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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Ch 14: Periodic Motion
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 14, Problem 46
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?
Verified step by step guidance1
Understand the formula for the period of a simple pendulum: , where is the period, is the length of the pendulum, and is the acceleration due to gravity.
Recognize that the period of the pendulum depends on the gravitational acceleration. On Earth, .
Since the period on Earth is given as 1.60 s, use the formula to express the length of the pendulum in terms of the period and Earth's gravity: .
Substitute the known values into the formula to find the length of the pendulum: .
Use the length of the pendulum and the gravitational acceleration on Mars to find the new period: . Substitute the value of from the previous step to calculate the period on Mars.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Pendulum
A simple pendulum consists of a mass (called the bob) attached to a string or rod of fixed length, which swings back and forth under the influence of gravity. The period of a simple pendulum is the time it takes to complete one full oscillation, and it depends on the length of the pendulum and the acceleration due to gravity.
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Simple Harmonic Motion of Pendulums
Period of a Pendulum
The period of a simple pendulum is given 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 shows that the period is directly proportional to the square root of the length and inversely proportional to the square root of the gravitational acceleration.
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Gravitational Acceleration
Gravitational acceleration (g) is the acceleration of an object due to the force of gravity acting on it. On Earth, g is approximately 9.81 m/s², but it varies on other planets. For example, on Mars, g is about 3.71 m/s². This difference in gravitational acceleration affects the period of a pendulum, as seen in the pendulum period formula.
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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 if the pendulum is released at an angle of 1.75° instead of 3.50°?
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Textbook Question
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?
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