A uniform beam of length L = 1.1 m and mass M = 29 kg has its lower end fixed to pivot at a point P on the floor, making an angle θ = 11° as shown in the diagram. A horizontal cable is attached at its upper end B to a point A on a wall. A box of the same mass M as the beam is suspended from a rope that is attached to the beam one-fourth L from its upper end.
Added by Deborah C.
Step 1
First, we need to find the tension in the cable. To do this, we can consider the torque about point P. The torque due to the tension in the cable is given by $T \times L \times \sin(\theta)$, where T is the tension in the cable. Show more…
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A uniform beam of mass $m$ is inclined at an angle $\theta$ to the horizontal. Its upper end (point $P$ ) produces a $90^{\circ}$ bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (Fig. $\mathrm{P} 12.35$ ). Let $\mu$, represent the coefficient of static friction between beam and floor. Assume $\mu_{s}$ is less than the cotangent of $\theta$. (a) Find an expression for the maximum mass $M$ that can be suspended from the top before the beam slips. Determine (b) the magnitude of the reaction force at the floor and (c) the magnitude of the force exerted by the beam on the rope at $P$ in terms of $m$ $M,$ and $\mu_{s}$
A uniform beam of mass $m$ is inclined at an angle $\theta$ to the horizontal. Its upper end produces a $90^{\circ}$ bend in a very rough rope tied to a wall, and its lower end rests on a rough floor (Fig. Pl2.47). (a) Let $\mu_{s}$ represent the coeffcient of static friction between beam and floor. Assume $\mu_{s}$ is less than the cotangent of $\theta .$ Determine an expression for the maximum mass $M$ that can be suspended from the top before the beam slips. (b) Determine the magnitude of the reaction force at the floor and the magnitude of the force exerted by the beam on the rope at $P$ in terms of $m, M,$ and $\mu_{s}$ .
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