Textbook Question
How much work must you do to push a 10 kg block of steel across a steel table at a steady speed of 1.0m/s for 3.0 s? What is your power output while doing so?
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Ch 09: Work and Kinetic Energy
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 9, Problem 34
Justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 11 m/s. How much thermal energy is created by friction during his descent?
Verified step by step guidance1
Step 1: Identify the energy transformations involved. Justin starts at rest, so his initial energy is purely gravitational potential energy. At the bottom of the slide, he has kinetic energy, and some energy is lost as thermal energy due to friction.
Step 2: Calculate Justin's initial gravitational potential energy using the formula: , where is his mass (30 kg), is the acceleration due to gravity (9.8 m/s²), and is the height of the slide (8.0 m).
Step 3: Calculate Justin's kinetic energy at the bottom of the slide using the formula: , where is his mass (30 kg) and is his speed at the bottom (11 m/s).
Step 4: Determine the total energy lost to friction by subtracting the final kinetic energy from the initial gravitational potential energy. Use the formula: .
Step 5: Verify the units of your calculations to ensure consistency (e.g., joules for energy) and interpret the result as the amount of thermal energy generated by friction during Justin's descent.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Conservation of Energy
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, Justin's potential energy at the top of the slide is converted into kinetic energy as he descends. Any difference between the initial potential energy and the final kinetic energy indicates energy lost to friction, which manifests as thermal energy.
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Conservation Of Mechanical Energy
Potential Energy
Potential energy is the energy stored in an object due to its position in a gravitational field. For Justin, this is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height. At the top of the slide, his potential energy is at its maximum, which decreases as he descends, converting into kinetic energy and thermal energy due to friction.
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Kinetic Energy
Kinetic energy is the energy of an object in motion, defined by the formula KE = 0.5mv², where m is mass and v is velocity. At the bottom of the slide, Justin's kinetic energy reflects his speed. The difference between the initial potential energy and the final kinetic energy helps quantify the thermal energy generated by friction during his descent.
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Related Practice
Textbook Question
An 8.0 kg crate is pulled 5.0 m up a 30° incline by a rope angled 18 ° above the incline. The tension in the rope is 120 N, and the crate's coefficient of kinetic friction on the incline is 0.25. What is the increase in thermal energy of the crate and incline?
Textbook Question
A 55 kg softball player slides into second base, generating 950 J of thermal energy in her legs and the ground. How fast was she running?
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Textbook Question
A baggage handler throws a 15 kg suitcase along the floor of an airplane luggage compartment with a speed of 1.2 m/s. The suitcase slides 2.0 m before stopping. Use work and energy to find the suitcase's coefficient of kinetic friction on the floor.
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Textbook Question
How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m?
Textbook Question
A horizontal spring with spring constant 85 N/m extends outward from a wall just above floor level. A 1.5 kg box sliding across a frictionless floor hits the end of the spring and compresses it 6.5 cm before the spring expands and shoots the box back out. How fast was the box going when it hit the spring?