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Why are mountain roads generally made winding upwards rather than going straight up?

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When talking about inclined planes, for a body going upwards, the force of friction is f_{s} = \mu N \cos \theta, where \theta  is the angle of inclination of a plane.

The force of friction is high if \theta  is small, and hence there is less chance of skidding.

The value of friction will be smaller for a road straight up the mountain since it will have a larger angle of inclination, and thus the chance of skidding will be more. 

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