Let's analyze how the potential and kinetic energy change during the process of the book sliding across the table.
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Potential Energy: The potential energy of the book does not change throughout this process as long as it stays on the flat table. Potential energy is determined by the height of the object in a gravitational field. Since the book remains at the same height above the ground while resting on the table, its potential energy remains constant.
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Kinetic Energy: When the person shoves the book, it gains kinetic energy due to the force applied. The kinetic energy is given by the equation \( KE = \frac{1}{2} mv^2 \), where \( m \) is the mass of the book and \( v \) is its velocity. As the book slides across the table, it starts with a certain kinetic energy that increases upon being shoved. However, due to friction between the book and the table, the kinetic energy gradually decreases as the book slows down until it eventually comes to rest.
Putting this together:
- Potential energy remains constant throughout the process because the height of the book does not change.
- Kinetic energy increases as the book is powered forward by the shove and then decreases as friction slows it down.
The correct statement among those provided is:
The potential energy will stay the same as long as the book stays on the table. The kinetic energy increases when the book is shoved and then gradually decreases as it slides across the table and then comes to rest on the edge.
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