Physics 111 during Spring 2017 128 Item 4 Item 4. At a certain instant, the eart
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Question
Physics 111 during Spring 2017 128 Item 4 Item 4. At a certain instant, the earth, the moon, and a stationary 1480 kg spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84 x 10 km in length. Signed in as Ahmed Aldhanhani previous l 4 of 6 l next Part A Find the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon. Express your answer to three significant figures. Submit My Answers Give Up Part B Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle measured from a line connecting the earth and the spacecraft. Express your answer to three significant fig Submit! My Answers Give Up Part C What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? You can ignore any gravitational effects due to the other planets or the sun.Explanation / Answer
a = 3.84 x 10^5 km = 3.84 x 10^8 m
m = 1480
a)Force from moon
Fm = G Mm m/r^2 = 6.67 x 10^-11 x 7.35 x 10^22 x 1480/(3.84 x 10^8)^2 = 0.049 N
that from earth
Fe = 6.67 x 10^-11 x 5.97 x 10^24 x 1480 / (3.84 x 10^8)^2 = 4 N
force in X direction
Fx = Fe + Fm cos60
Fx = 0.049 + 4 x cos60 = 2.049 N
Fy = Fm sin60 = 4 x sin60 = 3.46 N
F = sqrt [Fx^2 + Fy^2] = sqrt [2.049^2 + 3.46^2] = 4.02 N
Hence, F = 4.02 N
b)theta = tan-1(Fy/Fx) = tan-1(3.46/2.049) = 59.37 deg
Hence, theta = 59.37 deg