Question 8.11: WALKING A HORIZONTAL BEAM GOAL Apply the two conditions of e...
WALKING A HORIZONTAL BEAM
GOAL Apply the two conditions of equilibrium.
PROBLEM A uniform horizontal beam 5.00 \mathrm{~m} long and weighing 3.00 \times 10^{2} \mathrm{~N} is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0^{\circ} with the horizontal (Fig. 8.18a). If a person weighing 6.00 \times 10^{2} \mathrm{~N} stands 1.50 \mathrm{~m} from the wall, find the magnitude of the tension \overrightarrow{\mathbf{T}} in the cable and the components of the force \overrightarrow{\mathbf{R}} exerted by the wall on the beam.
STRATEGY See Figure 8.18a-c (Steps 1 and 2). The second condition of equilibrium, \Sigma_{\tau_{i}}=0, with torques computed around the pin, can be solved for the tension T in the cable. The first condition of equilibrium, \sum \overrightarrow{\mathbf{F}}_{i}=0, gives two equations and two unknowns for the two components of the force exerted by the wall, R_{x} and R_{y}.
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