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What do you need to know to determine how fast a car can go through a curve without slipping?
Radius of curve Coefficient of friction
What are the conditions for maximum speed? When the centripetal force is equal to the frictional force. F c = mv 2 /r F f = µ Fnand Fn = mg
What are the conditions for maximum speed? When the centripetal force is equal to the frictional force. F c = mv 2 /r F f = µ Fnand Fn = mg Therefore: mv 2 /r = µmg
What are the conditions for maximum speed? When the centripetal force is equal to the frictional force. F c = mv 2 /r F f = µ Fnand Fn = mg Therefore: mv 2 /r = µmg v 2 = µgr v = (µgr) 1/2
Calculate the maximum speed a car can go through a 50 m curve with rubber tires on dry asphalt.
Solution: F c = mv 2 /r F f = µ Fnand Fn = mg Therefore: mv 2 /r = µmg v 2 = µgr v = (µgr) 1/2 v = ((.85)(9.81m/s 2 )(50m)) 1/2 v = 20.14 m/s
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