Question
A highway curve with a radius of 430 m is banked properly for a car traveling 115 km/h. If a 1550- kg Porshe 928S rounds the curve at 220 km/h, how much sideways force must the tires exert against the road if the car does not skid?
Answers
Porsche is misspelled.
First, figure out the bank angle A from the statement that the car is "propertly banked" for v = 115 km/h. That means no lateral friction force is required to keep the tires from skidding. (At this angle, occupants will also not tend to slide in their seats)
v = 31.9 m/s
m v^2/R = m g tan A
tan A = v^2/(Rg) = 0.241
A = 13.5 degrees
At the higher speed of V = 220 km/h = 51.7 m/s, there is a centripetal force component mV^2*cos A/R up the bank, that must be balanced by friction force F and the weight component in the opposite direction.
m g sin A + F = m V^2/R cos A
Solve for F
First, figure out the bank angle A from the statement that the car is "propertly banked" for v = 115 km/h. That means no lateral friction force is required to keep the tires from skidding. (At this angle, occupants will also not tend to slide in their seats)
v = 31.9 m/s
m v^2/R = m g tan A
tan A = v^2/(Rg) = 0.241
A = 13.5 degrees
At the higher speed of V = 220 km/h = 51.7 m/s, there is a centripetal force component mV^2*cos A/R up the bank, that must be balanced by friction force F and the weight component in the opposite direction.
m g sin A + F = m V^2/R cos A
Solve for F
you misspelled properly. nice.