# The Naked Scientists Forum

### Author Topic: How does earth exert same acceleration on all kinds of objects ?  (Read 764 times)

#### Dr Amrutha

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##### How does earth exert same acceleration on all kinds of objects ?
« on: 20/04/2016 12:10:10 »
I would be very grateful if someone answers to the point in a way that it makes sense for a high school student.

#### evan_au

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##### Re: How does earth exert same acceleration on all kinds of objects ?
« Reply #1 on: 20/04/2016 13:06:05 »
You could perhaps explain it with Newton's law: F=ma
Where:
• F: Force in Newtons
• m: Mass in kilograms
• a: acceleration in m/s
• g: the acceleration due to gravity that we find at the surface of the Earth (about 9.8 m/s)

If you have an object of mass m1 sitting on the ground, it exerts a force of F1 =m1g Newtons.
This applies if the mass m1 is 1g, 1 kg or 1 ton(ne).

If you now drop this object of mass m1 down a hole in the ground, you could imagine the object being subject to a gravitational force F1.

Rearranging the equation F=ma, you find that the acceleration of the object is now a=F1/m1 = g = 9.8m/s

It may seem like a circular argument, but this says that regardless of whether the object is 1g, 1 kg or 1 ton(ne), it will accelerate downwards at about 9.8m/s (...in a vacuum, near the Earth's surface).

In physics, there are several types of mass (the above description referred to "passive gravitational mass" and "inertial mass"), which always seem to be identical when we compare them, but nobody is totally sure why.
See: https://en.wikipedia.org/wiki/Mass#Inertial_vs._gravitational_mass

#### PmbPhy

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##### Re: How does earth exert same acceleration on all kinds of objects ?
« Reply #2 on: 20/04/2016 17:51:36 »
I would be very grateful if someone answers to the point in a way that it makes sense for a high school student.
Think of it like this: Drop a ball from rest and record how long it takes to hit the ground. If you now drop another object from the same height then it too will fall. However since the object is more massive the force on it is greater. However being more massive means that it takes a larger force to accelerate it at the same rate as the ball. These effects cancel out with the end effect of the object falling at the same rate as the ball hitting the ground in the same amount of time as the ball.

#### Arthur Geddes

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##### Re: How does earth exert same acceleration on all kinds of objects ?
« Reply #3 on: 20/04/2016 18:09:37 »
Would it hurt to tell H.S. students that in Newtonian theory this is a coincidence; gravitational mass & inertial mass are equal for some as yet unknown reason: in G.R., inertial mass & gravitational mass are asserted to be equal, indistinguishable; they could handle that, eh?

#### PmbPhy

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##### Re: How does earth exert same acceleration on all kinds of objects ?
« Reply #4 on: 21/04/2016 06:06:25 »
Would it hurt to tell H.S. students that in Newtonian theory this is a coincidence; gravitational mass & inertial mass are equal for some as yet unknown reason: in G.R., inertial mass & gravitational mass are asserted to be equal, indistinguishable; they could handle that, eh?
Sure. Of course they can handle it. Never make the mistake that high school students aren't smart. When they ask questions like this it's to learn the answer. That means they're climbing out of a state of ignorance using their inherent intelligence.

By the way. This isn't true just in Newtonian mechanics but also in GR. In both theories its an experimental fact. It's the reason why particles move on geodesics.

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##### Re: How does earth exert same acceleration on all kinds of objects ?
« Reply #4 on: 21/04/2016 06:06:25 »