Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780136139225
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 16.1, Problem 1AE
To determine
The rule if the distance is in kilometer.
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
Chapter 16 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 16.1 - Prob. 1AECh. 16.3 - If an increase of 3 dB means twice as intense,...Ch. 16.3 - Trumpet players. A trumpeter plays at a sound...Ch. 16.4 - Two strings have the same length and tension, but...Ch. 16.7 - Prob. 1GECh. 16.7 - How fast would a source have to approach an...Ch. 16 - What is the evidence that sound travels as a wave?Ch. 16 - What is the evidence that sound is a form of...Ch. 16 - Children sometimes play with a homemade telephone...Ch. 16 - When a sound wave passes from air into water, do...
Ch. 16 - What evidence can you give that the speed of sound...Ch. 16 - The voice of a person who has inhaled helium...Ch. 16 - What is the main reason the speed of sound in...Ch. 16 - Two tuning forks oscillate with the same...Ch. 16 - How will the air temperature in a room affect the...Ch. 16 - Explain how a lube might be used as a filler to...Ch. 16 - Prob. 11QCh. 16 - A noisy truck approaches you from behind a...Ch. 16 - Standing waves can he said to be due to...Ch. 16 - In Fig. 16-15, if the frequency of the speakers is...Ch. 16 - Traditional methods of protecting the hearing of...Ch. 16 - Consider the two waves shown in Fig. 1630. Each...Ch. 16 - Is there a Doppler shift if the source and...Ch. 16 - If a wind is blowing, will this alter the...Ch. 16 - Figure 1631 shows various positions of a child on...Ch. 16 - Approximately how many octaves are there in the...Ch. 16 - At a race track, you can estimate the speed of...Ch. 16 - (I) A hiker determines the length of a lake by...Ch. 16 - Prob. 2PCh. 16 - (I) (a) Calculate the wavelengths in air at 20C...Ch. 16 - (I) On a warm summer day (27C), it takes 4.70 s...Ch. 16 - (II) A motion sensor can accurately measure the...Ch. 16 - Prob. 6PCh. 16 - A stone is dropped from the top of a cliff. The...Ch. 16 - A person, with his ear to the ground, sees a huge...Ch. 16 - Prob. 9PCh. 16 - (I) The pressure amplitude of a sound wave in air...Ch. 16 - (I) What must be the pressure amplitude in a sound...Ch. 16 - (II) Write an expression that describes the...Ch. 16 - (II) The pressure variation in a sound wave is...Ch. 16 - What is the intensity of a sound at the pain level...Ch. 16 - (I) What is the sound level of a sound whose...Ch. 16 - (I) What are the lowest and highest frequencies...Ch. 16 - (II) Your auditory system can accommodate a huge...Ch. 16 - (II) You are trying to decide between two new...Ch. 16 - (II) At a painfully loud concert, a 120-dB sound...Ch. 16 - (II) If two firecrackers produce a sound level of...Ch. 16 - A person standing a certain distance from an...Ch. 16 - (II) A cassette player is said to have a...Ch. 16 - (II) (a) Estimate the power output of sound from a...Ch. 16 - (II) A 50-dB sound wave strikes an eardrum whose...Ch. 16 - Expensive amplifier A is rated at 250 W, while the...Ch. 16 - (II) At a rock concert, a dB meter registered...Ch. 16 - A fireworks shell explodes 100m above the ground,...Ch. 16 - If the amplitude of a sound wave is made 2.5 times...Ch. 16 - Two sound waves have equal displacement...Ch. 16 - What would be the sound level (in dB) of a sound...Ch. 16 - (a) Calculate the maximum displacement of air...Ch. 16 - A jet plane emits 5.0 105 J of sound energy per...Ch. 16 - What would you estimate for the length of a bass...Ch. 16 - The A string on a violin has a fundamental...Ch. 16 - An organ pipe is 124 cm long. Determine the...Ch. 16 - (a) What resonant frequency would you expect from,...Ch. 16 - Prob. 37PCh. 16 - Prob. 38PCh. 16 - An unfingered guitar string is 0.73m long and is...Ch. 16 - (II) (a) Determine the length of an open organ...