Ch 11: Equilibrium & Elasticity

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 11: Equilibrium & Elasticity

Problem 18b

Chapter 11, Problem 18b

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

(a) 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 cen-ter of gravity of the load car-ried in the wheelbarrow is also 0.50 m from the center of the wheel. (b) Where does the force come from to enable you to lift more than 650 N using the wheelbarrow?

Verified step by step guidance

Step 1: Understand the problem setup. You have a wheelbarrow with a total length of 1.4 m. The center of gravity of the wheelbarrow itself and the load it carries are both 0.50 m from the wheel. You can lift a maximum of 650 N unaided.

Step 2: Apply the principle of moments (torque) to solve part (a). The torque due to the load and the wheelbarrow's weight must be balanced by the torque you apply. The torque is calculated as the force times the distance from the pivot point (the wheel).

Step 3: Calculate the torque due to the wheelbarrow's weight. The force is 80.0 N and the distance is 0.50 m. Use the formula: \( \text{Torque}_{\text{wheelbarrow}} = \text{Force}_{\text{wheelbarrow}} \times \text{Distance}_{\text{wheelbarrow}} \).

Step 4: Calculate the torque due to the load. Assume the load's weight is \( F_{\text{load}} \) and the distance is also 0.50 m. Use the formula: \( \text{Torque}_{\text{load}} = F_{\text{load}} \times 0.50 \).

Step 5: Set up the equation for equilibrium. The torque you apply (650 N at 1.4 m) must equal the sum of the torques from the wheelbarrow and the load. Solve for \( F_{\text{load}} \) using: \( 650 \times 1.4 = 80 \times 0.50 + F_{\text{load}} \times 0.50 \).

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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 the context of the wheelbarrow, torque helps determine how much weight can be lifted by considering the distances from the wheel to the center of gravity of the load and the handles where the force is applied.

Lever Principle

The lever principle states that a lever amplifies an input force to provide a greater output force, allowing a smaller force to lift a heavier load. The wheelbarrow acts as a second-class lever, where the wheel is the fulcrum, the load is between the fulcrum and the effort, enabling the user to lift more than their unaided capacity by increasing the effective force applied.

Center of Gravity

The center of gravity is the point where the total weight of a body or system is considered to be concentrated. For the wheelbarrow, understanding the center of gravity of both the wheelbarrow itself and the load is crucial for calculating the torque and ensuring balance, as it affects how the weight is distributed and how much force is needed to lift the load.

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Related Practice

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 9.00-m-long uniform beam is hinged to a vertical wall and held horizontally by a 5.00-m-long cable attached to the wall 4.00 m above the hinge (Fig. E11.17). The metal of this cable has a test strength of 1.00 kN, which means that it will break if the tension in it exceeds that amount. What is the heaviest beam that the cable can support in this configuration?

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Textbook Question

A 15,000-N crane pivots around a friction-free axle at its base and is supported by a cable making a 25° angle with the crane (Fig. E11.18). The crane is 16 m long and is not uniform, its center of gravity being 7.0 m from the axle as measured along the crane. The cable is attached 3.0 m from the upper end of the crane. When the crane is raised to 55° above the horizontal holding an 11,000-N pallet of bricks by a 2.2-m, very light cord, find the tension in the cable. Start with a free-body diagram of the crane.

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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

A 9.00 m-long uniform beam is hinged to a vertical wall and held horizontally by a 5.00 m-long cable attached to the wall 4.00 m above the hinge (Fig. E11.17). The metal of this cable has a test strength of 1.00 kN, which means that it will break if the tension in it exceeds that amount. Find the horizontal and vertical components of the force the hinge exerts on the beam. Is the vertical component upward or downward?

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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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