Textbook Question
A -kg box moving at m/s on a horizontal, frictionless surface runs into a light spring of force constant N/cm. Use the work–energy theorem to find the maximum compression of the spring.
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Ch 06: Work & Kinetic Energy
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 6, Problem 16a
A -kg book is sliding along a rough horizontal surface. At point it is moving at m/s, and at point it has slowed to m/s. How much work was done on the book between and ?
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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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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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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Related Practice
Textbook Question
A factory worker pushes a -kg crate a distance of m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is . What is the total work done on the crate?
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Textbook Question
You throw a -N rock vertically into the air from ground level. You observe that when it is m above the ground, it is traveling at m/s upward. Use the work–energy theorem to find its maximum height.
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Textbook Question
Two tugboats pull a disabled supertanker. Each tug exerts a constant force of N, one west of north and the other east of north, as they pull the tanker km toward the north. What is the total work they do on the supertanker?
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Textbook Question
You throw a -N rock vertically into the air from ground level. You observe that when it is m above the ground, it is traveling at m/s upward. Use the work–energy theorem to find the rock's speed just as it left the ground.
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Textbook Question
A factory worker pushes a -kg crate a distance of m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is . How much work is done on the crate by the normal force? By gravity?
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