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Do the same as in .2, but for the force F = (y, x) and for

Chapter 4, Problem 4.3

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QUESTION:

Do the same as in 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 0.)

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QUESTION:

Do the same as in 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 0.)

ANSWER:

Step 1 of 6

(a)

Given  .

Therefore,  and .

The work done is given as,

Here,  is the two-dimensional force exerted on the object,  is the displacement,  is the force in the  direction and  is the force in the  direction.

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