A sewing machine needle moves up and down in simple harmonic motion with an ampl

Question

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle? You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string A) faster than before. B) slower than before. C) at the same speed as before.

Explanation / Answer

22) we know that x = Acos(wt)

v =- Awsin(wt)

a =- Aw2cos(wt)

vmax = A*w =A*2pi*f = 1.27x10-2 *2*3.14*2.55 =20.33x10-2.m/s...........Ans.

amax =A*w2=w*vmax = 20.33x10-2*2*3.14*2.55 = 3.256 m/s2...........Ans.

23). A

You cause the transverse wave made up by the wiggling string to move faster, so as one part of the rope moves at an increased pace (the part that you are wiggling faster) the increased speed of the vibration that you are causing forces the rope to move more quickly. The vibration travels back and forth across the rope, so if you increase the speed of the vibration, you increase the speed at which the rope is moving. (think of the rope as acting as ONE segment, or a single wavelength. by making this single wavelength shorter, you are increasing the speed of the wave) *This is NOT true for electromagnetic waves.

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