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Physics For Scientists & Engineers
Found in: Page 472
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

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Short Answer

If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when it is moved to the top of the mountain? Explain.

No. It won’t keep perfect time when it is moved to the top of the mountain.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Relationship between displacement and time period

A simple pendulum of length L can be modeled to move in simple harmonic motion for small angular displacements from the vertical. Its period is

T=2πLg

T = Time period of oscillation

L = Length of string

g = Gravitational acceleration

Step 2: Explain the reasoning

  • The period of a pendulum depends on the acceleration of gravity T=2πLg.
  • If the acceleration of gravity is different at the top of the mountain, the period is different and the pendulum does not keep perfect time.
  • Two things will affect the acceleration of gravity; the top of the mountain is farther from the center of the Earth, and the nearby large mass of the mountain under the pendulum.

Most popular questions for Physics Textbooks

A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined. (i) When the elevator accelerates upward, is the period (a) greater, (b) smaller, or (c) unchanged? (ii) When the elevator has a downward acceleration, is the period (a) greater, (b) smaller, or (c) unchanged? (iii) When the elevator moves with constant upward velocity, is the period of the pendulum (a) greater, (b) smaller, or (c) unchanged?

Figure CQ15.5 shows graphs of the potential energy of four different systems versus the position of a particle in each system. Each particle is set into motion with a push at an arbitrarily chosen location. Describe its subsequent motion in each case (a), (b), (c), and (d).

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Consider the simplified single-piston engine in Figure CQ15.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion.

A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension. Find the frequency of vibration of the system for small values of the amplitude (small θ ). Assume the vertical suspension rod of length L is rigid, but ignore its mass.
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