Ch. 14 - Oscillations

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 14 - Oscillations

Problem 46b

Chapter 14, Problem 46b

What is the period of a simple pendulum 47 cm long when it is in a freely falling elevator?

Verified step by step guidance

Step 1: Recall the formula for the period of a simple pendulum in normal conditions:

T = 2π√(L/g)

, where

T

is the period,

L

is the length of the pendulum, and

g

is the acceleration due to gravity.

Step 2: For part (b), consider the scenario of a freely falling elevator. In this case, the effective acceleration due to gravity,

g_{\(\text{eff}\)}

, becomes zero because the elevator and the pendulum are both in free fall.

Step 3: Substitute

g_{\(\text{eff}\)} = 0

into the formula for the period. The equation becomes undefined because the denominator contains

g

, and division by zero is not possible.

Step 4: Conclude that in a freely falling elevator, the pendulum does not oscillate because there is no restoring force acting on it. The concept of a period is therefore not applicable in this situation.

Step 5: Summarize that the pendulum's motion ceases in free fall, and the period cannot be determined under these conditions.

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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 (or bob) attached to a string or rod of negligible mass, swinging back and forth under the influence of gravity. The period of a simple pendulum, which is the time taken for one complete cycle of motion, is primarily determined by its length and the acceleration due to gravity. The formula for the period (T) is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

Effect of Gravity on Period

The period of a simple pendulum is directly influenced by the acceleration due to gravity (g). In a standard environment, g is approximately 9.81 m/s². However, if the pendulum is in a freely falling elevator, the effective gravitational force acting on it becomes zero, as both the pendulum and the elevator are accelerating downwards at the same rate. This results in the pendulum experiencing weightlessness, which alters its oscillatory motion.

Free Fall and Weightlessness

Free fall occurs when an object is falling under the influence of gravity alone, without any other forces acting on it. In a freely falling elevator, both the elevator and any objects inside it, including a pendulum, experience weightlessness. This means that the pendulum does not exert tension on the string, leading to a situation where it cannot oscillate in the traditional sense, effectively making its period undefined in this scenario.

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