Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 14, Problem 3Q
Explain why the motion of a piston in an automobile engine is approximately simple harmonic.
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The figure below shows a piston from your car engine. Don't worry, you will not be required to understand an internal combustion engine for this problem. Instead, we simply notice that the up/down motion of the piston is exactly described as Simple Harmonic Motion. The tachometer on your dashboard tells you that your engine is turning at ? = 2600 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is ymax = A = 0.071 meters.Determine all the following:The angular frequency in proper units ? = _ rad/secThe period of the piston, ? = _ secondsThe frequency of the piston, f = _ HzThe maximum velocity of the piston, vmax = _ meters/secThe piston velocity when y = 42% of full stroke, v(y = 0.42 ymax) = _ meters/sec
The figure below shows a piston from your car engine. Don't worry, you will not be required to understand an internal combustion engine for this problem. Instead, we simply
notice that the up/down motion of the piston is exactly described as Simple Harmonic Motion. The tachometer on your dashboard tells you that your engine is turning at w =
1660 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is Ymax = A = 0.099 meters.
Simple
Harmonic
Motion
wrist
pin
500 grams
Crankshaft
A (top of stroke)
B (midpoint)
-C (bottom of stroke) y=-A
y=+A
Determine all the following:
The angular frequency in proper units w =
The period of the piston, T =
The frequency of the piston, f =
The maximum velocity of the piston, Vmax =
meters/sec
The piston velocity when y = 58% of full stroke, v(y = 0.58 Ymax) =
seconds
Hz
rad/sec
meters/sec
In the bookPhysics for scientist and engineers, 6th editionChapter 14- OscillationsProblem 37:
to find v(max) and a(max) we use x=Acos(wt)in the solution, we substitute sin(wt) and cos(wt) with -1. Why?
Chapter 14 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 14.1 - An object is oscillating back and forth. Which of...Ch. 14.1 - A mass is oscillating on a frictionless surface at...Ch. 14.1 - If an oscillating mass has a frequency of 1.25 Hz,...Ch. 14.2 - Which of the following represents a simple...Ch. 14.2 - By how much should the mass on the end of a spring...Ch. 14.2 - The position of a SHO is given by x = (0.80 m)...Ch. 14.3 - Suppose the spring in Fig. 1410 is compressed to x...Ch. 14.5 - If a simple pendulum is taken from sea level to...Ch. 14.5 - Return to the Chapter-Opening Question, p. 369,...Ch. 14.5 - (a) Estimate the length of a simple pendulum that...
Ch. 14 - Give some examples of everyday vibrating objects....Ch. 14 - Is the acceleration of a simple harmonic...Ch. 14 - Explain why the motion of a piston in an...Ch. 14 - Real springs have mass. Will the true period and...Ch. 14 - How could you double the maximum speed of a simple...Ch. 14 - A 5.0-kg trout is attached to the hook of a...Ch. 14 - If a pendulum clock is accurate at sea level, will...Ch. 14 - A tire swing hanging from a branch reaches nearly...Ch. 14 - For a simple harmonic oscillator, when (if ever)...Ch. 14 - A 100-g mass hangs from a long cord forming a...Ch. 14 - Two equal masses are attached to separate...Ch. 14 - Does a car bounce on its springs faster when it is...Ch. 14 - What is the approximate period of your walking...Ch. 14 - What happens to the period of a playground swing...Ch. 14 - A thin uniform rod of mass m is suspended from one...Ch. 14 - A tuning fork of natural frequency 264 Hz sits on...Ch. 14 - Why can you make water slosh back and forth in a...Ch. 14 - Give several everyday examples of resonance.Ch. 14 - Is a rattle in a car ever a resonance phenomenon?...Ch. 14 - Over the years, buildings have been able to be...Ch. 14 - (I) If a particle undergoes SHM with amplitude...Ch. 14 - (I) An elastic cord is 65 cm long when a weight of...Ch. 14 - (I) The springs of a 1500-kg car compress 5.0 mm...Ch. 14 - (I) (a) What is the equation describing the motion...Ch. 14 - (II) Estimate the stiffness of the spring in a...Ch. 14 - (II) A fishermans scale stretches 3.6 cm when a...Ch. 14 - (II) Tall buildings are designed to sway in the...Ch. 14 - (II) Construct a Table, indicating the position x...Ch. 14 - (II) A small fly of mass 0.25 g is caught in a...Ch. 14 - (II) A mass m at the end of a spring oscillates...Ch. 14 - (II) A uniform meter stick of mass M is pivoted on...Ch. 14 - (II) A balsa wood block of mass 55g floats on a...Ch. 14 - (II) Figure 1429 shows two examples of SHM,...Ch. 14 - (II) Determine the phase constant in Eq. 144 if,...Ch. 14 - (II) A vertical spring with spring stiffness...Ch. 14 - (II) The graph of displacement vs. time for a...Ch. 14 - (II) The position of a SHO as a function of time...Ch. 14 - (II) A tuning fork oscillates at a frequency of...Ch. 14 - (II) An object of unknown mass m is hung from a...Ch. 14 - (II) A 1.25-kg mass stretches a vertical