A bend of radius 150 m is to be banked so that cars at 63 km/h need no friction at all.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bend of radius is to be banked so that cars at need no friction at all. Taking , at what angle should it be banked?
Need a reminder? The key ideaShow
On a flat bend, friction supplies the force toward the centre, so . On a bend banked at , the tilted normal reaction supplies it, and no friction is needed when
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , , .
Plan. At the design speed the tilted normal reaction alone supplies the force toward the centre, so .
Step 1. Speed. .
Step 2. Angle. , so .
Answer: About .
Check. A gentle angle for a wide bend at a modest speed. A tighter bend would need a steeper bank.
Watch out. Using directly in gives an angle near . Always work in m/s.
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