Textbook Question
A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s2?
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Ch 14: Periodic Motion
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 14, Problem 47
A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?
Verified step by step guidance1
Identify the problem as a simple pendulum problem, where the light fixture acts as a pendulum bob. The frequency of a simple pendulum depends on the length of the pendulum and the acceleration due to gravity.
Recall the formula for the period of a simple pendulum: , where is the length of the pendulum and is the acceleration due to gravity (approximately 9.81 m/s²).
Substitute the given length of the cord, m, into the period formula: .
Calculate the period using the formula. This will give you the time it takes for one complete swing back and forth.
Determine the frequency of the pendulum, which is the number of swings per second, by taking the reciprocal of the period: .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion
Simple harmonic motion describes the oscillatory motion of objects like pendulums, where the restoring force is proportional to the displacement. In this context, the light fixtures act as pendulums, swinging back and forth due to gravitational forces, which can be modeled using the principles of simple harmonic motion.
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Simple Harmonic Motion of Pendulums
Pendulum Formula
The period of a simple pendulum is determined by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula helps calculate the time it takes for one complete swing, which is essential for determining the frequency of oscillation during an earthquake.
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Frequency of Oscillation
Frequency refers to the number of complete cycles or swings per second, calculated as the inverse of the period (f = 1/T). Understanding frequency is crucial for determining how many swings per second the light fixtures will make during an earthquake, providing insight into their oscillatory behavior.
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Related Practice
Textbook Question
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take the pendulum bob to reach its highest speed?
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Textbook Question
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?
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Textbook Question
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is at its highest point.
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Textbook Question
A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35). (c) Which of the answers in parts (a) and (b) is more accurate? What is the percentage error of the less accurate answer compared with the more accurate one?
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Textbook Question
A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35).
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