Domanda del libro di testo
A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium. What is the book's maximum speed?
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Ch 15: Oscillations
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 15, Problema 25
A pendulum is made by tying a 75 g ball to a 130-cm-long string. The ball is pulled 5.0° to the side and released. How many times does the ball pass through the lowest point of its arc in 7.5 s?
Guida verificata passo dopo passo1
Convert the given mass of the ball (75 g) into kilograms by dividing by 1000, as SI units require mass in kilograms.
Determine the length of the pendulum in meters by converting the given length of 130 cm into meters (divide by 100).
Use the formula for the period of a simple pendulum: , where is the length of the pendulum and is the acceleration due to gravity (approximately 9.8 m/s²). Substitute the value of into the formula to calculate the period .
Determine the number of oscillations the pendulum completes in 7.5 seconds by dividing the total time (7.5 s) by the period .
Since the ball passes through the lowest point of its arc twice per oscillation (once in each direction), multiply the number of oscillations by 2 to find the total number of times the ball passes through the lowest point in 7.5 seconds.
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Pendulum Motion
A pendulum exhibits periodic motion, swinging back and forth around a pivot point. The time it takes to complete one full cycle is called the period, which depends on the length of the string and the acceleration due to gravity, but not on the mass of the pendulum bob. For small angles, the motion can be approximated as simple harmonic motion.
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07:52
Simple Harmonic Motion of Pendulums
Period of a Pendulum
The period of a simple pendulum can be calculated using the formula T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity (approximately 9.81 m/s²). This formula shows that the period increases with the length of the pendulum and is independent of the mass of the bob, making it crucial for determining how often the pendulum swings.
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06:28Satellite Period
Frequency of Motion
Frequency is the number of complete cycles of motion that occur in a unit of time, typically measured in hertz (Hz). It is the reciprocal of the period (f = 1/T). In the context of the pendulum, knowing the frequency allows us to calculate how many times the pendulum passes through the lowest point in a given time frame, such as 7.5 seconds.
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05:08Circumference, Period, and Frequency in UCM
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A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is the frequency of oscillation?
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In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum's damping constant is only 0.010 kg/s. At exactly 12:00 noon, how many oscillations will the pendulum have completed and what is its amplitude?
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Domanda del libro di testo
A spring is hanging from the ceiling. Attaching a 500 g physics book to the spring causes it to stretch 20 cm in order to come to equilibrium. From equilibrium, the book is pulled down 10 cm and released. What is the period of oscillation?
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