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 64b

Chapter 12, Problem 64b

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.

Verified step by step guidance

Identify the forces acting on the system: The sign exerts a downward gravitational force due to its weight, which is given by $ F_g = m \cdot g $, where $ m = 6.1 \, \text{kg} $ and $ g = 9.8 \, \text{m/s}^2 $. This force acts at a distance of 2.2 m from the wall, creating a torque about the point where the pole is attached to the wall.

Understand the concept of torque: Torque is the rotational equivalent of force and is calculated as $ \tau = F \cdot r \cdot \sin(\theta) $, where $ F $ is the force, $ r $ is the distance from the pivot point, and $ \theta $ is the angle between the force and the lever arm. In this case, $ \theta = 90^\circ $, so $ \sin(\theta) = 1 $.

Determine the torque due to the sign: The torque caused by the sign is $ \tau_{\text{sign}} = F_g \cdot r = (m \cdot g) \cdot r $. Substituting the values, $ \tau_{\text{sign}} = (6.1 \cdot 9.8) \cdot 2.2 $. This torque acts in a clockwise direction about the point where the pole is attached to the wall.

Identify the balancing torque: To prevent the pole from falling, there must be an equal and opposite (counterclockwise) torque exerted. This balancing torque is typically provided by a support force at the wall or a tension force in a supporting cable attached to the pole. The direction of this torque must oppose the torque caused by the sign.

Visualize the system: Draw a diagram showing the pole, the sign hanging from it, the gravitational force acting downward at 2.2 m from the wall, and the balancing force (e.g., tension in a cable or a reaction force at the wall) acting at an appropriate angle to create a counterclockwise torque. Ensure the torques are balanced, i.e., $ \tau_{\text{sign}} = \tau_{\text{balancing}} $.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). In this scenario, the weight of the sign creates a torque about the point where the pole is attached to the wall, which must be countered to prevent the pole from tipping over.

Equilibrium

Equilibrium in physics refers to a state where all forces and torques acting on an object are balanced, resulting in no net force or rotation. For the pole to remain stable, the torque produced by the weight of the sign must be balanced by an equal and opposite torque, ensuring that the pole does not rotate or fall.

Support Forces

Support forces are the forces exerted by a surface or structure to counteract the weight of an object resting on it. In this case, the wall provides a support force that helps to balance the torque created by the hanging sign, preventing the pole from falling due to the gravitational force acting on the sign.

Recommended video:

Guided course

14:31

Equilibrium with Multiple Supports

Related Practice

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.]

views

Textbook Question

The subterranean tension ring that surrounds the dome in Fig. 12–39 exerts the balancing horizontal force on the abutments for the dome and is 36-sided, so each segment makes a 10° angle with the adjacent one (Fig. 12–83). Calculate the tension F that must exist in each segment so that the required force of 4.2 x 10⁵ N can be exerted at each corner (Example 12–14).

views

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.

views

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?

views

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). Discuss whether compression, tension, and/or shear play a role in part (b).

views

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?

views