1. Frankly friction is frightening In this problem, you’ll determine the approxi

Question

1.     Frankly friction is frightening

In this problem, you’ll determine the approximate coefficient of static friction between your shoes and a smooth surface.

a. Suppose that your shoe has mass m and is resting on an incline (you could, for example, rest one of your shoes on a textbook that you hold at an angle). You find that if the incline isn’t too steep, the shoe will sit at rest on the incline, but as you increase the angle the surface makes with the horizontal direction, there will be a maximum angle max above which the shoe will slide down the incline. Suppose that your shoe has mass m, and determine µs, the coefficient of static friction, in terms of max.

b. Use your result from a. to estimate the coefficient of static friction between your shoes and a smooth surface (like the surface of your textbook). Hint. Do the experiment described above, and measure maxusing either a protractor or a ruler and some trigonometry.

Explanation / Answer

The gravity component acting on shoe will be:

Fg = mg sin(theta)

The normal force is

Fn = mg cos(theta)

The frictional force on the shoe is:

Ff = u N = u mg cos(theta)

For the shoe, not to slide, the gravoty should be equal to the static frictioanl force

Ff = Fg

u mg cos(theta) = mg sin(theta)

u = sin(theta)/cos(theta) = tan(theta)

Hence, u = tan(theta) [theta is theta, max as in the question]

Let, we measured, theta-max = 40 deg

u = tan40 = 0.84

u = 0.84

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