(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Part 1: Rounding a flat, unbanked curve, which has a radius (r), the coefficient of static friction between the car and the road is 0.5. Find the max speed you can take the curve without sliding.

Radius (r) = 25 m

I'll be using (Us) to denote the coefficient of static friction.

Part 2: If the curve is banked at some angle (theta), find theta so that no frition is required to make the curve.

2. Relevant equations

fsmax = Us * N

N= mg

NcosTheta = mg

NsinTheta = mv²/r

3. The attempt at a solution

For the first part, I concluded that any sideways motion would be the sliding of the car. So static friction has not exceeded maximum friction. So Us < Fsmax. Since theres no vertical motion, N = mg. I figured when the car is about to skid (the max speed) Us = Fsmax.

I came up with the equation: V = √(Us * r * g). Plugging in the #s I got √(.5 * 25m * 9.81m/s²). Which gave me an answer of 11.07 m/s.

Does that sound right?

I'm much more confused with part 2 of the equation. Im assuming the velocity is needed to figure out the angle, so apparently the velocity from part 1 is used. I came up with the equations listed above

NcosTheta = mg

NsinTheta = mv²/r

But if theres no friction at all, wouldnt the angle then have to be zero? I'm really lost on the 2nd part of this problem, but confirmation on the first part would be helpful also.

Thanks.

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# Homework Help: Static Friction and Circular Motion problem

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