2- Three uniform spheres of masses m 1 = 3.00 kg, m 2 = 4.00 kg, and m 3 = 7.00
ID: 2253540 • Letter: 2
Question
2-Three uniform spheres of masses m1 = 3.00 kg, m2 = 4.00 kg, and m3 = 7.00 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.
2-Three uniform spheres of masses m1 = 3.00 kg, m2 = 4.00 kg, and m3 = 7.00 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.Explanation / Answer
mass m1 is at (0,3.00) m
mass m2 is at (0,0)
mass m3 is at (-4.00,0) m
force between masses m1 and m2 is
F1 = (Gm1m2/r1^2)
where G = 6.67 x 10^-11 Nm^2/kg^2 and r1^2 = [(0 - 0)^2 + (3.00 - 0)^2] m^2
force between masses m2 and m3 is
F2 = (Gm2m3/r2^2)
where r2^2 = [(-4.00 - 0)^2 + (0 - 0)^2] m^2
the net gravitational force on m2 is
F = (Fx^2 + Fy^2)^1/2
where Fx = F1x + F2x = F1 x cosA + F2 x cosB
and Fy = F1y + F2y = F1 x sinA + F2 x sinB
where the angles are
A = tan^-1(3.00 - 0/0 - 0) = 90o
and B = tan^-1(0 - 0/-4.00 - 0) = 0o
the angle made by the net force is
theta = tan^-1(Fy/Fx)
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