Many racetracks have banked turns, which allow the cars to travel faster around

Question

Many racetracks have banked turns, which allow the cars to travel faster around the curves than if the curves were flat. Actually, cars could also make turns on these banked curves if there were no friction at all. Explain this statement using the free-body diagram 4Acenter-fleeing force? See Conceptual Question 11. terms of Newton's laws for a ground-based observer, this pseudo, or false, force doesn't really exist. Analyze the sif uation in the figure to show that this is the case (that is, that the force does not exist). [Hint: Start with Newton's first law.] 2. Many curves have banked turns, which allow the cars t travel faster around the curves than if the road were fla Actually, cars could also make turns on these banked curves if there were no friction at all. Explain this state ment using the free-body diagram shown in Fig. 7.28 Ncos Nsin mg Banking safety See Conceptua F I G U R E 7 . 2 8 Question 12.

Explanation / Answer

If the car is on a banked turn, the normal force (which is always perpendicular to the road's surface) is no longer vertical. The normal force now has a horizontal component (N sin()), and this component can act as the centripetal force on the car. The car will have to move with just the right speed so that it needs a centripetal force equal to this available force. Given just the right speed, a car could safely negotiate a banked curve even if there is no friction present.
m is the mass of Car.
v is the speed of Car
r is the radius of the circle.

N*cos() = m*g
m = N*cos()/ g

Fnet = Fcentripetal
N sin() = m*v^2/r
N sin() = (N*cos()/ g) *v^2/r
v = sqrt(rg*tan())

This is the speed with which a car can turn the banked road even without friciton.

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