# Car Suspension System#

A car is moving over a hump in the road with a constant speed $$v \ \rm{ms^{-1}}$$.

## Part 1#

What is the maximum speed, $$v$$ with which the car can move without it losing contact with the road at the top of the hump.
Treat the car as a particle. Neglect friction and air resistance.
$$m = {{ params.m }} \ \rm{kg}$$, $$R = {{ params.r }} \ \rm{m}$$

Please enter value of $$v$$ in $$m/s$$.

## Part 2#

In order to reduce the likelihood of loss of contact when navigating the curvature of the hump, a suspension system consisting of a series of springs is connected to the wheels to absorb some of the excess kinetic energy of the vehicle before it encounters the circular arc.
If the maximum compression ($$\delta x$$) of the springs are $${{ params.x }}\ \rm{mm}$$ at the top of the hump, what must the equivalent spring stiffness constant, $$k$$, be if the speed of the car goes at the top of the hump is $${{ params.v }} \ \rm{km/h}$$.
The speed of the car just before the hump is $${{ params.u }} \ \rm{km/h}$$. The height of the hump above the ground plane is $$0.5 \ \rm{m}$$.

Please enter the value of $$k$$ in $$Nm^{-1}$$.