spring...Ch. 14 - (II) Consider two objects, A and B, both...Ch. 14 - (II) A 1.60-kg object oscillates from a vertically...Ch. 14 - (II) A bungee jumper with mass 65.0 kg jumps from...Ch. 14 - (II) A block of mass m is supported by two...Ch. 14 - (III) A mass m is connected to two springs, with...Ch. 14 - (III) A mass m is at rest on the end of a spring...Ch. 14 - (I) A l.15-kg mass oscillates according to the...Ch. 14 - (I) (a) At what displacement of a SHO is the...Ch. 14 - (II) Draw a graph like Fig. 1411 for a horizontal...Ch. 14 - (II) A 0.35-kg mass at the end of a spring...Ch. 14 - (II) It takes a force of 95.0 to compress the...Ch. 14 - (II) A 0.0125-kg bullet strikes a 0.240-kg block...Ch. 14 - (II) If one oscillation has 5.0 times the energy...Ch. 14 - (II) A mass of 240g oscillates on a horizontal...Ch. 14 - (II) A mass resting on a horizontal, frictionless...Ch. 14 - (II) An object with mass 2.7 kg is executing...Ch. 14 - (II) Agent Arlene devised the following method of...Ch. 14 - (II) Obtain the displacement x as a function of...Ch. 14 - (II) t t = 0, a 785-g mass at rest on the end of a...Ch. 14 - (II) A pinball machine uses a spring launcher that...Ch. 14 - (I) A pendulum has a period of 1.35s on Earth....Ch. 14 - (I) A pendulum makes 32 oscillations in exactly 50...Ch. 14 - (II) A simple pendulum is 0.30m long. At t = 0 it...Ch. 14 - (II) What is the period of a simple pendulum 53cm...Ch. 14 - (II) A simple pendulum oscillates with an...Ch. 14 - (II) Your grandfather clocks pendulum has a length...Ch. 14 - (II) Derive a formula for the maximum speed vmax...Ch. 14 - (II) A pendulum consists of a tiny bob of mass M...Ch. 14 - (II) The balance wheel of a watch is a thin ring...Ch. 14 - (II) The human leg can be compared to a physical...Ch. 14 - (II) (a) Determine the equation of motion (for as...Ch. 14 - (II) A student wants to use a meter stick as a...Ch. 14 - (II) A meter stick is hung at its center from a...Ch. 14 - (II) An aluminum disk. 12.5cm in diameter and 375g...Ch. 14 - (II) A plywood disk of radius 20.0cm and mass...Ch. 14 - (II) A 0.835-kg block oscillates on the end of a...Ch. 14 - (II) Estimate how the damping constant changes...Ch. 14 - (II) A physical pendulum consists of an...Ch. 14 - (II) A damped harmonic oscillator loses 6.0% of...Ch. 14 - (II) A vertical spring of spring constant 115 N/m...Ch. 14 - (III) (a) Show that the total mechanical energy,...Ch. 14 - (III) A glider on an air track is connected by...Ch. 14 - (II) (a) For a forced oscillation at resonance ( =...Ch. 14 - Prob. 64PCh. 14 - (II) An 1150 kg automobile has springs with k =...Ch. 14 - (II) Construct an accurate resonance curve, from ...Ch. 14 - (II) The amplitude of a driven harmonic oscillator...Ch. 14 - (III) By direct substitution, show that Eq. 1422,...Ch. 14 - (III) Consider a simple pendulum (point mass bob)...Ch. 14 - A 62-kg person jumps from a window to a fire net...Ch. 14 - An energy-absorbing car bumper has a spring...Ch. 14 - The length of a simple pendulum is 0.63 m, the...Ch. 14 - A simple pendulum oscillates with frequency f....Ch. 14 - A 0.650-kg mass oscillates according to the...Ch. 14 - (a)A crane has hoisted a 1350-kg car at the...Ch. 14 - An oxygen atom at a particular site within a DNA...Ch. 14 - A seconds pendulum has a period of exactly 2.000...Ch. 14 - A 320-kg wooden raft floats on a lake. When a...Ch. 14 - At what displacement from equilibrium is the speed...Ch. 14 - A diving board oscillates with simple harmonic...Ch. 14 - A rectangular block of wood floats in a calm lake....Ch. 14 - A 950-kg car strikes a huge spring at a speed of...Ch. 14 - A 1.60-kg table is supported on four springs. A...Ch. 14 - In some diatomic molecules, the force each atom...Ch. 14 - A mass attached to the end of a spring is...Ch. 14 - Carbon dioxide is a linear molecule. The...Ch. 14 - Imagine that a 10-cm-diameter circular hole was...Ch. 14 - A thin, Straight, uniform rod of length = 1.00 m...Ch. 14 - A mass m is gently placed on the end of a freely...Ch. 14 - A child of mass m sits on top of a rectangular...Ch. 14 - Estimate the effective spring constant of a...Ch. 14 - In Section 145, the oscillation of a simple...Ch. 14 - (II) A mass m on a frictionless surface is...Ch. 14 - (III) Damping proportional to v2. Suppose the...
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- Consider the simplified single-piston engine in Figure CQ12.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in simple harmonic motion. Figure CQ12.13arrow_forwardCheck Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.arrow_forwardAn automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100 kg of passengers. It is driven with a constant horizontal component of speed 20 km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4 m. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs and assume that the wheels are always in contact with the road.arrow_forward
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