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Chapter 13: Problem 14

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 the mass-spring system will not change when in an accelerating jetliner, while the period of the pendulum will decrease due to the increase in effective gravity.

Step by step solution

01

Analyze the mass-spring system

A mass-spring system's period \(T_{spring} = 2 \pi \sqrt{\frac{m}{k}}\), depends only on mass (m) and the spring constant (k), and not on the force of gravity. So, even when the system is in an accelerating jetliner, the period remains the same as there is no direct dependence on gravity.
02

Analyze the pendulum

A pendulum's period \(T_{pendulum} = 2 \pi \sqrt{\frac{l}{g}}\), is dependent on its length (l) and the gravitational acceleration (g). If it's in an accelerating jetliner, the acceleration of the jetliner adds to the effective gravitational acceleration. If the plane is accelerating forward, it makes the effective gravity greater and hence the pendulum's period decreases.
03

Summary

The period of a mass-spring system won't change in an accelerating jetliner because its period does not depend on gravity, while the period of a pendulum will change because its period is dependent on gravity.

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