Ch 14: Periodic Motion

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 15th Edition

Ch 14: Periodic Motion

문제 45

14장, 문제 45

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?

검증된 단계별 안내

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:

T = 2 π \sqrt{\frac{l}{g}}

, where

l

is the length of the pendulum and

g

is the acceleration due to gravity (approximately 9.81 m/s²).

Substitute the given length of the cord,

l = 1.50

m, into the period formula:

T = 2 π \sqrt{\frac{1.50}{9.81}}

Calculate the period

T

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:

f = \frac{1}{T}

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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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