# A 4.00-kg particle moves from the origin to position ©, having coordinates x = 5.00 m and y = 5.00 m (Fig. P7.31). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 7.3, calculate the work done by the gravitational force on the particle as it goes from O to © along (a) the purple path, (b) the red path, and (c) the blue path, (d) Your results should all be identical. Why? Figure P7.31

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553292

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553292
Chapter 7, Problem 31P
Textbook Problem
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## A 4.00-kg particle moves from the origin to position ©, having coordinates x = 5.00 m and y = 5.00 m (Fig. P7.31). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 7.3, calculate the work done by the gravitational force on the particle as it goes from O to © along (a) the purple path, (b) the red path, and (c) the blue path, (d) Your results should all be identical. Why?Figure P7.31

(a)

To determine

The amount of work done by the gravitational force along the purple path

### Explanation of Solution

Given info: The coordinates of point (C) is (5.00m, 5.00m) , the mass of the body is 4.00kg .

The acceleration due to gravity is 9.8m/s2 .

Work done along OA is,.

WOA=mg(OA)cos90.0°

Here,

m is the mass of the object.

g is the acceleration due to gravity.

Work done along AC is,

WAC=mg(AC)cos180.0°

The work done along purple path is,

Wpurple=WOA+WAC

Substitute mg(OA)cos90.0° for WOA and mg(AC)cos180.0° for WAC in the above equation.

Wpurple=(mg(OA)cos90.0°)+(mg(AC)cos180.0°)

Substitute 4.00kg for m , 9

(b)

To determine

The amount of work done by the gravitational force along the red path.

(c)

To determine

The amount of work done by the gravitational force along the blue path.

(c)

To determine

The reason for which the results for the above part is identical.

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