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

Problem 29a

Chapter 1, Problem 29a

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

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Identify the mass (m) of the automobile and its velocity (v). In this problem, the mass is 1200 kg and the velocity is 18 m/s.

Recall the formula for kinetic energy (KE), which is given by KE = \(\frac{1}{2}mv^2\).

Substitute the values of mass and velocity into the kinetic energy formula. So, plug in m = 1200 kg and v = 18 m/s into the equation.

Perform the squaring of the velocity, which is 18 m/s. Calculate \(18^2\).

Multiply the result from the previous step by the mass and then by 0.5 (or divide by 2) to find 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

Kinetic energy 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 of the object in kilograms and 'v' is its velocity in meters per second. This concept is fundamental in physics and helps in understanding how the speed and mass of an object contribute to its energy.

Units of Measurement

In physics, it is crucial to use consistent units when performing calculations. Kinetic energy is measured in joules (J), where 1 joule is equivalent to 1 kg·m²/s². Understanding how to convert and apply these units correctly is essential for accurate calculations in problems involving energy.

Mass and Velocity Relationship

The relationship between mass and velocity is significant in determining kinetic energy. As mass increases, kinetic energy increases linearly, while an increase in velocity results in a quadratic increase in kinetic energy. This means that small changes in velocity can lead to large changes in kinetic energy, highlighting the importance of both factors in motion-related calculations.

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Textbook Question

For each of the following processes, would filtration, distillation, or chromatography be the most effective separation technique:

a. removing the pulp from freshly squeezed orange juice,

b. separating a food dye into its individual components,

c. desalinating seawater?

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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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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

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. a. This is an example of potential energy being converted into what form of energy?

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 electrostatic potential energy of the two particles increase or decrease as the distance between them is increased?