Domanda del libro di testo
FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. Where are the particle's turning points?
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Ch 10: Interactions and Potential 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 10, Problema 31
A system in which only one particle moves has the potential energy shown in FIGURE EX10.31. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?
Guida verificata passo dopo passo1
Step 1: Recall the relationship between force and potential energy. The force acting on a particle is given by the negative gradient of the potential energy function: F_x = -dU/dx.
Step 2: Analyze the graph of potential energy (U) versus position (x). The graph shows linear segments where the slope of U changes. Identify the slope of U in the regions of interest: x = 5 cm, x = 15 cm, and x = 25 cm.
Step 3: For x = 5 cm, observe that this point lies in the region where U is increasing linearly from 0 to 10 J between x = 0 cm and x = 4 cm. Calculate the slope of this segment using the formula: slope = (change in U) / (change in x).
Step 4: For x = 15 cm, note that this point lies outside the range of the graph provided (x = 0 cm to x = 10 cm). Since the graph does not extend to x = 15 cm, the force at this position cannot be determined from the given data.
Step 5: For x = 25 cm, similarly, this point lies outside the range of the graph provided. The force at this position cannot be determined from the given data.
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Potential Energy (U)
Potential energy is the energy stored in a system due to the position of an object within a force field, such as gravitational or elastic fields. In the context of the given graph, potential energy is plotted against position, indicating how the energy changes as the particle moves. The shape of the graph reveals regions of stable and unstable equilibrium, which are crucial for understanding the forces acting on the particle.
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Percorso guidato
06:35
Gravitational Potential Energy
Force and Potential Energy Relationship
The force acting on a particle can be derived from the potential energy function using the relationship F = -dU/dx, where F is the force and U is the potential energy. This means that the force is equal to the negative gradient of the potential energy with respect to position. By analyzing the slope of the potential energy graph at specific positions, one can determine the x-component of the force acting on the particle.
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Percorso guidato
03:43Relationships Between Force, Field, Energy, Potential
Equilibrium Points
Equilibrium points occur where the net force acting on a particle is zero, which corresponds to the local maxima or minima of the potential energy graph. At these points, the particle experiences no net force and can be in stable (minimum) or unstable (maximum) equilibrium. Understanding these points is essential for predicting the behavior of the particle as it moves through different positions along the x-axis.
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Percorso guidato
10:13Torque & Equilibrium
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