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

Giancoli Douglas 5th edition

Ch. 07 - Work and Energy

Problem 4

Chapter 7, Problem 4

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?

Verified step by step guidance

Determine the potential energy of the hammer at the initial height using the formula for gravitational potential energy:

E p_{i} = m g h

, where

m

is the mass of the hammer (1.2 kg),

g

is the acceleration due to gravity (9.8 m/s²), and

h

is the height (0.65 m).

Recognize that the maximum work the hammer can do on the nail is equal to the initial potential energy of the hammer, assuming no energy is lost to air resistance or other factors. This is because the potential energy is fully converted into kinetic energy at the moment of impact, which is then transferred to the nail.

Substitute the given values into the potential energy formula:

E p_{i} = (1.2 \, kg)(9.8 \, m/s ²)(0.65 \, m)

. This will give the maximum work the hammer can do on the nail.

Understand why people add their own force to the hammer as it falls: By applying an additional force, they increase the total energy of the system. This added force increases the hammer's kinetic energy at the moment of impact, allowing it to do more work on the nail than it would if it were simply allowed to fall under gravity alone.

Conclude that the maximum work calculated assumes ideal conditions (no energy losses), but in real-world scenarios, adding force compensates for energy losses and increases the efficiency of driving the nail into the material.

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Key Concepts

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

Work and Energy

Work is defined as the transfer of energy that occurs when a force is applied over a distance. In this context, the work done by the hammer on the nail can be calculated using the formula W = F × d, where W is work, F is the force applied, and d is the distance over which the force is applied. The maximum work done by the hammer is equal to its potential energy at the height from which it falls, which can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height.

Potential Energy

Potential energy is the energy stored in an object due to its position in a gravitational field. For the hammer, as it is raised to a height of 0.65 m, it accumulates gravitational potential energy, which is given by the equation PE = mgh. When the hammer falls, this potential energy is converted into kinetic energy and ultimately into work done on the nail upon impact, illustrating the conservation of energy principle.

Force Addition in Hammering

When people swing a hammer, they apply additional force to increase the hammer's speed and momentum before it strikes the nail. This added force not only increases the kinetic energy of the hammer but also enhances the work done on the nail upon impact. By applying their own force, users can ensure that the hammer delivers a greater impact, making it more effective in driving the nail compared to simply letting it fall under gravity.

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Related Practice

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 55.0-kg firefighter climbs a flight of stairs 28.0 m high at constant speed. How much work does she do?

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Textbook Question

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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