Calculating the Speedbump Radius to Stop a Car: A Homework Challenge

[DannyTatas]

Homework Statement

A car goes over a speedbump, which has the cross-section of a cylinder of radius R embedded in the roadway. If you want a car driving with a speed Vo to be impeded, how large must R be?

I'm very confused about this problem because we have not discussed the topic in class and I have a terrible book. I want to say that you use the centripetal force equation, but that is for when velocity is constant? I'm not sure...

Knowns:
V initial = Vo
V final = 0
mass = m
Radius = height of the speed bump

Unknowns:
Radius

Homework Equations

F = m(v^2)/R

The Attempt at a Solution

Again, I am having trouble and do not know where to begin. I want to learn how to do this; not get a quick answer. Any and all help will be greatly appreciated.

 

[Spinnor]

We need two numbers to better define the speed bump, the radius R and the height of the section of a cylinder. Is it half a cylinder, a quarter? I hope you understand.

As for impeding the car you need to be more specific. A car with a very stiff suspension will handle the speed bump differently then a car with a very soft suspension. I think we need more information.

 

[DannyTatas]

This is just how my professor operates. He makes us solve variables with other variables rather than numeric values.

 

[rcgldr]

A speed bump won't slow down a car much (assuming it doesn't damage the car's tires, wheels or suspension). Perhaps the goal is to find R so that v0² / R translates into 1 g of acceleration, but even that would not slow down a car much.