Question

The masses and coordinates of three spheres are as follows:

Sphere 1: 14 kg, x = 2.25 m, y = 2.00 m

Sphere 2: 38 kg, x = -2.00 m, y = -2.50 m

Sphere 3: 52 kg, x = 0.00 m, y= -0.25 m

What is the magnitude of the gravitational force on a 22 kg sphere located at the origin due to the other spheres?

Answer 1

SOLUTION:

Components of gravitational forces along X axis:

Sphere 1:

(along positive x axis)

Sphere 2:

(along negative x axis)

Sphere 3:

Therefore, Net magnitude of component of gravitational force along x axis is given by:

(along negative x axis)

Components of gravitational forces along Y axis:

Sphere 1:

(along positive Y axis)

Sphere 2:

(along negative Y axis)

Sphere 3:

(along negative Y axis)

Therefore, Net magnitude of component of gravitational force along Y axis is given by:

(along negative Y axis)

Therefore, Net magnitude of gravitational force on the sphere at the origin is given by:

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