# Slipping on Curved Road

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• Jan 5th 2012, 07:24 AM
question
Slipping on Curved Road
Excellent, Thank you.

Another little teaser, think i have this one but not sure.

A level single carriageway road has a speed limit of 50km/h, and has a sharp left-hand bend with a radius of 25m.

Given that the coefficient of friction is 0.30, and that to avoid side slip v2/R > μg , at what speed would side slip occur?

extra info for you

g = 9.81 m/s2
V = speed in km/h
v = speed in m/s
R = radius (m)
u= coefficient of friction

Thanks a lot for you help on the other question
• Jan 7th 2012, 12:53 PM
earboth
Re: Slipping on Curved Road
Quote:

Originally Posted by question
Excellent, Thank you.

Another little teaser, think i have this one but not sure.

A level single carriageway road has a speed limit of 50km/h, and has a sharp left-hand bend with a radius of 25m.

Given that the coefficient of friction is 0.30, and that to avoid side slip v2/R > μg <--- are you sure that this is correct? (see below!) , at what speed would side slip occur?

extra info for you

g = 9.81 m/s2
V = speed in km/h
v = speed in m/s
R = radius (m)
u= coefficient of friction

Thanks a lot for you help on the other question

1. $\displaystyle \frac{m v^2}r$ decribes the centrifugal force and

$\displaystyle \mu \cdot m \cdot g$ describes the friction.

In my opinion the friction has to be greater than the centrifugal force (otherwise you'll leave the lane and land in the ditch).

2. If I'm right you only have to plug in the given values into the inequatlity

$\displaystyle \frac{v^2}r < \mu g$

and solve for v.

3. You'll get the speed in m/s. Convert it into km/h and compare with the allowed speed. You'll see, that the limitation is not sufficient.