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

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

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

Problem 25a

Chapter 1, Problem 25a

(a) Calculate the kinetic energy, in joules, of a 15-g bullet moving at 120 m/s.

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Identify the formula for kinetic energy: \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass in kilograms and \( v \) is the velocity in meters per second.

Convert the mass of the bullet from grams to kilograms by dividing by 1000. For a 15-g bullet, the mass \( m = 0.015 \) kg.

Substitute the mass \( m = 0.015 \) kg and the velocity \( v = 120 \) m/s into the kinetic energy formula.

Calculate the expression \( \frac{1}{2} \times 0.015 \times (120)^2 \) to find the kinetic energy in joules.

Ensure the units are consistent and the calculation is correct to determine the kinetic energy in joules.

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Key Concepts

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

Kinetic Energy Formula

Kinetic energy (KE) is the energy an object possesses due to its motion. It is calculated using the formula KE = 0.5 * m * v², where m is the mass in kilograms and v is the velocity in meters per second. This formula highlights the relationship between mass, velocity, and energy, indicating that kinetic energy increases with the square of the velocity.

Unit Conversion

In physics, it is often necessary to convert units to ensure consistency in calculations. In this question, the mass of the bullet is given in grams, which must be converted to kilograms (1 g = 0.001 kg) to use the kinetic energy formula correctly. Proper unit conversion is crucial for obtaining accurate results in scientific calculations.

Joules as a Unit of Energy

The joule (J) is the standard unit of energy in the International System of Units (SI). It is defined as the energy transferred when a force of one newton is applied over a distance of one meter. Understanding that kinetic energy will be expressed in joules helps in interpreting the results of the calculation and its relevance in physical contexts.

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Related Practice

Textbook Question

What is the kinetic energy and velocity of the aluminum sphere in Problem 1.4 at the moment it hits the ground? (Assume that energy is conserved during the fall and that 100% of the sphere's initial potential energy is converted to kinetic energy by the time impact occurs.)

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Textbook Question

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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Textbook Question

Two positively charged particles are first brought close together and then released. Once released, the repulsion between particles causes them to move away from each other. (b) Does the potential energy of the two particles prior to release increase or decrease as the distance between them is increased.

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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