A 3.00-kg particle moves from the origin to position having coordinates x = 6.50

Question

A 3.00-kg particle moves from the origin to position having coordinates x = 6.50 m and y = 6.50 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 = FDeltar cos theta = Frightarrow.Deltar), calculate the work done by the gravitational force in going from O to along the following paths. the purple path (O ) Does the gravitational force to any work while the particle moves from O to ? J the red path (O ) J the blue path (O ) J Your results should all be identical.? why?

Explanation / Answer

Gravitational Force is acting along the negative y axis , F = 9.8*3 = 29.4 N
(a)
Work done from O to A = 0 (As angle between the Force and Displacement is 90degree & cos(90) = 0)
Work done from A to C = - 29.4 * 6.5
Work done from OAC = - 191.1 J

(b)
Work done from O to B = - 29.4 * 6.5 = -191.1 J
Work done from B to C = 0 J (As angle between the Force and Displacement is 90degree & cos(90) = 0)
Work done from OBC = - 191.1 J
(c)
Work done from O to C = - 29.4*d*cos(45)
Where d = sqrt(6.5^2 + 6.5^2)
d = 6.5*sqrt(2) m

Work done from O to C = - 29.4*6.5*sqrt(2) *cos(45)
Work done from O to C = - 191.1 J
Work done from OC = - 191.1 J

(d)
Yes Results are same, becuase Gravitational Force is a conservative force and work done by it does not depend on the path taken to reah final positon from initial position.

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