Answer to Question #116590 in Classical Mechanics for Richard Robinson

Question

A car’s suspension is being tested, made from a single spring of stiffness k = 150 kNm-1. The suspension is attached to a testing system which can compress and extend the suspension many times a second given a certain input . An accelerometer is placed at the bottom of the spring.The system is tested in a lab under two different conditions for which you are asked to calculate different parameters.
A) The acceleration picked up by the sensor matches the following equation:

Answer 1

As per the question,

Stiffness of the spring$(k)=150 kN/m=150000 N/m$

Let the mass of the car = m,

Let the acceleration be=a

Extension in the spring $=x$

Now, applying the force balance equation,

$\Rightarrow ma=kx$

$\Rightarrow a=\dfrac{kx}{m}=\dfrac{150kN}{m}$