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Chapter 4: Q38. (page 103)

Suppose you are standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?

Short Answer

Expert verified

The coefficient of static friction is 0.20 between your feet and the floor.

Step by step solution

01

Step 1. Given data and assumption

The non-sliding condition is the static friction force, which is equal to the reaction force due to acceleration.

Given data:

The acceleration of the train is a=0.20g.

Assumption:

Let μsbe the coefficient of static friction between your feet and the floor.

02

Step 2. Calculation of the coefficient of static friction

The normal force acting on you is N=mg.

Then, the static friction force is

fs=μsN=μsmg

You do not slide, which means that the static friction force equals the force due to the train’s acceleration. So,

fs=maμsmg=maμs=ag

Now, substituting the values in the above equation,

μs=0.20gg=0.20

Hence, the coefficient of static friction is 0.20.

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