Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 15, Problem 15.13CQ
Consider the simplified single-piston engine in Figure CQ15.13. Assuming the wheel rotates with constant angular speed, explain why the piston rod oscillates in
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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 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
A spring-mass system oscilates on a frictionless surface without air resistance at an angular frequency of w =
4.50 rad/s.
Then the same spring-mass system is placed inside a gas-filled chamber with an air resistance constant b =
0.012 kg/s.
If the system's spring has a constant of k = 32 N/m,
1) What is the new angular frequency (w') for the system?
2) What is the damping coefficient (y) for the spring-mass system?
Justify your answer using your reasoning and rationale used.
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
Chapter 15 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 15 - A block on the end of a spring is pulled to...Ch. 15 - Consider a graphical representation (Fig. 15.3) of...Ch. 15 - Figure 15.4 shows two curves representing...Ch. 15 - An object of mass m is hung from a spring and set...Ch. 15 - The ball in Figure 15.13 moves in a circle of...Ch. 15 - The grandfather clock in the opening storyline...Ch. 15 - If a simple pendulum oscillates with small...Ch. 15 - You attach a block to the bottom end of a spring...Ch. 15 - A block-spring system vibrating on a frictionless,...Ch. 15 - An object-spring system moving with simple...
Ch. 15 - An object of mass 0.40 kg, hanging from a spring...Ch. 15 - A runaway railroad car, with mass 3.0 105 kg,...Ch. 15 - The position of an object moving with simple...Ch. 15 - If an object of mass m attached to a light spring...Ch. 15 - You stand on the end of a diving board and bounce...Ch. 15 - A mass-spring system moves with simple harmonic...Ch. 15 - A block with mass m = 0.1 kg oscillates with...Ch. 15 - For a simple harmonic oscillator, answer yes or no...Ch. 15 - The top end of a spring is held fixed. A block is...Ch. 15 - Which of the following statements is not true...Ch. 15 - A simple pendulum has a period of 2.5 s. (i) What...Ch. 15 - A simple pendulum is suspended from the ceiling of...Ch. 15 - A particle on a spring moves in simple harmonic...Ch. 15 - You are looking at a small, leafy tree. You do not...Ch. 15 - Prob. 15.2CQCh. 15 - If the coordinate of a particle varies as x = -A...Ch. 15 - A pendulum bob is made from a sphere filled with...Ch. 15 - Figure CQ15.5 shows graphs of the potential energy...Ch. 15 - A student thinks that any real vibration must be...Ch. 15 - The mechanical energy of an undamped block-spring...Ch. 15 - Is it possible to have damped oscillations when a...Ch. 15 - Will damped oscillations occur for any values of b...Ch. 15 - If a pendulum clock keeps perfect time al the base...Ch. 15 - Prob. 15.11CQCh. 15 - A simple pendulum can be modeled as exhibiting...Ch. 15 - Consider the simplified single-piston engine in...Ch. 15 - A 0.60-kg block attached to a spring with force...Ch. 15 - When a 4.25-kg object is placed on lop of a...Ch. 15 - A vertical spring stretches 3.9 cm when a 10-g...Ch. 15 - In an engine, a piston oscillates with simpler...Ch. 15 - The position of a particle is given by the...Ch. 15 - A piston in a gasoline engine is in simple...Ch. 15 - A 1.00-kg object is attached to a horizontal...Ch. 15 - A simple harmonic oscillator takes 12.0 s to...Ch. 15 - A 7.00-kg object is hung from the bottom end of a...Ch. 15 - At an outdoor market, a bunch of bananas attached...Ch. 15 - A vibration sensor, used in testing a washing...Ch. 15 - (a) A hanging spring stretches by 35.0 cm when an...Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - A ball dropped from a height of 4.00 m makes an...Ch. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - A particle moves in simple harmonic motion with a...Ch. 15 - A 1.00-kg glider attached to a spring with a force...Ch. 15 - A 0.500-kg object attached to a spring with a...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - To test the resiliency of its bumper during...Ch. 15 - A 200-g block is attached to a horizontal spring...Ch. 15 - A block of unknown mass is attached to a spring...Ch. 15 - A block-spring system oscillates with an amplitude...Ch. 15 - A particle executes simple harmonic motion with an...Ch. 15 - The amplitude of a system moving in simple...Ch. 15 - A 50.0-g object connected to a spring with a force...Ch. 15 - A 2.00-kg object is attached to a spring and...Ch. 15 - A simple harmonic oscillator of amplitude A has a...Ch. 15 - Review. A 65.0-kg bungee jumper steps off a bridge...Ch. 15 - Review. A 0.250-kg block resting on a...Ch. 15 - Prob. 15.32PCh. 15 - While driving behind a car traveling at 3.00 m/s,...Ch. 15 - A seconds pendulum is one that moves through its...Ch. 15 - A simple pendulum makes 120 complete oscillations...Ch. 15 - A particle of mass m slides without friction...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - The angular position of a pendulum is represented...Ch. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - Prob. 15.41PCh. 15 - A very light rigid rod of length 0.500 m extends...Ch. 15 - Review. A simple pendulum is 5.00 m long. What is...Ch. 15 - A small object is attached to the end of a string...Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...Ch. 15 - A pendulum with a length of 1.00 m is released...Ch. 15 - A 10.6-kg object oscillates at the end of a...Ch. 15 - Show that the time rate of change of mechanical...Ch. 15 - Show that Equation 15.32 is a solution of Equation...Ch. 15 - A baby bounces up and down in her crib. Her mass...Ch. 15 - As you enter a fine restaurant, you realize that...Ch. 15 - A block weighing 40.0 N is suspended from a spring...Ch. 15 - A 2.00-kg object attached to a spring moves...Ch. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - Damping is negligible for a 0.150-kg object...Ch. 15 - The mass of the deuterium molecule (D2) is twice...Ch. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Review. This problem extends the reasoning of...Ch. 15 - A small ball of mass M is attached to the end of a...Ch. 15 - Review. A rock rests on a concrete sidewalk. An...Ch. 15 - Four people, each with a mass of 72.4 kg, are in a...Ch. 15 - To account for the walking speed of a bipedal or...Ch. 15 - Prob. 15.63APCh. 15 - An object attached to a spring vibrates with...Ch. 15 - Review. A large block P attached to a light spring...Ch. 15 - Review. A large block P attached to a light spring...Ch. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - A block of mass m is connected to two springs of...Ch. 15 - A horizontal plank of mass 5.00 kg and length 2.00...Ch. 15 - A horizontal plank of mass m and length L is...Ch. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - A ball of mass m is connected to two rubber bands...Ch. 15 - Review. One end of a light spring with force...Ch. 15 - People who ride motorcycles and bicycles learn to...Ch. 15 - A simple pendulum with a length of 2.23 m and a...Ch. 15 - When a block of mass M, connected to the end of a...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - Consider the damped oscillator illustrated in...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - Your thumb squeaks on a plate you have just...Ch. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Prob. 15.82APCh. 15 - Two identical steel balls, each of mass 67.4 g,...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - An object of mass m1 = 9.00 kg is in equilibrium...Ch. 15 - Review. Why is the following situation impassible?...Ch. 15 - A block of mass M is connected to a spring of mass...Ch. 15 - Review. A system consists of a spring with force...Ch. 15 - A light, cubical container of volume a3 is...
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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_forwardA uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around an axis perpendicular to the plane of the ring at point P (Fig. P16.35). Determine its period of oscillation. FIGURE P16.35arrow_forwardA particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.arrow_forward
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SIMPLE HARMONIC MOTION (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=XjkUcJkGd3Y;License: Standard YouTube License, CC-BY