Question

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.

Answer 1

Answer:

$F = m \cdot x \cdot g$

Explanation:

The centrifugal net force experimented by driver is:

$F = m \cdot \frac{v^{2}}{R}$

Let make the following consideration:

$\frac{v^{2}}{R} = x \cdot g\\v^{2} = x \cdot g \cdot R$

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

$F = m \cdot x \cdot g$

Answer 2

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;

• speed of the car, = v
• mass of the driver, = m
• Weight of the driver = x

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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