A 5.00-kg particle moves from the origin to position o, having coordinates x 4.5

Question

A 5.00-kg particle moves from the origin to position o, having coordinates x 4.50 m and y 4.50 m as shown in the figure. One force on the particle is the gravitational force acting in the negative y direction. Using the equation (W-FAr cos -i ), calculate the work done by the gravitational force in going from O to o along the following paths. x, y (a) the purple path (Ooo) (b) the red path (Oso) (c) the blue path (Oo) (d) Your results should all be identical. Why? This answer has not been graded yet

Explanation / Answer

Given that

mass of the particle m = 5.00 kg

acceleratin due to gravity g =9.80 m/s2

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a) The formula for work done by the gravitational force on the particle is

                  W = - (mg j).[ (4.50 )i + (0.00)j] - (mg j).[ (0.00 )i + (4.50)j]

                      =- (5.00 kg)(9.80 m/s2) (4.50 m)

                      =-220.5 J

b) The formula for work done by the gravitational force on the particle is

                  W = - (mg j).[ (0.00 )i + (4.50)j] - (mg j).[ (4.50 )i + (0.00)j]+

                      =- (5.000 kg)(9.80 m/s2) (4.50 m)

                      =- 220.5 J

c) The formula for work done by the gravitational force on the particle is

                  W = - (mg j).[ (4.50)i + (4.50)j]

                      =- (5.00 kg)(9.80 m/s2) (4.50 m)

                      =- 220.5 J

d) The gravitational force is conservative.

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