient.

Solution

Let\'s assume, toatal mass of car = 1000Kg

Car has 4 wheels and corresponding shock absorbers. Rach sock absorber can work with .5m long.

Assume mass is uniformly distributed on 4 shock absorber. Each shock absorber use spring. Each one has to support a mass of atleast 250 kg.

Then weighs on each shock absorber, F = mg =(250 kg)(9.8 m/s2) = 2450 N

Where, F= force, m= mass of object, g= acceleration due to gravity.

The spring in the shock absorber will, at a minimum, have to give you 2450 N of force at the maximum comparison of 0.5 m.

Using hooks law, F =kx

K= F/x = 2450N/0.5 m = 4900 N/m

The springs used in the shock absorbers must have spring constant of at least 4900 N/m.

Tire damping is quite small compared to damping provided by the shock absorber. According to milliken and milliken 15% of critical damping is where the most comfort is achieved.

So, critical damping Ccr= 2*sqrt(k*m) = 2*sqrt(4900*250)=2*1106.78= 2213.59 Ns/m

Let , damping ratio for shock absorber is .2

We know that,

c/Ccr= damping ratio

Hence, c= Ccr×damping ratio

c= 2213.59*.2= 442.72 Ns/m

Where, c= damping coefficient