Q.343. Work done by force - Mechanics

Question 343.

F = [2yi + x^2j] N, where x and y are in meters.
The particle moves from the origin to a final position having coordinates x = 5m and y = 5m as shown in the adjoining figure.
a) Calculate the work done by F along OC
b)  Is F conservative or non-conservative? Please explain.

Answer 343.

The particle moves along y = x under the action of a variable force F = 2y i + x^2 j.

a)
Work done for displacement in the x -direction
= ∫ (x = 0 to 5) 2y dx
= ∫ (x = 0 to 5) 2x dx
... [because for the path of displacement y = x]
= [x^2] ... (x = 0 to 5)
= 25 J
Work done for displacement in the y-direction
= ∫ (y = 0 to 5) x^2 dy
= ∫ (y = 0 to 5) y^2 dy
... [because for the path of displacement y = x]
= [(1/3) y^3] ... (y = 0 to 5)
= 125/3 J
=> Total work done for the displacement along OC
= 25 + 125/3
= 200/3 J.

b)
In the absence of any frictional or resistive force, work done is conservative.

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