The three spheres in the figure, with massesm A =1050 g , m B = 100 g , andm C =

Question

The three spheres in the figure, with massesmA =1050 g, mB = 100 g, andmC = 250 g have their centers on a common line,with L = 12 cm and d = 4.0 cm. You move themiddle sphere until its center-to-center separation frommC is d = 4.0 cm. How much work is done onmB by you?
How much work is done on mB by the netgravitational force on mB due to mA andmC? The three spheres in the figure, with massesmA =1050 g, mB = 100 g, andmC = 250 g have their centers on a common line,with L = 12 cm and d = 4.0 cm. You move themiddle sphere until its center-to-center separation frommC is d = 4.0 cm. How much work is done onmB by you?
How much work is done on mB by the netgravitational force on mB due to mA andmC?

Explanation / Answer

(a)
    in the given problem we can see that the workdone by you in moving the sphere of mass mB equals thechange in the
    potential energy of the three-sphere syatem
    the initial potential energy is
    Ui = - (G mA mB/ d) - (G mA mC / L) - (G mCmB / (L - d))
    the final potential energy is
    Uf = - (G mA mB/ (L - d)) - (G mA mC / L) - (G mCmB / d)
    the work done will be
    W = Uf - Ui
         = ......... J
(b)
    the work done by the force of gravity is
    - (Uf - Ui) = .........J

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