Non uniform circular motion and friction

[newcool]

A car is at rest in a circle of radius r. The car then accelerates, but friction limits the speed to some max speed v. At what angle is the max speed v reached? (calculus is involved).

The key is to draw a detailed FBD, which I need help with. So far the forces I have are: centripital, component of friction pointing perpendicular to the radius, and another component of friction pointing towards the center of the circle.

Also, how to relate the angle to the FBD?

Thanks

 

[Gokul43201]

I didn't use calc for this, so I may be wrong...have you posted the question EXACTLY as it appears in your hw/text ?

Can you find the coefficient of static friction from the FBD ? (Hint : The centripetal force provides the centripetal acceleration.)

Next draw the FBD for a wheel of the car. What are the forces acting on it ? Can you thus calculate the maximum linear acceleration of the car ? Now use the relevant equation of motion to find the distance traveled. From this, you should be able to get the angle traversed.

 

[newcool]

I think you can't use V^2 = 2ax because the linear acceleration is not constant. It starts at p and then goes down to 0.

thanks

 

[Gokul43201]

I believe it goes down to zero only after the car has reached a velocity v. I assumed that the maximum speed was set by that velocity at which there was sufficient friction to be able to take the curve at the given radius...and that further acceleration is prevented only by the driver not wanting to skid off the road.

 

[newcool]

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