Domanda del libro di testo
A 4.0-cm-diameter, 55 g ball is shot horizontally into a tank of 40°C honey. How long will it take for the horizontal speed to decrease to 10% of its initial value?
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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 66
What is the magnitude of the acceleration of a skydiver at the instant she is falling at one-half her terminal speed?
Guida verificata passo dopo passo1
Understand the problem: The skydiver is falling at half of her terminal speed. At terminal velocity, the net force acting on the skydiver is zero because the gravitational force is balanced by the drag force. At half the terminal speed, the forces are not balanced, so we need to calculate the net force and use Newton's second law to find the acceleration.
Express the drag force: The drag force is proportional to the square of the velocity. Mathematically, it can be written as \( F_{\text{drag}} = k v^2 \), where \( k \) is a proportionality constant and \( v \) is the velocity.
Relate the drag force at half terminal speed: At terminal velocity \( v_t \), the drag force equals the gravitational force \( F_g = mg \). Therefore, \( k v_t^2 = mg \). At half the terminal speed, the drag force becomes \( F_{\text{drag}} = k (v_t / 2)^2 = \frac{1}{4} k v_t^2 \). Substituting \( k v_t^2 = mg \), we get \( F_{\text{drag}} = \frac{1}{4} mg \).
Determine the net force: The net force acting on the skydiver is the difference between the gravitational force and the drag force. Thus, \( F_{\text{net}} = F_g - F_{\text{drag}} = mg - \frac{1}{4} mg = \frac{3}{4} mg \).
Apply Newton's second law: Use \( F_{\text{net}} = ma \) to find the acceleration. Substituting \( F_{\text{net}} = \frac{3}{4} mg \), we get \( a = \frac{F_{\text{net}}}{m} = \frac{\frac{3}{4} mg}{m} = \frac{3}{4} g \). The magnitude of the acceleration is \( \frac{3}{4} g \).
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Terminal Velocity
Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. For a skydiver, this occurs when the force of gravity is balanced by the drag force due to air resistance, resulting in zero net acceleration.
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Percorso guidato
7:27
Escape Velocity
Acceleration
Acceleration is the rate of change of velocity of an object with respect to time. In the context of a skydiver, it is influenced by gravitational force and air resistance. At one-half terminal speed, the skydiver experiences a net force that results in a specific acceleration, which can be calculated using Newton's second law.
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Percorso guidato
05:47Intro to Acceleration
Newton's Second Law of Motion
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as F = ma. This principle is essential for determining the acceleration of the skydiver, as it allows us to calculate the forces acting on her at different speeds, including the effects of gravity and drag.
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Percorso guidato
06:54Intro to Forces & Newton's Second Law
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