The net force on the car is the friction that keeps it on the road, which points toward the center of the circle of the curve. Then by Newton's second law, we have
• net vertical force:
∑ <em>F</em> = <em>N</em> - <em>W</em> = 0
• net horizontal force:
∑ <em>F</em> = <em>Fs</em> = <em>m a</em>
where
<em>N</em> = magnitude of normal force
<em>W</em> = car's weight
<em>Fs</em> = mag. of static friction
<em>m</em> = car's mass
<em>a</em> = <em>v</em> ²/<em>R</em> = mag. of the centripetal acceleration
<em>v</em> = car's speed
<em>R</em> = radius of curve
Now,
• compute the car's weight:
<em>W</em> = <em>m g</em> = (1500 kg) (9.8 m/s²) = 14,700 N
• solve for the mag. of the normal force:
<em>N</em> = 14,700 N
• solve for the mag. of the friction force, using the given friction coefficient:
<em>Fs</em> = 0.5 <em>N</em> = 7350 N
• solve for the (maximum) acceleration:
7350 <em>N</em> = (1500 kg) <em>a</em> → <em>a</em> = 4.9 m/s²
• solve for the (maximum) speed:
4.9 m/s² = <em>v</em> ²/ (35 m) → <em>v</em> ≈ 13 m/s
