Question

Newton’s Gravitational Law predicts the force of attraction between two massive objects that are some distance...

Newton’s Gravitational Law predicts the force of attraction between two massive objects that are some distance apart: Fgravity = G m1m2/ r^2

(a) Given F is in units of Newtons, m is units of kilograms and r is in units of meters, what are the units of the universal gravitational constant, G, in meters, kilograms and seconds? Show your working.[2]

(b) If one of the objects doubles in mass, how much does the predicted force of attraction change between the two objects? [1]

(c) If both objects double in mass, how much does the predicted force of attraction change between the two objects? [1]

(d) If the distance between the two objects doubles, how much does the predicted force of attraction change between the two objects? [1]

(e) If the distance between the two objects halves, how much does the predicted force of attraction change between the two objects? [1]

(f) Given Newton’s laws predict that Fgravity = m1a1, and assuming that m2 = mEarth ≈ 1025kg, r = rEarth ≈ 107m and G ≈ 10^−10 hidden-units,

(i) what is the predicted gravitational acceleration a1 of m1 toward the Earth? [2]

(ii) what is the predicted gravitational acceleration a2 of the Earth toward m1, if m1 equals your body mass? Hint: use Newton’s law F1,2 = F2,1, where F1,2 = m2a2 and F2,1 = m1a [2]

(iii) Given your result for a2, if you jump off your bed and are in free-fall for √ 2 seconds, how far does the Earth move toward you? Hint: y = at^2/2 [2]