Static friction (magnitude <em>Fs</em>) keeps the car on the road, and is the only force acting on it parallel to the road. By Newton's second law,
<em>Fs</em> = <em>m a</em> = <em>W</em> <em>a</em> / <em>g</em>
(<em>a</em> = centripetal acceleration, <em>m</em> = mass, <em>g</em> = acceleration due to gravity)
We have
<em>a</em> = <em>v</em> ² / <em>R</em>
(<em>v</em> = tangential speed, <em>R</em> = radius of the curve)
so that
<em>Fs</em> = <em>W</em> <em>v</em> ² / (<em>g</em> <em>R</em>)
Solving for <em>v</em> gives
<em>v</em> = √(<em>Fs g R</em> / <em>W</em>)
Perpendicular to the road, the car is in equilibrium, so Newton's second law gives
<em>N</em> - <em>W</em> = 0
(<em>N</em> = normal force, <em>W</em> = weight)
so that
<em>N</em> = <em>W</em>
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We're given a coefficient of static friction <em>µ</em> = 0.4, so
<em>Fs</em> = <em>µ</em> <em>N</em> = 0.4 <em>W</em>
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Substitute this into the equation for <em>v</em>. The factors of <em>W</em> cancel, so we get
<em>v</em> = √((0.4 <em>W</em>)<em> g R</em> / <em>W</em>) = √(0.4 <em>g R</em>) = √(0.4 (9.80 m/s²) (105 m)) ≈ 20.3 m/s