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Chapter 10: Problem 74

A naval aviator had to eject from her plane before it crashed at sea. She is rescued from the water by helicopter and dangles from a cable that is 45 m long while being carried back to the aircraft carrier. What is the period of her vibration as she swings back and forth while the helicopter hovers over her ship?

Short Answer

Expert verified
Answer: The period of the naval aviator's vibration is approximately 13.5 seconds.

Step by step solution

01

Write down the formula for the period of a simple pendulum

The formula for the period of a simple pendulum is given by T = 2π√(L/g), where T is the period we want to find, L is the length of the pendulum (the cable), and g is the acceleration due to gravity (approx. 9.81 m/s²).
02

Plug in the known values

We know that the length of the cable is L = 45 meters and the acceleration due to gravity is g = 9.81 m/s². Now, plug these values into the formula: T = 2π√(45/9.81).
03

Calculate the period

Using a calculator to find the value under the square root, we get T = 2π√(45/9.81) ≈ 2π√(4.59). Now, calculate the period: T ≈ 2π(2.14) ≈ 13.5 seconds.
04

Write the final answer

The period of the naval aviator's vibration as she swings back and forth while the helicopter hovers over the ship is approximately 13.5 seconds.

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Most popular questions from this chapter

A 0.50 -m-long guitar string, of cross-sectional area $1.0 \times 10^{-6} \mathrm{m}^{2},\( has Young's modulus \)Y=2.0 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ By how much must you stretch the string to obtain a tension of \(20 \mathrm{N} ?\)
A pendulum (mass \(m\), unknown length) moves according to \(x=A\) sin $\omega t .\( (a) Write the equation for \)v_{x}(t)$ and sketch one cycle of the \(v_{x}(t)\) graph. (b) What is the maximum kinetic energy?
A pendulum of length \(120 \mathrm{cm}\) swings with an amplitude of $2.0 \mathrm{cm} .\( Its mechanical energy is \)5.0 \mathrm{mJ} .$ What is the mechanical energy of the same pendulum when it swings with an amplitude of \(3.0 \mathrm{cm} ?\)
(a) Given that the position of an object is \(x(t)=A\) cos \(\omega t\) show that \(v_{x}(t)=-\omega A\) sin \(\omega t .\) [Hint: Draw the velocity vector for point \(P\) in Fig. \(10.17 \mathrm{b}\) and then find its \(x\) component.] (b) Verify that the expressions for \(x(t)\) and \(v_{x}(t)\) are consistent with energy conservation. [Hint: Use the trigonometric identity $\sin ^{2} \omega t+\cos ^{2} \omega t=1.1$.]
Show, using dimensional analysis, that the frequency \(f\) at which a mass- spring system oscillates radical is independent of the amplitude \(A\) and proportional to Whim. IHint: Start by assuming that \(f\) does depend on \(A\) (to some power).]
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