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Ch. 07 - Work and Energy
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 07 - Work and EnergyProblem 10
Chapter 7, Problem 10

In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.25 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

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Determine the height of each shelf above the ground. The first shelf is 15.0 cm above the ground, and each subsequent shelf is spaced 38.0 cm higher. Convert these heights to meters for consistency in SI units: h₁ = 0.15 m, h₂ = 0.15 m + 0.38 m, h₃ = 0.15 m + 2(0.38 m), h₄ = 0.15 m + 3(0.38 m), h₅ = 0.15 m + 4(0.38 m).
Calculate the gravitational potential energy change for moving one book to each shelf. The formula for gravitational potential energy is ΔU = m * g * h, where m is the mass of the book (1.25 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the shelf. Compute ΔU for each shelf height.
Determine the total work required to fill one shelf. Each shelf holds 28 books, so the total work for one shelf is W_shelf = 28 * ΔU, where ΔU is the gravitational potential energy change for one book on that shelf.
Sum the work required for all shelves. Add the work for all five shelves: W_total = W₁ + W₂ + W₃ + W₄ + W₅, where W₁, W₂, etc., are the work values for each shelf.
Ensure all units are consistent and verify the calculations. The final result will represent the total work required to move all the books from the floor to their respective shelves.

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Key Concepts

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

Work in Physics

In physics, work is defined as the energy transferred when a force is applied to an object over a distance. It is calculated using the formula W = F × d, where W is work, F is the force applied, and d is the distance moved in the direction of the force. In this context, the work done to lift the books to the shelves involves calculating the gravitational force acting on the books and the height they are raised.
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Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It is given by the formula GPE = m × g × h, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height above a reference point. In this problem, the GPE of each book when lifted to a shelf height must be calculated to determine the total work done.
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Kinematics and Height Calculation

Kinematics involves the study of motion without considering the forces that cause it. In this scenario, understanding the vertical spacing of the shelves is crucial for calculating the height each book must be lifted. The first shelf is at 15.0 cm, and each subsequent shelf is spaced 38.0 cm above the previous one, leading to a systematic way to determine the height for each shelf and the total work required to fill them.
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Related Practice
Textbook Question

The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.65 m. What is the maximum amount of work it could do on the nail? Why do people not just “let it fall” but add their own force to the hammer as it falls?

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Textbook Question

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a horizontal force of about 15 N.

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Textbook Question

A 2.0-kg block slides across a rough surface with a constant coefficient of kinetic friction of 0.50 (Fig. 7–38a). The block starts at x= 0 with an initial velocity of 4.9 m/s. Pushing the block is a force directed at 36.8° below the horizontal and whose magnitude increases with position as shown in Fig. 7–38b.

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(d) Draw a line on the graph showing the magnitude of the friction force versus distance x.

Textbook Question

A grocery cart with mass of 16 kg is pushed at constant speed up a 12° ramp by a force FP which acts at an angle of 17° below the horizontal. Find the work done by each of the forces (mg→\(\overrightarrow{g}\), FN→\(\overrightarrow{F_{N}\)}_{}, FN→\(\overrightarrow{F_{N}\)}) on the cart if the ramp is 7.5 m long.

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Textbook Question

If the hill in Example 7–2 (Fig. 7–4) was not an even slope but rather an irregular curve as in Fig. 7–23, show that the same result would be obtained as in Example 7–2: namely, that the work done by gravity depends only on the height of the hill and not on its shape or the path taken.

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Textbook Question

The net force exerted on a particle acts in the positive x direction. Its magnitude increases linearly from zero at x = 0, to 380 N at x = 3.0m. It remains constant at 380 N from x = 3.0m to x = 7.0m, and then decreases linearly to zero at x = 12.0m. Determine the work done to move the particle from x = 0 to x = 12.0m graphically, by determining the area under the Fₓ versus x graph.

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