Question

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]

Answer 1