Solution Found!
(Note: In Problems, assume a number like 6.4 is
Chapter 2, Problem 14P(choose chapter or problem)
(Note: In Problems, assume a number like 6.4 is accurate to \(\pm 0.1\); and 950 is \(\pm 10\) unless 950 is said to be “precisely” or “very nearly” 950, in which case assume \(950 \pm 1\). See Section 1–4.)
(II) Digital bits on a 12.0-cm diameter audio CD are encoded along an outward spiraling path that starts at radius \(R_{1}=2.5\) cm and finishes at radius \(R_{2}=5.8\) cm. The distance between the centers of neighboring spiral windings is \(1.6\ \mu\mathrm{m}\) \(\left(=1.6\times10^{-6}\mathrm{\ m}\right)\). (a) Determine the total length of the spiraling path. [Hint: Imagine "unwinding" the spiral into a straight path of width \(1.6\ \mu\mathrm{m}\), and note that the original spiral and the straight path both occupy the same area.] (b) To read information, a CD player adjusts the rotation of the so that the player's readout laser moves along the spiral path at a constant speed of about \(1.2 \mathrm{\ m} / \mathrm{s}\). Estimate the maximum playing time of such a
.
Equation Transcription:
Text Transcription:
+/-0.1
+/-10
95+/-01
R_1=2.5
R_2=5.8
1.6 mu m
(=1.610^{-6} m)
1.6 mu m
1.2 m/s
Questions & Answers
QUESTION:
(Note: In Problems, assume a number like 6.4 is accurate to \(\pm 0.1\); and 950 is \(\pm 10\) unless 950 is said to be “precisely” or “very nearly” 950, in which case assume \(950 \pm 1\). See Section 1–4.)
(II) Digital bits on a 12.0-cm diameter audio CD are encoded along an outward spiraling path that starts at radius \(R_{1}=2.5\) cm and finishes at radius \(R_{2}=5.8\) cm. The distance between the centers of neighboring spiral windings is \(1.6\ \mu\mathrm{m}\) \(\left(=1.6\times10^{-6}\mathrm{\ m}\right)\). (a) Determine the total length of the spiraling path. [Hint: Imagine "unwinding" the spiral into a straight path of width \(1.6\ \mu\mathrm{m}\), and note that the original spiral and the straight path both occupy the same area.] (b) To read information, a CD player adjusts the rotation of the so that the player's readout laser moves along the spiral path at a constant speed of about \(1.2 \mathrm{\ m} / \mathrm{s}\). Estimate the maximum playing time of such a
.
Equation Transcription:
Text Transcription:
+/-0.1
+/-10
95+/-01
R_1=2.5
R_2=5.8
1.6 mu m
(=1.610^{-6} m)
1.6 mu m
1.2 m/s
ANSWER:
Step 1 of 3
Initial radius is
Final radius
Width of the spiral:
The original spiral and the straight path both occupy the same area.
Area of the original spiral is the Area between the two concentric circles.
