In Fig. 12-34, a uniform beam of weight 500 N and length 3.0 m is suspended horizontally. On the

step 1 For this problem on the topic of equilibrium and elasticity, we are shown a uniform beam which h

In Fig. 12-34, a uniform beam of weight 500 N and length 3.0...

In Fig. $12-34,$ a uniform beam of weight 500 $\mathrm{N}$ and length 3.0 $\mathrm{m}$ is suspended horizontally. On the left it is hinged to a wall; on the right it is supported by a cable bolted to the wall at distance $D$ above the beam. The least tension that will snap the cable is 1200 N. (a) What value of $D$ corresponds to that tension? (b) To prevent the cable from snapping, should $D$ be increased or decreased from that value?

In Fig. $12-34,$ a uniform beam of weight 500 $\mathrm{N}$ and length 3.0 $\mathrm{m}$ is suspended horizontally. On the left it is
hinged to a wall; on the right it is supported by a cable bolted to the wall at distance $D$ above the beam. The least
tension that will snap the cable is 1200
N. (a) What value of $D$ corresponds to
that tension? (b) To prevent the cable
from snapping, should $D$ be increased
or decreased from that value?

Key Concepts

Center of Gravity

The center of gravity is the point at which the entire weight of a body can be considered to act. For uniformly distributed masses, this point is typically at the geometric center. Recognizing and utilizing the center of gravity simplifies the analysis by reducing distributed forces to a single equivalent force, making calculations of torque and equilibrium more straightforward.

Free-Body Diagram

A free-body diagram is a simplified representation of a body, isolated from its surroundings, showing all external forces and moments acting on it. This tool helps in systematically identifying all forces, such as weights, tensions, and reaction forces, which is essential for setting up the equilibrium equations needed to solve many statics problems.

Static Equilibrium

This principle states that a body at rest has no net force acting on it in any direction and no net moment (torque) about any point. In solving such problems, one sets up equations ensuring that the sum of all horizontal forces, vertical forces, and torques is zero, which is fundamental to analyzing structures like beams and cables.

Torque and Rotational Equilibrium

Torque, or moment, is the turning effect produced by a force applied at a distance from a pivot point. For a system in equilibrium, the sum of all torques about any axis must be zero. This concept is crucial when analyzing beams or levers where forces act at different points, and it enables the calculation of unknown forces or distances.

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