# Centripetal acceleration problem

**1. The problem statement, all variables and given/known data**

A car is traveling round a bend which is banked at an angle of 30 to the horizontal. The bend is assumed to be in the shape of an arc of a circle of radius 80m. the surface of the road is rough and the coefficient of friction between the tyres of the and the surface of the road is 0.3. Find the greatest speed and the least speed without slipping occurring

**2. Relevant equations**

Cp= v^2/r

**3. The attempt at a solution**

So, here the bend is assumed to be an arc of a circle which is why the angle θ=30 is assumed to be formed at the center of the circle. The centripetal acceleration is also caused by the maximum frictional force which has a coefficient of 0.3. The equation that best describes the motion of the car is as follows frictional force – mgcosθ= mv^2/r

or, fs-mgcos=mv^2/r

or, μR- mgcosθ=mv^2/r

What befuddles me about this problem is the value of R which is supposed to be the normal reaction force. How do I go about solving for R?? Can any of you guys drop a hint as to where I am going wrong.??

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