Question

(a) If the Earth’s gravitational force on a mass depends on the distance between it and the center of the Earth why doesn’t the magnitude of the acceleration of an object dropped from the ceiling of a laboratory increase as the object gets closer and closer to the floor of the laboratory?
(b) If the Earth’s gravitational force on an object is proportional to its mass, why isn’t the acceleration of an object that is twice the mass double that of the original mass? Hint: Examine the consequences of Newton’s Second Law!

Answer 1

the force on body at the floor is proportional to the inverse square of the distance (i.e. 1/r^2)

Look up the radius of the earth (in meters - not km or miles...)- that is the distance between the body and the earth's centre of gravity so force is proportional to 1/r^2

If your ceiling is say 3m then the distance is "radius of earth+3m"
So force on body at the ceiling is proportional to 1/ (radius earth +3m)^2

So the question is slightly misleading - the acceleration IS less the further you are away - but the 3 m difference to the ceiling is insignificant compared to radius of earth

Answer 2

F = m a

a = F1/m

a = 2F1/2m = F1/m

Answer 3

???

Answer 4

I think Douglas's answer is to part b) it shows why the acceleration is the same for both masses
Mine is to part a) It shows that acceleration IS affected by distance to the centre of earth.

Answer 5

Right, @MrNood. Am trying to help without giving the answer. Tricky, sometimes.