Suppose that you are standing on a train accelerating at 0.20g (where g is the acceleration due to gravity). What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide

0.2

Explanation:

The given parameters are;

The acceleration of the train, a = 0.2·g

The mass of the person standing on the train = m

Let μ represent the coefficient of static friction, we have;

The force acting on the person, F = m × a = m × 0.2·g

The force of friction acting between the feet and the floor, = m·g·μ

For the person not to slide we have;

The force acting on the person = The force of friction acting between the feet and the floor

F =

∴ m × 0.2·g = m·g·μ

From which we get;

0.2 = μ

The coefficient of static friction that must exist between the feet and the floor if the person is not to slide, μ = 0.2.

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