Chapter 1, Problem 24PS

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

A book is held at a height above the floor. It has a certain amount of potential energy. When the book is released, its potential energy is converted to kinetic energy as it falls to the floor. The book hits the floor and comes to rest. According to the law of conservation of energy the amount of energy in the universe is constant. Where has the energy gone?

Interpretation Introduction

Interpretation:

The transformation of energy by the book as it falls on the floor has to be given.

Concept introduction:

Energy:

Energy is the capacity to do work, and can neither be created nor destroyed.  Generally, chemical reaction almost always either release or absorb energy.

Law of energy conservation: The total energy of an isolated system remains constant, it is conserved over time.

Types of energy:

Kinetic energy: Energy associated with motion. Thermal energy, mechanical energy, electrical energy, and acoustic energy are categorized in kinetic energy.

Potential energy: Energy results from an object’s position or state. Gravitational energy, chemical energy, and electrostatic energy.

Explanation

Case 1: When a book is placed at height â€˜hâ€™ above the floor.

When the book is placed at height â€˜hâ€™, it will gain potential energy. The potential energy of the book at height â€˜hâ€™ is,

PotentialÂ energyÂ (P.E)Â =Â â€‰mgh

The kinetic energy of book at height â€˜hâ€™ is

â€‚Â KineticÂ energyÂ (K.E)Â =Â â€‰12mV2whereÂ velocityÂ ofÂ bookÂ isÂ 'zero'(K.E)Â =Â â€‰12m(0)2Â =â€‰Â 0

The total energy is given as,

â€‚Â TotalÂ energyÂ =Â P.EÂ +Â KineticÂ energyÂ (K.E)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =Â mghÂ +Â 0Total energy (T.E) = mgh (P.E) --------> (1)

Case 2: When a book is placed at height â€˜hâ€™ and reaches the floor.

When the book is dropped, it moves freely downwards due to gravitational force. Â Hence, gradually its potential energy decreases and the kinetic energy increase. Â Finally, the book reaches the ground.

On the floor, the potential energy of book is,

â€‚Â PotentialÂ energyÂ (P.E)Â =Â â€‰mghwhereÂ 'h'Â isÂ zero(P

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