Domanda del libro di testo
A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if: The box moves at a steady 5.0 m/s?
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Ch 06: Dynamics I: Motion Along a Line
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 6, Problema 13c
A 50 kg box hangs from a rope. What is the tension in the rope if: The box has vy = 5.0 m/s and is speeding up at 5.0 m/s2
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Identify the forces acting on the box: The box is subject to two forces: the gravitational force (weight) acting downward and the tension in the rope acting upward. The net force is responsible for the box's acceleration.
Write the equation for the net force using Newton's Second Law: \( F_{\text{net}} = ma \), where \( m \) is the mass of the box and \( a \) is its acceleration. The net force is also the difference between the tension \( T \) and the gravitational force \( F_g \).
Express the gravitational force: \( F_g = mg \), where \( g \) is the acceleration due to gravity (approximately \( 9.8 \ \text{m/s}^2 \)). Substitute \( m = 50 \ \text{kg} \) into this equation.
Combine the equations: The net force is \( T - F_g = ma \). Rearrange this to solve for the tension: \( T = ma + F_g \). Substitute \( F_g = mg \) into the equation, resulting in \( T = ma + mg \).
Substitute the known values: Use \( m = 50 \ \text{kg} \), \( a = 5.0 \ \text{m/s}^2 \), and \( g = 9.8 \ \text{m/s}^2 \) into the equation \( T = ma + mg \). Simplify to find the tension in the rope.
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Newton's Second Law of Motion
Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for analyzing the forces acting on the box, including gravitational force and tension in the rope, especially when the box is accelerating.
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Percorso guidato
06:54
Intro to Forces & Newton's Second Law
Tension in a Rope
Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the rope must counteract both the weight of the box and provide the additional force required for its upward acceleration.
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Percorso guidato
06:34Calculating Tension in a Pendulum with Energy Conservation
Weight of an Object
The weight of an object is the force exerted on it due to gravity, calculated as the product of its mass and the acceleration due to gravity (W = mg). For the 50 kg box, this weight must be considered alongside the upward tension when determining the net force acting on the box as it accelerates.
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Percorso guidato
10:19Torque Due to Weight
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