Calculate the work done by gravity as a 40 kg object is move

Calculate the work done by gravity as a 4.0 kg object is moved from point A to point B in the figure(Figure 1) along paths 1, 2, and 3. Full answers please.

w1=

w2=

w3=

See link below for image of figure 1.

https://www.chegg.com/homework-help/questions-and-answers/calculate-work-done-gravity-34-kg-object-moved-point-point-b-figure-along-paths-1-2-3-q1537585?trackid=14f65822&strackid=3e344279&ii=3

Solution

as gravitational force is conservative in nature, work done wont depend upon the path taken and will only depend upon starting and end point.

gravitational force=4*9.8=39.2 N

work done=force*distance*cos(theta)

where theta=angle between direction of motion and direction of force

from A to B, height=2 m

hence work done=-force*height (as force in opposite direction to the movement)

=-78.4 J

[to check that it is really the case, you can take any path and find the work done for each part of the oath.

for path 1:

work done=-39.2*4+39.2*1+39.2*1=-78.4 J

(+ve sign when the object is moving down (along the direction of force) and negative for when moving up)

similarly for path 2:

work done=-39.2*2=-78.4 J

for path 3:

work done=39.2*1-39.2*3=-78.4 J