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January 30, 2015

Posted by **Zac** on Thursday, July 26, 2012 at 12:01pm.

the top of the curve) and is banked at 31.0

O

.

a) What speed would be necessary to make this turn if there was no friction on the road?

b) If the coefficient of static friction between the tires and the road is 0.70, what are the minimum

and maximum speeds that a car could take this turn and not slide?

- Physics -
**Elena**, Thursday, July 26, 2012 at 1:17pm(a)

x: ma=N•sinα

y: 0=N•cosα –mg, => N=mg/cosα

a=v²/R

m• v²/R = N•sinα= mg•sinα/cosα= mg•tanα

v=sqrt(R• g•tanα)

(b)

x: ma=N•sinα+F(fr) •cosα

y: mg= N•cosα –mg-F(fr) •sinα

Since F(fr)=μ•N,

ma=N(sinα+μ•cosα)

mg= N(cosα - μ• sinα)

ma/mg = (sinα+μ•cosα)/ (cosα - μ• sinα)

a=v² /R

v² /Rg= (sinα+μ•cosα)/ (cosα - μ• sinα)

v=sqrt[Rg (sinα+μ•cosα)/ (cosα - μ• sinα)]

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