Domanda del libro di testo
A proton's speed as it passes point 1 is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton's speed at point 2?
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Ch 25: The Electric Potential
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 25, Problema 42
The four 1.0 g spheres shown in FIGURE P25.42 are released simultaneously and allowed to move away from each other. What is the speed of each sphere when they are very far apart?
Guida verificata passo dopo passo1
Identify the key concept: The problem involves the conservation of energy. Initially, the system has only electrostatic potential energy due to the charges on the spheres. As the spheres move far apart, this potential energy is converted into the kinetic energy of the spheres.
Write the expression for the initial electrostatic potential energy of the system. For four charges, calculate the potential energy between each pair of charges using the formula: \( U = \frac{k q_1 q_2}{r} \), where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them. Sum the potential energy contributions for all unique pairs.
Apply the conservation of energy principle: The total initial potential energy of the system is equal to the total final kinetic energy of the spheres. Use the formula for kinetic energy: \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass of each sphere and \( v \) is their speed.
Set up the equation: \( U_{initial} = 4 \times \frac{1}{2} m v^2 \), since there are four spheres, each with the same mass and speed. Solve for \( v \) in terms of the known quantities (\( k \), \( q \), \( r \), and \( m \)).
Substitute the given values for the charges, masses, and initial distances into the equation to calculate the speed \( v \). Ensure all units are consistent (e.g., convert grams to kilograms for mass).
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Conservation of Energy
The principle of conservation of energy states that the total energy in a closed system remains constant over time. In this scenario, the potential energy stored in the system due to the gravitational or electrostatic forces between the spheres will convert into kinetic energy as they move apart. This relationship allows us to calculate the final speed of the spheres when they are far apart.
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Percorso guidato
06:24
Conservation Of Mechanical Energy
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, defined mathematically as KE = 1/2 mv², where m is the mass and v is the velocity of the object. As the spheres move away from each other, their potential energy decreases while their kinetic energy increases, allowing us to determine their speeds at large distances based on the initial conditions.
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Percorso guidato
06:07Intro to Rotational Kinetic Energy
Electrostatic Force
Electrostatic force is the attractive or repulsive force between charged objects, described by Coulomb's law. In this problem, if the spheres are charged, the electrostatic repulsion will cause them to accelerate away from each other. Understanding this force is crucial for calculating the initial potential energy and how it transforms into kinetic energy as the spheres separate.
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Percorso guidato
06:48Intro to Centripetal Forces
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