Why is it that acceleration due to gravity and not force due to gravity is constant?

Question

A ball weighing 10kg would accelerate at 9.8m.s^-2 with a force of 98 Nm
A ball weighing 20kg would accelerate at 9.8m.s^-2 with a force of 196 Nm

Why is this the case and not the other way around (constant force variable acceleration)?

Answer 1

The Universal Law of Gravitation states that the attractive force due to gravity between two bodies is linearly proportional to the product of the masses of those two objects. The 20 kg ball will be attracted to the earth twice as strongly as the 10 kg ball is. However, the 20 kg ball also has twice as much mass to move, and so the acceleration with which the 20 kg ball falls to earth is exactly equal to the acceleration of the 10 kg ball. In terms of acceleration, all that matters is the gravitational potential at a given location, not the mass of involved objects.



P.S. acceleration due to gravity is not truly constant. It does vary with distance, but since the distance to earth's center dwarfs the difference between standing on top of Mt. Everest and sitting in Death Valley Basin, this variation is negligible. Even orbiting satellites experience nearly exactly the same potential we do here on the planet's surface.

Answer 2

Mass of an object is a constant.

Hence [force/acceleration] is a constant = mass of the object.



A force of 98 N on a mass of 10kg moves the mass with an acceleration of 9.8m/s^2.

A force of 196 N on a mass of 10kg moves the mass with an acceleration of 19.6 m/s/s^2.

If force is increased 10 times the acceleration increases 10 times.



Changing the force ON ONE AND THE SAME MASS changes the acceleration of the object proportionally.



Earth on the other hand cannot change the force ON ONE AND THE SAME MASS.

It applies the SAME force on all objects which have the SAME MASSES.

(This can be understood by equal arm balance)

If mass is different then the force is different.

If mass is doubled the force is doubled.



We know that force/ acceleration is a constant and equals the mass.

Since the earth cannot apply different force on one and the same object, it follows that the acceleration must be the same for different objects but with the same mass.



Since earth cannot change the force on all objects of equal masses, we want to know how the force is changed if mass is changed.



If mass is doubled then the force is also doubled implying the fact that the acceleration should remain the same as for the mass before doubling.

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Answer 3

Suppose that gravity pulled on everything with constant force. Let's say the force was 9.8N.



If I gave you a box of mass 1kg, then you would say if dropped it would accelerate at 9.8m/s^2.



But suppose I tell you the box is filled with 1000 packing peanuts that weigh 1g each. If you think of each packing peanut accelerating individually, pulled by a force of 9.8N, you would say they would all accelerate at 9800m/s^2. The box itself might weigh 50g or so, so it would slow the whole thing down to no less than 196m/s^2. In reality it would be somewhere between that, with the box exerting a support force to diminish the acceleration of the peanuts and the peanuts pushing back and accelerating the box a bit faster than gravity would itself.



Obviously the force on the box cannot be the same as the force on each of its parts. Maybe you would exclude objects that are made up of smaller parts from your rule of constant gravitational force. Since in fact most everything is made up of smaller parts, that rule wouldn't apply to much. The force on everyday items would at least depend on how many parts were in them. Approximately, that's accurate. The force depends on how many protons and neutrons are in something. Though it's not perfect; electrons and other particles have to be counted at a different weight.

Answer 4

Gravity pulls things down at the same acceleration. So all objects regardless of their weight would ideally fall at the same rate, same acceleration. It's their mass that affects their momentum, i.e. their force relative to their speed. With greater mass comes greater momentum, and force, and vice-versa. But same acceleration.