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

Problem 28

Chapter 1, Problem 28

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.

Verified step by step guidance

insert step 1> Identify the concepts involved in the problem: kinetic energy, potential energy, and gravitational force.

insert step 2> Understand that kinetic energy (KE) is the energy of motion, given by the formula KE = \( \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity.

insert step 3> Recognize that potential energy (PE) in this context is gravitational potential energy, given by the formula PE = \( mgh \), where \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is height.

insert step 4> Analyze statement i: At the moment the ball is dropped, its velocity is zero, so its kinetic energy is zero. Therefore, statement i is false.

insert step 5> Analyze statements ii and iii: As the ball falls, its height decreases, reducing potential energy and increasing kinetic energy, confirming statement ii. The potential energy is due to gravity, confirming statement iii.

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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, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. As the soccer ball falls, its velocity increases, leading to an increase in kinetic energy. However, at the moment it is dropped, its kinetic energy is zero since it is not yet in motion.

Potential Energy

Potential energy is the stored energy of an object due to its position or state, commonly associated with gravitational potential energy, which is calculated as PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height. In this scenario, the soccer ball has maximum potential energy when it is at the window height, which decreases as it falls.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. As the soccer ball falls, its potential energy is converted into kinetic energy, illustrating this principle. The total mechanical energy (potential + kinetic) remains constant in the absence of air resistance.

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