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Ch 06: Work & Kinetic Energy
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 16a

A 1.501.50-kg book is sliding along a rough horizontal surface. At point AA it is moving at 3.213.21 m/s, and at point BB it has slowed to 1.251.25 m/s. How much work was done on the book between AA and BB?

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Step 1: Identify the given values from the problem. The mass of the book is \( m = 1.50 \, \text{kg} \), the initial velocity at point A is \( v_A = 3.21 \, \text{m/s} \), and the final velocity at point B is \( v_B = 1.25 \, \text{m/s} \).
Step 2: Recall the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. The formula for kinetic energy is \( KE = \frac{1}{2} m v^2 \).
Step 3: Calculate the initial kinetic energy at point A using \( KE_A = \frac{1}{2} m v_A^2 \). Substitute \( m = 1.50 \, \text{kg} \) and \( v_A = 3.21 \, \text{m/s} \) into the formula.
Step 4: Calculate the final kinetic energy at point B using \( KE_B = \frac{1}{2} m v_B^2 \). Substitute \( m = 1.50 \, \text{kg} \) and \( v_B = 1.25 \, \text{m/s} \) into the formula.
Step 5: Determine the work done on the book by finding the change in kinetic energy: \( W = KE_B - KE_A \). Substitute the values of \( KE_A \) and \( KE_B \) calculated in the previous steps.

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Concetti chiave

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Work-Energy Principle

The Work-Energy Principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, the work done on the book as it slides from point A to point B can be calculated by finding the difference in kinetic energy at these two points, which is determined by the mass of the book and its velocities.
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Percorso guidato
04:10
The Work-Energy Theorem

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity. For the book in this problem, we will compute its kinetic energy at both points A and B to determine how much it has changed as it slows down.
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Percorso guidato
06:07
Intro to Rotational Kinetic Energy

Friction and Work

Friction is a force that opposes the motion of an object, and it does work on the object by removing energy from the system. In this case, the rough surface exerts a frictional force on the book, which contributes to the work done on the book as it slows down from point A to point B, affecting its kinetic energy.
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Percorso guidato
04:29
Work Done By Friction
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