Question

A student wants to use the inclined plane to measure the coefficient of friction but he was not supplied with a protractor. He measures the height h and the horizontal distance of the free end of the plane from the floor x when the wooden block on the plane just begins to move. Which of the following correctly gives the coefficient of friction?

A. h/x
B. sin(h/x)
C. tan(h/x)
D. cos(h/x)

Answer 1

Answer on Question #55630, Physics / Mechanics | Relativity

A student wants to use the inclined plane to measure the coefficient of friction but he was not supplied with a protractor. He measures the height $h$ and the horizontal distance of the free end of the plane from the floor $x$ when the wooden block on the plane just begins to move. Which of the following correctly gives the coefficient of friction?

A. h/x

B. $\sin (h / x)$

C. tan(h/x)

D. $\cos (h / x)$

Solution:

It is found experimentally that the force of friction $f$ is proportional to the normal component $N$ of the plane's reaction. Stated algebraically

$$f = \mu N$$

where the constant of proportionality $\mu$ is called the coefficient of kinetic friction.

If a body slides down an inclined plane without acceleration, it is in equilibrium and the vector diagram of forces is a closed polygon. For example, if the body B (Fig.) is sliding down the incline with constant velocity, the vector diagram formed by the weight W of the block, the force of friction f and the normal component N of the plane's reaction is a closed triangle. Since the coefficient of friction is the ratio f/N, it follows from the similarity of triangles that

$$\mu = \frac {h}{x} = \tan \theta$$

Answer: A. h/x

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