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Ch 11: Equilibrium & Elasticity
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 11: Equilibrium & ElasticityProblem 13b
Chapter 11, Problem 13b

Find the tension T in each cable and the magnitude and direction of the force exerted on the strut by the pivot in each of the arrangements in Fig. E11.13. In each case let w be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight w. Start each case with a free-body diagram of the strut.

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Begin by drawing a free-body diagram for the strut in arrangement (b). Identify all forces acting on the strut: the tension T in the cable, the weight of the strut (w), the weight of the crate (w), and the reaction forces at the pivot (horizontal and vertical components).
Apply the equilibrium condition for torques about the pivot point. Choose the pivot as the point of rotation to eliminate the reaction forces from the torque equation. Set the sum of the torques equal to zero. Consider the perpendicular distances from the pivot to the line of action of each force.
Write the torque equation: \( T \cdot L \cdot \sin(45^\circ) - w \cdot \frac{L}{2} \cdot \cos(30^\circ) - w \cdot L \cdot \cos(30^\circ) = 0 \), where L is the length of the strut. Solve this equation for the tension T.
Apply the equilibrium conditions for forces in the horizontal and vertical directions. For horizontal forces: \( T \cdot \cos(45^\circ) = F_{horizontal} \). For vertical forces: \( T \cdot \sin(45^\circ) + F_{vertical} = 2w \).
Solve the system of equations obtained from the force equilibrium conditions to find the horizontal and vertical components of the force exerted by the pivot. Use these components to determine the magnitude and direction of the force exerted by the pivot.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. In this context, it helps identify all forces acting on the strut, including tension in the cables, gravitational forces due to the weights of the crate and the strut, and any reaction forces at the pivot. This diagram is essential for applying Newton's laws to solve for unknown forces.
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Tension in Cables

Tension is the force exerted along a cable or rope when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the cables must balance the weight of the suspended crate and the strut. Understanding how to calculate tension involves analyzing the angles and applying trigonometric functions to resolve forces into their components.
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Equilibrium of Forces

The concept of equilibrium states that an object at rest has a net force of zero acting on it. For the strut in this problem, this means that the sum of all vertical and horizontal forces must equal zero. This principle is crucial for determining the magnitudes and directions of the forces exerted on the strut by the pivot and the tension in the cables.
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Related Practice
Textbook Question

A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver weighing 500 N stands at the free end (Fig. E11.11). The diving board is of uniform cross section and weighs 280 N. Find the force at the support point.


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Textbook Question

The horizontal beam in Fig. E11.14 weighs 190 N, and its center of gravity is at its center. Find the tension in the cable.


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Textbook Question

A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 740 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. What is the maximum friction force that the ground can exert on the ladder at its lower end?

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Textbook Question

The horizontal beam in Fig. E11.14 weighs 190 N, and its center of gravity is at its center. Find the horizontal and vertical components of the force exerted on the beam at the wall.

Textbook Question

Find the tension T in each cable and the magnitude and direction of the force exerted on the strut by the pivot in each of the arrangements in Fig. E11.13. In each case let w be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight w. Start each case with a free-body diagram of the strut.

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Textbook Question

Suppose that you can lift no more than 650 N (around 150 lb) unaided.


How much can you lift using a 1.4 m-long wheelbarrow that weighs 80.0 N and whose center of gravity is 0.50 m from the center of the wheel (Fig. E11.16)? The center of gravity of the load carried in the wheelbarrow is also 0.50 m from the center of the wheel.

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