Three uniform spheres of masses mi-3.50 kg, m2 = 4.00 kg, and m3 6.50 kg are pla

Question

Three uniform spheres of masses mi-3.50 kg, m2 = 4.00 kg, and m3 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. Does the sphere of mass mi contribute any force in the x direction? + 1037.6 Remember that superposition allows us to calculate the forces do to each sphere separately and then add the results together. j) x 10-11 (0, 3.00) m 12 (-4.00, 0) m ms 32 Need Help?

Explanation / Answer

We know that the force of gravity between two masses is given by:

F = G m1 m2/r^2

So, F12 = 6.67 x 10^-11 x 3.5 x 4/3^2 = 1.04 x 10^-10 N j

F32 = 6.67 x 10^-11 x 6.5 x 4/4^2 = - 1.08 x 10^-10 i N

Resultant force will be:

F = - 1.08 x 10^-10 i + 1.04 x 10^-10 N j

F = ( -10.8 i + 10.4 j ) x 10^-11 N

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