Quote:
Originally posted by Bob Lentil
Here's where I disagree with you. The acceleration an object experiences due to a force is not independent of its mass. According to Newton's second law, Acceleration = Force/Mass. If I exert a force on a basketball, it's going to accelerate a whole lot faster than if I exert the same force on the sun. [/b]
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Don't worry - this one can be tricky. I'm probably not explaining it as well as I could.
The acceleration two objects experience by the same force is independant of the mass of those objects. In my example, the acceleration on a bowling ball and the feather on the earth are 9.8 m/s^2 for both objects, even though the mass of the feather is much less than the bowling ball. This phenomena was first described by Galileo. The forces on those objects toward the earth are different because of their different masses (it hurts a lot more get a bowling ball dropped on your head than a feather!), but the acceleration they experience toward the ground is the same (again, we're neglecting the gravity generated by the objects themselves). It's that point where Newton improves on Galileo's findings.
For our example on earth, it goes something like this mathematically:
F=ma
The force of gravity is equal to the mass of the object times the gravitational acceleration, so (g)
mg=ma
the masses cancel out on each side, so...
a=g
The acceleration the object experiences is equal to the gravitational acceleration. The acceleration of that object due to gravity is independant of its mass (no m in that equation).
In another more basic mathematical example, Newton found that the gravitational force between two objects is:
F=GmM/r^2
Where G is a constant, m is the mass of object one, M is the mass of object two, and r is the distance between them.
Okay, again, the force on the object can also be desribed as
mg (its mass times the acceleration due to gravity), so...
mg=GmM/r^2
You can probably see where this is going again. The object's mass appears on both sides of the equation. They cancel out, and we're left with
g=GM/r^2
That says the acceleration due to gravity the object experiences depends on the mass of the other object and the distance to it. The object's own mass is not a factor.
The Apollo astronauts demonstrated this in a great experiment on TV. While on the moon, an astronaut held out an hammer and a feather. He dropped them both at the same time in the near-vacuum environment of the moon, and they both hit the lunar surface simultaneously.
But the acceleration doesn't have to be be gravitational acceleration (g) - it can be any acceleration by any external force. A spaceship and a black hole. A baseball and the earth. Chris Squire and Spandex.
Avian