# How fast can a motorcyclist ride on a horizontal plane, describing an arc with a radius of 83 m

March 24, 2021 | education

| **How fast can a motorcyclist ride on a horizontal plane, describing an arc with a radius of 83 m, if the coefficient of friction of rubber on the ground is 0.4?**

Newton’s second law:

m * a = F, where m is body mass, a is acceleration, F is force.

In this case, the force is the friction force and is determined by the formula:

F = η * m * g, where η is the coefficient of friction, g is the acceleration of gravity.

When moving in a circle, the body moves with acceleration:

a = v ^ 2 / R, where R is the radius of the circle, v is the speed.

We get equality:

m * v ^ 2 / R = η * m * g.

Reducing by mass, we get:

v ^ 2 / R = η * g;

v = √η * g * R.

v = √0.4 * 10 * 83 = 18 m / s.

Answer: the maximum speed is 18 m / s.

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