Domanda del libro di testo
You throw a 5.5 g coin straight down at 4.0 m/s from a 35-m-high bridge. What is the speed of the coin just as it hits the water?
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Ch 09: Work and Kinetic Energy
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 9, Problema 3
A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio vson/vmother of their speeds?
Guida verificata passo dopo passo1
Start by recalling the formula for kinetic energy: , where is the kinetic energy, is the mass, and is the velocity.
Since the mother and son have the same kinetic energy, set their kinetic energy expressions equal to each other: , where the mother's mass is four times the son's mass.
Cancel out the common terms, such as and , from both sides of the equation. This simplifies to: .
Take the square root of both sides to solve for the ratio of their speeds: .
Simplify the square root to find the ratio: . Thus, the son's speed is twice the mother's speed.
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Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Kinetic Energy
Kinetic energy (KE) is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, both the mother and son have the same kinetic energy, which implies a relationship between their masses and velocities that can be analyzed to find their speed ratio.
Video consigliato:
Percorso guidato
06:07
Intro to Rotational Kinetic Energy
Mass and Velocity Relationship
In physics, when two objects have the same kinetic energy, their masses and velocities are inversely related. Specifically, if one object has a greater mass, it must have a lower velocity to maintain the same kinetic energy as a lighter object. This principle is crucial for determining the speed ratio between the mother and son in the given problem.
Video consigliato:
Percorso guidato
20:32Mass Spectrometers
Ratio of Speeds
The ratio of speeds (v(son)/v(mother)) can be derived from the relationship between their masses and kinetic energies. Since the mother has four times the mass of her son and both have equal kinetic energy, we can set up a proportion based on their kinetic energy equations to find the exact ratio of their speeds, illustrating how mass affects velocity in motion.
Video consigliato:
Percorso guidato
07:59Speed Distribution & Special Speeds of Ideal Gases
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