Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 32

Chapter 1, Problem 32

For each of the following processes, does the potential energy of the object(s) increase or decrease? (b) Water is pumped from ground level to the reservoir of a water tower 30 m above the ground.

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Identify the initial and final positions of the water: initially at ground level and finally at 30 m above ground in the reservoir.

Understand that potential energy is related to the height of an object above a reference point, typically calculated using the formula: \(PE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height above the reference point.

Recognize that as the water is pumped from ground level to a higher elevation, its height \(h\) increases.

Since the height \(h\) increases, the potential energy of the water also increases according to the formula \(PE = mgh\).

Conclude that the potential energy of the water increases as it is pumped to the reservoir 30 m above the ground.

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Key Concepts

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

Potential Energy

Potential energy is the energy stored in an object due to its position or configuration. In the context of gravitational potential energy, it is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above a reference point. As an object is raised to a higher position, its potential energy increases because it has the capacity to do work due to its elevated position.

Work Done Against Gravity

When an object is moved against the force of gravity, work is done on the object. This work results in an increase in the object's potential energy. In the case of pumping water to a height, energy is expended to lift the water, which translates into an increase in its gravitational potential energy as it is elevated to the reservoir.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the scenario of pumping water, the mechanical energy used to pump the water is converted into gravitational potential energy as the water is raised to a higher elevation. This principle helps to understand how energy is transferred and transformed in physical processes.

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Textbook Question

(a) Calculate the kinetic energy (in joules) of a 1200-kg automobile moving at 18 m/s.

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Textbook Question

A soccer ball is dropped out of a window on the second floor of a dormitory to the ground below. Which of the following statements is or are true?

i. The kinetic energy of the ball is greatest at the time it is dropped out the window.

ii. As the ball falls, potential energy is converted into kinetic energy.

iii. The potential energy of the ball is due to the force of gravity acting on it.

Textbook Question

Use appropriate metric prefixes to write the following measurements without use of exponents: c. 6.48×10^-7L

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Textbook Question

Use appropriate metric prefixes to write the following measurements without use of exponents: d. 1.81×10^-2 s

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Textbook Question

Use appropriate metric prefixes to write the following measurements without use of exponents: g. 5.1×10²cm

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Textbook Question

A silvery metal is put inside a beaker of water. Bubbles form on the surface of the metal and it dissolves gradually. (a) Is this an example of a chemical or a physical change?

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