As shown in the figure below, a uniform beam of mass m and length L is inclined
ID: 2297201 • Letter: A
Question
As shown in the figure below, a uniform beam of mass m and length L is inclined at an angle ? to the horizontal and held in place by a horizontal cord at the top and friction at the bottom. The coefficient of static friction between the beam and horizontal surface is ?s and the angle is such that the static friction force is at its maximum value.
A) Using the first condition of equilibrium, find a second expression for T in terms of ?s, m, and g.
B)Using the foregoing results, determine an expression for the coefficient of static friction ?s in terms of only the angle?.
Explanation / Answer
alon vertical
N = m*g
along horizontal
T - f = 0
sin
T = f = us*N = us*m*g
B) Net torque = 0
T*L*sin? = m*g*(L/2)*cos?
us*m*g*sin? = m*g*cos?
tan? = 1/us
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