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4.3** Do the same as in Problem 4.2, but for the force F = (-y, x) and for the three paths joining and Q shown in Figure 4.24(b) and defined as follows: (a) This path goes straight from P = (1, 0) the origin and then straight to Q = (0, 1). (b) This is a straight line from P to Q. (Write y as a funct of x and rewrite the integral as an integral over x.) (c) This is a quarter-circle centered on the orig (Write x and y in polar coordinates and rewrite the integral as an integral over p.)

4.3** Do the same as in Problem 4.2, but for the force F = (-y, x) and for the three paths joining and Q shown in Figure 4.24(b) and defined as follows: (a) This path goes straight from P = (1, 0) the origin and then straight to Q = (0, 1). (b) This is a straight line from P to Q. (Write y as a funct of x and rewrite the integral as an integral over x.) (c) This is a quarter-circle centered on the orig (Write x and y in polar coordinates and rewrite the integral as an integral over p.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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4.3

4.3** Do the same as in Problem 4.2, but for the force F = (-y, x) and for the three paths joining P and Q shown in Figure 4.24(b) and defined as follows: (a) This path goes straight from P = (1, 0) to the origin and then straight to Q = (0, 1). (b) This is a straight line from P to Q. (Write y as a function of x and rewrite the integral as an integral over x.) (c) This is a quarter-circle centered on the origin. (Write x and y in polar coordinates and rewrite the integral as an integral over p.) 4.4** A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ro with angular velocity wo, but I now pull the string down through the hole until a length r remains between the hole and the particle. (a) What is the particle's angular velocity now? (b) Assuming that I pull the string so slowly that we can approximate the particle's path by a 1 Q (a) a a 0 b (b) Figure 4.24 (a) Problem 4.2. (b) Problem 4.3 P
Transcribed Image Text:4.3** Do the same as in Problem 4.2, but for the force F = (-y, x) and for the three paths joining P and Q shown in Figure 4.24(b) and defined as follows: (a) This path goes straight from P = (1, 0) to the origin and then straight to Q = (0, 1). (b) This is a straight line from P to Q. (Write y as a function of x and rewrite the integral as an integral over x.) (c) This is a quarter-circle centered on the origin. (Write x and y in polar coordinates and rewrite the integral as an integral over p.) 4.4** A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I am holding it. Initially the particle is moving in a circle of radius ro with angular velocity wo, but I now pull the string down through the hole until a length r remains between the hole and the particle. (a) What is the particle's angular velocity now? (b) Assuming that I pull the string so slowly that we can approximate the particle's path by a 1 Q (a) a a 0 b (b) Figure 4.24 (a) Problem 4.2. (b) Problem 4.3 P
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