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Chapter 13: Problem 10

What will happen to the period of a mass-spring system if it's placed in a jetliner accelerating down a runway? What will happen to the period of a pendulum in the same situation?

Short Answer

Expert verified
The period of a mass-spring system remains the same when placed in a jetliner accelerating down a runway, whereas the period of a pendulum shortens in the same situation due to the change in effective gravity.

Step by step solution

01

Analyze the mass-spring system

The period \(T\) of a mass-spring system is given by \(T= 2\pi\sqrt{\frac{m}{k}}\), where \(m\) is the mass of the object and \(k\) is the spring constant. Neither \(m\) nor \(k\) depends on gravity or any external acceleration, hence the period remains the same, even if the system is accelerating down a runway in a jetliner.
02

Analyze the pendulum system

The period \(T\) of a simple pendulum, however, is given by \(T= 2\pi\sqrt{\frac{l}{g}}\), where \(l\) is the length of the pendulum and \(g\) is the acceleration due to gravity. When the jetliner accelerates down the runway, the effective gravity inside the jetliner changes, which changes the period.
03

Calculate the change in period

The exact change in period for the pendulum would depend on the acceleration of the jetliner. If the acceleration increases, it increases the effective gravity \(g'\) inside the jetliner, shortening the period of the pendulum: \(T'=2\pi\sqrt{\frac{l}{g'}}\), where \(g' > g\).

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Most popular questions from this chapter

The vibration of a piano string can be described by an equation analogous to Equation \(13.17 .\) If the quantity analogous to \(b / 2 m\) in that equation has the value \(4.4 \mathrm{~s}^{-1}\), how long will it take the amplitude to drop to half its original value?

Two mass-spring systems with the same mass are undergoing oscillatory motion with the same amplitudes. System 1 has thrice the frequency of system 2. How do (a) their energies and (b) their maximum accelerations compare?

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