Gravitation
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Four spheres, labeled 1, 2, 3 and 4, are arranged as shown in the figure (in the attachment). The spheres interact with each other through gravitational forces. They are far from the surface of the Earth and any other massive bodies.
Spheres 2, 3 and 4 have the same distance d from the sphere 1; the masses are m1 = m2 = m3 = m and m4 = 3m.
(a) Draw the free-body diagram for sphere 1.
(b) Calculate the net force on sphere 1, x and y components.
(c) Where do you have to place an additional sphere of mass m in order for the net force on sphere 1 to be zero? Calculate the position and indicate it in a sketch.
Please show all the work.
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Solution Summary
A step by step solution is provided for a problem on gravitational force in an arrangement of four spheres.
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Please refer to the attachment for the full solution.
a) Forces acting on sphere 1 due to other three spheres are shown in the fig..
b) Magnitude of gravitational force on 1 due to 2 = F21 = Gm1m2/d2 = Gxmxm/d2
= Gm2/d2
Magnitude of gravitational force on 1 due to 3 = F31 = Gm1m3/d2 = Gxmxm/d2
= Gm2/d2
Magnitude of gravitational force on 1 due to 4 = F41 = Gm1m4/d2 = Gxmx3m/d2
= ...
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