Solve for Maximum Speed of a Car on a Circular Turn | Centripetal Force Problem

AI Thread Summary
A car with a mass of 2000 kg is trying to navigate a circular turn with a radius of 20 m, where the coefficient of friction is 0.7. The centripetal force equation, Fc = m(v²/r), is used to determine the maximum speed without skidding. An initial calculation incorrectly squared the radius, leading to an erroneous velocity of 52.38 m/s instead of the correct value of 11.7 m/s. The mistake was acknowledged and corrected in the discussion. Understanding the proper application of the centripetal force formula is crucial for solving such problems accurately.
BrainMan
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Homework Statement


A car of mass 2000 kg rounds a circular turn of radius 20 m. If the road is flat and the coefficient of friction is 0.7 between the tires and road, how fast can the car go without skidding?


Homework Equations


Fc = m(v2/r)


The Attempt at a Solution


I tried to find the centripetal force by doing
2000(9.8) = 19600
19600(.7) = 13720
then I plugged that into the above equation to find the velocity
13720 = 2000v2/202
5488000/2000 = v2
2744 = v2
\sqrt{}2744 = v
v= 52.38 m/s. The correct answer is 11.7 m/s
 
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BrainMan said:
Fc = m(v2/r)
...
13720 = 2000v2/202

Why did you square the radius?Edit:
Other than that you are correct.
 
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Nathanael said:
Why did you square the radius?


Edit:
Other than that you are correct.

That was my mistake. Thanks!
 
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