Ch. 12 - Static Equilibrium; Elasticity and Fracture

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 12 - Static Equilibrium; Elasticity and Fracture

Problem 64c

Chapter 12, Problem 64c

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). Discuss whether compression, tension, and/or shear play a role in part (b).

Verified step by step guidance

Identify the forces acting on the pole: The pole experiences the weight of the sign (gravitational force), which acts vertically downward at a distance of 2.2 m from the wall. Additionally, the wall exerts a reaction force on the pole, which can be broken into horizontal and vertical components.

Understand the role of tension: Tension is a pulling force that acts along the length of an object. In this case, if the pole were a cable or rope, tension would be the primary force resisting the weight of the sign. However, since the pole is rigid, tension is not the dominant force here.

Understand the role of compression: Compression is a pushing force that acts along the length of an object. If the pole were oriented at an angle (not horizontal), compression could play a role in resisting the weight of the sign. However, since the pole is horizontal, compression is not significant in this scenario.

Understand the role of shear: Shear forces act perpendicular to the length of an object and can cause deformation. In this case, the weight of the sign creates a shear force at the point where the pole is attached to the wall. This shear force is significant because it resists the downward pull of the sign's weight.

Conclude the discussion: In this scenario, shear is the primary force acting on the pole at the wall attachment point. Compression and tension do not play significant roles because the pole is rigid and horizontal. The pole must be strong enough to resist the shear force caused by the weight of the sign.

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Key Concepts

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

Tension

Tension is the force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In the context of the sign hanging from the pole, the weight of the sign creates a downward force due to gravity, which results in tension in the pole or any supporting cables. Understanding tension is crucial for analyzing how the sign is supported and how forces are distributed.

Compression

Compression is the force that acts to reduce the volume of a material, effectively pushing its particles closer together. In this scenario, the pole experiences compression due to the weight of the sign hanging from it. This force must be considered to ensure that the pole can withstand the load without buckling or failing, making it essential for structural integrity.

Shear

Shear refers to the force that causes parts of a material to slide past one another in opposite directions. In the case of the sign and pole, shear forces may arise at the connection points where the sign is attached to the pole, especially if there are any lateral forces acting on the sign. Analyzing shear is important to ensure that the connections can handle these forces without failing.

Related Practice

Textbook Question

A uniform 95-kg flagpole of length 8.4 m is being erected by pulling on a rope attached 2/3 of the way to the top (Fig. 12–94). When the pole is inclined at 35° and the rope makes an angle with the ground of 18°, what is the tension in the rope?

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Textbook Question

A 50-story building is being planned. It is to be 180.0 m high with a base 46.0 m by 76.0 m. Its total mass will be about 1.8 x 10⁷ kg, and its weight therefore about 1.8 x 10⁸ N. Suppose a 200-km/h wind exerts a force of 950N/m² over the 76.0-m-wide face (Fig. 12–86). Calculate the torque about the potential pivot point, the rear edge of the building (where $\vec{F_{E}}$ acts in Fig. 12–86), and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building’s face, and that the building is not anchored in bedrock. [Hint: $\vec{F_{E}}$ in Fig. 12–86 represents the force that the Earth would exert on the building in the case where the building would just begin to tip.]

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Textbook Question

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). If the pole is not to fall off, there must be another torque exerted to balance it. What exerts this torque? Use a diagram to show how this torque must act.

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Textbook Question

When a mass of 25 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12° with the horizontal as shown in Fig. 12–90. Determine the radius of the wire.

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Textbook Question

A 25-kg object is being lifted by two people pulling on the ends of a 1.15-mm-diameter nylon cord that goes over two 3.00-m-high poles that are 4.5 m apart, as shown in Fig. 12–93. How high above the floor will the object be when the cord breaks?

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Textbook Question

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88). What is the torque due to this sign calculated about the point where the pole meets the wall?

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