6. -14 points SerPOP5 6.P.042.MI My Notes A 3.00-kg particle moves from the orig

Question

6. -14 points SerPOP5 6.P.042.MI My Notes A 3.00-kg particle moves from the origin to position C, having coordinates X -6.50 m and y 6.50 m (see figure below). One force on the particle is the gravitational force acting in the negative y direction. (x, y) x (m) 0 using the equation W = Får cos ? = F·?? , calculate the work done by the gravitational force on the particle as it goes from O to C along the following paths. (a) the purple path (OAC) (b) the red path (OBC) (c) the blue path (Oc) (d) Your results should all be identical. Why? o because the gravitational force is conservative o because the gravitational force is nonconservative Need Help? Read ItMaster

Explanation / Answer

part a:

purple path (OAC):

work done along OA:

here force and displacement have an angle of 90 degree with each other.

as cos(90)=0, work done=0

work done along AC:

displacement=(6.5,6.5)-(6.5,0)=(0,6.5)

force=3*9.8*(0,-1)=(0,-29.4) N

then work done=dot product of force and displacement

=-191.1 J

total work done=-191.1+0=-191.1 J

part b:

red path (OBC):

work done along OB:

displacement=(0,6.5)-(0,0)=(0,6.5)

force=3*9.8*(0,-1)=(0,-29.4) N

then work done=dot product of force and displacement

=-191.1 J

work done along BC:

here force and displacement have an angle of 90 degree with each other.

as cos(90)=0, work done=0

total work done=-191.1+0=-191.1 J

part c:

blue path (OC):

displacement=(6.5,6.5)-(0.0)=(6.5,6.5)

force=3*9.8*(0,-1)=(0,-29.4) N

then work done=dot product of force and displacement

=-191.1 J

part d:

results are identical because gravitational force is conservative.

conservative forces are path independent, hence work done does not depend upon the path taken from origin to desitnation.

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