A sewing machine needle moves with a rapid oscillatory motion, essentially in simpleharmonic motion, as it sews a seam. Suppose the needle moves 8.4 mm from its highest to itslowest position as it makes 24 stiches in 9.0 s. (a) What is the angular frequency, w, of theneedle? (b) What is the maximum speed of the needle? (c) What is the magnitude of themaximum acceleration of the needle? (d) Include a diagram of the situation that indicateswhere the location of the maximum speed and acceleration are located in the motion of theneedle.

Step 1:Given the data in the problem:Distance between two extreme positions, d = 8.4 mm.Number of…

Answered: A sewing machine needle moves with a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Similar questions

A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I= 2/5 mR^2
An object is undergoing simple harmonic motion with period 1.250 s and amplitude 0.650 m. At t = 0 the object is at x = 0 and is moving in the negative x-direction. How far is the object from the equilibrium position when t = 0.485 s?
A small bird’s wings can undergo a maximum displacement amplitude of 4.60 cm (distance from the tip of the wing to the horizontal). If the maximum acceleration of the wings is 18.7 m/s2, and we assume the wings are undergoing simple harmonic motion when beating, what is the oscillation frequency of the wingtips?
A piston in a gasoline engine oscillates with simple harmonic motion. The displacement of the piston varies according to x(t) = (6.00 cm) cos (2t + ), where x is in cm and t is in seconds. At t= 0, find: i) the position of the particle, ii) its velocity, iii) its acceleration, iv) the period, and v) the amplitude.
Do it without any delay
A particle executes simple harmonic motion with an amplitude of 5.00 cm. At what positions does its speed equal one third of its maximum speed? larger number cm smaller number cm
A particle undergoes a simple harmonic motion with an amplitude A and a total energy E. When the displacement is one-fourth the amplitude (x A/4), the ratio of the kinetic energy, K. to the total energy, E, is: O K/E = 15/16 O K/E= 3/4 O K/E = 1/4 O KE= 8/9 K/E 1/16 KE=1/9
A particle executes simple harmonic motion with an amplitude of 9.00 cm. At what positions does its speed equal one-half of its maximum speed? larger number cm smaller number cm
The function x = (6 m) cos[(4π rad/s)t + π/8 rad] gives the simple harmonic motion of a body. At t =3 s, what are the (a) acceleration, and (b) phase of the motion?
A piston in a gasoline engine is in simple harmonic motion. The engine is running at the rate of 3 600 rev/min. Taking the extremes of its position relative to its center point as ±5.00 cm, find the magnitudes of the (a) maximum velocity and (b) maximum acceleration of the piston.
A particle moves in simple harmonic motion with a period of 0.3 s and an amplitude of 6 cm. What are the speed and acceleration of the particle when it is 4 cm from the equilibrium position?
The motion of a nightingale’s wingtips can be modeled as simple harmonic motion. In one study, the tips of a bird’s wings were found to move up and down with an amplitude of 8.8 cm and a period of 0.82 s. What are the wingtips’ (a) maximum speed and (b) maximum acceleration?

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