A uniform beam of length L and mass m shown in the figure below is inclined at an angle 0 to the horizontal. Its upper end is connected to a wa by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is u.. Assume the angle 0 is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and 0. T = (c) Using the condition of translational equilibrium, find a second expression for T in terms of H, m, and g. T =

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Chapter1: Units, Trigonometry. And Vectors
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A uniform beam of length L and mass m shown in the figure below is inclined at an angle 0 to the horizontal. Its upper end is connected to a wal
by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is µ.. Assume
the angle 0 is such that the static friction force is at its maximum value.
(a) Draw a force diagram for the beam.
(b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and 0.
T =
(c) Using the condition of translational equilibrium, find a second expression for T in terms of u, m, and g.
T =
Transcribed Image Text:A uniform beam of length L and mass m shown in the figure below is inclined at an angle 0 to the horizontal. Its upper end is connected to a wal by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is µ.. Assume the angle 0 is such that the static friction force is at its maximum value. (a) Draw a force diagram for the beam. (b) Using the condition of rotational equilibrium, find an expression for the tension T in the rope in terms of m, g, and 0. T = (c) Using the condition of translational equilibrium, find a second expression for T in terms of u, m, and g. T =
(c) Using the condition of translational equilibrium, find a second expression for T in terms of ue, m, and g.
T =
(d) Using the results from parts (a) through (c), obtain an expression for µ̟ involving only the angle 0.
Hs =
(e) What happens if the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure
above?
O The beam slips.
O The beam remains stationary.
Explain.
Transcribed Image Text:(c) Using the condition of translational equilibrium, find a second expression for T in terms of ue, m, and g. T = (d) Using the results from parts (a) through (c), obtain an expression for µ̟ involving only the angle 0. Hs = (e) What happens if the beam is lifted upward and its base is placed back on the ground slightly to the left of its position in the figure above? O The beam slips. O The beam remains stationary. Explain.
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