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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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