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Physics For Scientists & Engineers
Found in: Page 472
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

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Short Answer

Is a bouncing ball an example of simple harmonic motion? Is the daily movement of a student from home to school and back simple harmonic motion? Why or why not?

Although they are both periodic motion, neither are examples of simple harmonic motion.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Simple Harmonic motion

Particle in Simple Harmonic Motion If a particle is subject to a force of the form of Hooke’s law F=-kx, the particle exhibits simple harmonic motion. Its position is described by

xt=Acosωt+ϕ

Where A is the amplitude of the motion, ω is the angular frequency, and ϕ is the phase constant. The value of ϕ depends on the initial position and initial velocity of the particle.

Step 2: Explain the reasoning

  • Although they are both periodic motion, neither are examples of simple harmonic motion.
  • In neither case is the acceleration proportional to the displacement from an equilibrium position. Neither motion is so smooth as SHM.
  • The ball’s acceleration is very large when it is in contact with the floor, and the student’s when the dismissal bell rings.

Most popular questions for Physics Textbooks

A 65.0-kg bungee jumper steps off a bridge with a light bungee cord tied to her body and to the bridge. The unstretched length of the cord is role="math" localid="1660198723821" 11.0 m . The jumper reaches the bottom of her motion role="math" localid="1660198746464" 36.0 m below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an role="math" localid="1660198763301" 11.0-m free fall and a role="math" localid="1660198776457" 25.0-m section of simple harmonic oscillation. (a) For the free-fall part, what is the appropriate analysis model to describe her motion? (b) For what time interval is she in free fall? (c) For the simple harmonic oscillation part of the plunge, is the system of the bungee jumper, the spring, and the Earth isolated or non- isolated? (d) From your response in part (c) find the spring constant of the bungee cord. (e) What is the location of the equilibrium point where the spring force balances the gravitational force exerted on the jumper? (f) What is the angular frequency of the oscillation? (g) What time interval is required for the cord to stretch by role="math" localid="1660198795390" 25.0 m? (h) What is the total time interval for the entire role="math" localid="1660198809416" 36.0-m drop?

A block with mass m = 0.1 kg oscillates with amplitude A = 0.1 m at the end of a spring with force constant k = 10 N/m on a frictionless, horizontal surface. Rank the periods of the following situations from greatest to smallest. If any periods are equal, show their equality in your ranking. (a) The system is as described above. (b) The system is as described in situation (a) except the amplitude is 0.2 m. (c) The situation is as described in situation (a) except the mass is 0.2 kg. (d) The situation is as described in situation (a) except the spring has force constant 20 N/m. (e) a small resistive force makes the motion under damped.

A system consists of a spring with force constant k=1250 N/m, length L=1.50 m, and an object of mass 5.00 kg attached to the end (Fig. P15.88). The object is placed at the level of the point of attachment with the spring unstretched, at position yi=L, and then it is released so that it swings like a pendulum. (a) Find the y position of the object at the lowest point. (b) Will the pendulum’s period be greater or less than the period of a simple pendulum with the same mass m and length L ? Explain

A mass spring system moves with simple harmonic motion along the x axis between turning points at x1=50 cm, and x2=60 cm. For parts (i) through (iii), choose from the same five possibilities. (i) At which position does the particle have the greatest magnitude of momentum? (a) 20 cm (b) 30 cm (c) 40 cm (d) some other position (e) The greatest value occurs at multiple points. (ii) At which position does the particle have greatest kinetic energy? (iii) At which position does the particle-spring system have the greatest total energy?

Will damped oscillations occur for any values of b and k? Explain.
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