You are in space, somewhat close to two objects arranged in the pattern shown ab

Question

You are in space, somewhat close to two objects arranged in the pattern shown above. The gravitational forces that you calculate will be much smaller than your weight because of the small masses of the objects. You can treat all the masses, including yourself, as point masses. Don’t worry about their shapes. A) What is the magnitude of the gravitational force that object A exerts on you? B) What is the magnitude of the gravitational force that object B exerts on you? C) Add those gravitational force vectors to find the combined gravitational force (magnitude and direction) exerted by the objects on you. Give direction as being above or below the x axis.

Explanation / Answer

Here ,

force betwen A and you is FA

FA = G * mA * m/d^2

FA = 6.673 *10^-11 * 100 * 60/(1000 *10^3)^2

FA = 4.004 *10^-19 N

the force between A and you is 4.004 *10^-19 N

B)

force between B and you

FB = G * mB * m/d^2

FB = 6.673 *10^-11 * 300 * 60/(1200 *10^3)^2

FB = 8.34 *10^-19 N

the magnitude of force extered by B on you is 8.34 *10^-19 N

C)

magnitude of net force = sqrt(FA^2 + FB^2 + 2 * FA * FB * cos(theta))

magnitude of net force = 10^-19 * sqrt(8.34^2 + 4.004^2 + 2 *8.34 * 4.004 * cos(50))

magnitude of net force = 1.134 *10^-18 N

the magnitude of net force is 1.134 *10^-18 N

theta = arctan(FA * sin(50)/(FB + FA * cos(50))) - 30

theta = arctan(4.004 * sin(50)/(4.004 * cos(50) + 8.34)) - 30

theta = -14.3 degree

the angle made with x axis below is -14.3 degree

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