# A turn has a radius of R and is banked at an angle theta so that on a perfectly icy (frictionless) day a car with a speed v will not slip. What is v in terms of R and theta?

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A turn has a radius of R and is banked at an angle theta so that on a perfectly icy (frictionless) day a car with a speed v will not slip. What is v in terms of R and theta?

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Step 1

Consider the FBD of the car on the frictionless banked road.

Step 2

Equate the net vertical force that acts on the car to zero. Assume that the force towards the upward direction is positive.

Step 3

Here, ϴ is the angle by which the road is banked, N is the Normal reaction force that acts on the car and m is the car’s mass.

Equate the net ho...

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