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - (II) A particular organ pipe can resonate at 264...Ch. 16 - A uniform narrow tube 1.80m long is open at both...Ch. 16 - (II) A pipe in air at 23.0C is to be designed to...Ch. 16 - How many overtones are present within the audible...Ch. 16 - Prob. 49PCh. 16 - (II) In a quartz oscillator, used as a stable...Ch. 16 - The human car canal is approximately 2.5 cm long....Ch. 16 - (II) Approximately what are the intensities of the...Ch. 16 - A piano tuner hears one beat every 2.0s when...Ch. 16 - What is the beat frequency if middle C (262 Hz)...Ch. 16 - A guitar string produces 4 beats/s when sounded...Ch. 16 - (II) The two sources of sound in Fig. 1615 face...Ch. 16 - Prob. 57PCh. 16 - (II) Two loudspeakers are placed 3.00 m apart, as...Ch. 16 - Two piano strings are supposed to be vibrating at...Ch. 16 - A source emits sound of wavelengths 2.64 m and...Ch. 16 - (I)The predominant frequency of a certain fire...Ch. 16 - A bat at rest sends out ultrasonic sound waves at...Ch. 16 - (II) (a) Compare the shift in frequency if a...Ch. 16 - Two automobiles are equipped with the same single...Ch. 16 - A police car sounding a siren with a frequency of...Ch. 16 - (II) A bat flies toward a wall at a speed of 7.0...Ch. 16 - In one of the original Doppler experiments, a tuba...Ch. 16 - (II) If a speaker mounted on an automobile...Ch. 16 - A wave on the surface of the ocean with wavelength...Ch. 16 - A factory whistle emits sound of frequency 720 Hz....Ch. 16 - The Doppler effect using ultrasonic waves of...Ch. 16 - (II) An airplane travels at Mach 2.0 where the...Ch. 16 - A space probe enters the thin atmosphere of a...Ch. 16 - A meteorite traveling 8800 m/s strikes the ocean....Ch. 16 - Show that the angle a sonic boom makes with the...Ch. 16 - Prob. 76PCh. 16 - (II) A supersonic jet traveling at Mach 2.2 at an...Ch. 16 - A fish finder uses a sonar device that sends...Ch. 16 - A science museum has a display called a sewer pipe...Ch. 16 - A single mosquito 5.0 m from a person makes a...Ch. 16 - What is the resultant sound level when an 82-dB...Ch. 16 - The sound level 9.00 m from a loudspeaker, placed...Ch. 16 - A stereo amplifier is rated at 175 W output at...Ch. 16 - Workers around jet aircraft typically wear...Ch. 16 - In audio and communications systems, the gain, ,...Ch. 16 - For large concerts, loudspeakers are sometimes...Ch. 16 - Manufacturers typically offer a particular guitar...Ch. 16 - The high-E string on a guitar is fixed at both...Ch. 16 - Prob. 89GPCh. 16 - Prob. 90GPCh. 16 - Two identical tubes, each closed at one end, have...Ch. 16 - Prob. 92GPCh. 16 - The diameter D of a tube does affect the node at...Ch. 16 - A person hears a pure tone in the 500 to 1000-Hz...Ch. 16 - The frequency of a steam train whistle as it...Ch. 16 - Two trains emit 516-Hz whistles. One train is...Ch. 16 - Two loudspeakers are at opposite ends of a...Ch. 16 - Two open organ pipes, sounding together, produce a...Ch. 16 - A bat flies toward a moth at speed 7.5 m/s while...Ch. 16 - If the velocity of blood flow in the aorta is...Ch. 16 - A bat emits a series of high-frequency sound...Ch. 16 - Prob. 102GPCh. 16 - Two loudspeakers face each other at opposite ends...Ch. 16 - Prob. 104GPCh. 16 - The wake of a speedboat is 15 in a lake where the...Ch. 16 - Prob. 106GPCh. 16 - Prob. 107GPCh. 16 - Prob. 108GP
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