A sports car moves around a banked curve at just the right constant speed v so that no friction is needed to make the turn. During the turn, the driver (mass m) feels as though she weighs x times her actual weight. Find the magnitude of the net force on the driver during the turn in terms of m, g, and x.

The magnitude of the net force on the driver during the turn is equal to the apparent weight of the driver = xmg.

The given parameters;

The actual weight of the driver is calculated as;

W = mg

The apparent weight of the driver is given as;

Fₙ = xmg

The frictional force between the driver  and the curve road = 0

At constant speed, acceleration = 0

The magnitude of the net force on the driver during the turn is equal to the apparent weight of the driver = xmg.

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Explanation:

The centrifugal net force experimented by driver is:

Let make the following consideration:

After a quick substitution and some algebraic handling, the following expression is formed: