One end of a uniform meter stick is placed against a vertical wall . The other e

Question

One end of a uniform meter stick is placed against a vertical wall. The other end is held by a lightweight cord that makes an angle ? with the stick. The coefficient of static friction between the end of the meter stick and the wall is 0.39.

A) What is the maximum value the angle

? can have if the stick is to remain in equilibrium?

B) Let the angle between the cord and the stick is

? = 15?. A block of the same weight as the meter stick is suspended from the stick, as shown, at a distance x from the wall. What is the minimum value of x for which the stick will remain in equilibrium?

C) When

? = 15?, how large must the coefficient of static friction be so that the block can be attached 15cm from the left end of the stick without causing it to slip?

Explanation / Answer

a)

T sin(theta) * 1 = m g * (1/2)

T cos(theta) = N

T sin(theta) = -u N + m g = -u (T cos(theta)) + 2 T sin(theta)

==> tan(theta) = u = 0.39

==> theta = 21.3 degrees

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