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Solved: You open a restaurant and hope to entice customers
Chapter 11, Problem 11.51(choose chapter or problem)
You open a restaurant and hope to entice customers by hanging out a sign (Fig. P11.51). The uniform horizontal beam supporting the sign is 1.50 m long, has a mass of 12.0 kg, and is hinged to the wall. The sign itself is uniform with a mass of 28.0 kg and overall length of 1.20 m. The two wires supporting the sign are each 32.0 cm long, are 90.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.00 m long.
(a) What minimum tension must your cable be able to support without having your sign come crashing down?
(b) What minimum vertical force must the hinge be able to support without pulling out of the wall?
Questions & Answers
QUESTION:
You open a restaurant and hope to entice customers by hanging out a sign (Fig. P11.51). The uniform horizontal beam supporting the sign is 1.50 m long, has a mass of 12.0 kg, and is hinged to the wall. The sign itself is uniform with a mass of 28.0 kg and overall length of 1.20 m. The two wires supporting the sign are each 32.0 cm long, are 90.0 cm apart, and are equally spaced from the middle of the sign. The cable supporting the beam is 2.00 m long.
(a) What minimum tension must your cable be able to support without having your sign come crashing down?
(b) What minimum vertical force must the hinge be able to support without pulling out of the wall?
Step 1 of 6
We know, for a system of rigid bodies to be in a state of equilibrium, the sum of the forces along any direction should be zero.
The sum of forces acting in the X and Y direction is given by,
\(\sum F_{x}=0 \quad \sum F_{y}=0 \dots \dots (1)\)
And the sum of the torque should be zero at any point in the system, i.e. we have
\(\sum \tau=0 \dots \dots (2)\)
Where the torque is defined as follows
\(\tau=\vec{r} \times \vec{F}\)