Gravity and Weight: Newton's Second Law

In summary: I would get a much smaller force pushing back than if I were to push a 10,000 kg truck.If I were to push a 1 kg supermarket...I would get a much smaller force pushing back than if I were to push a 10,000 kg truck.
  • #1
nDever
76
1
Hey,

About Newton's Second Law. To compute our weight on Earth using standard g, we use F=ma replacing F and a with W and g (or -g), respectively. So then from this, I gather that weight is a consequence of gravitational acceleration (and mass). So then, it is appropriate to say that our weight, which is a force, is caused by another force (gravity)?
 
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  • #2
nDever said:
So then, it is appropriate to say that our weight, which is a force, is caused by another force (gravity)?
Your weight is the gravitational force on you exerted by the earth. It happens to equal mg near the Earth's surface.
 
  • #3
Doc Al said:
Your weight is the gravitational force on you exerted by the earth. It happens to equal mg near the Earth's surface.

But g is an acceleration. Acceleration is caused by force (according to the first law of motion). What force causes g?
 
  • #4
nDever said:
What force causes g?
The gravitational force of the Earth on the object.
 
  • #5
Doc Al said:
Your weight is the gravitational force on you exerted by the earth. It happens to equal mg near the Earth's surface.

nDever said:
But g is an acceleration. Acceleration is caused by force (according to the first law of motion). What force causes g?

Doc Al said:
The gravitational force of the Earth on the object.

So our weight causes our own acceleration..?
 
  • #6
nDever said:
So our weight causes our own acceleration..?
Of course. What we call 'our weight' is the force of the Earth's gravity pulling us down. If that's the only force acting on us, we will have a downward acceleration equal to g.
 
  • #7
Far be it from me to disagree with Doc Al but I just don't like this:

So our weight causes our own acceleration..?

Of course.


I would much prefer to say our MASS causes our own acceleration. This distinction becomes significant in relativity...and it turns out other stuff like pressure
also affects gravitational acceleration.

This from Doc Al is much better in my opinion:
Your weight is the gravitational force on you exerted by the earth.

Check here for a good discussion of various aspects of WEIGHT:

http://en.wikipedia.org/wiki/Weight
 
  • #8
So the acceleration due to Earth's gravity is constant because we are in the reference frame of the Earth, correct? Whenever an object accelerates towards Earth, Earth accelerates towards that object at a rate directly proportional to the other object's mass, correct? Is this why the mass of the other object cancels out?
 
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  • #9
nDever said:
So the acceleration due to Earth's gravity is constant because we are in the reference frame of the Earth, correct?
Acceleration due to Earth's gravity is approximately constant. It varies with latitude, with altitude, and even from place to place at the same latitude/altitude. Gravitational acceleration at the poles is about half a percent more than that at the equator, gravitational acceleration atop a high mountain measurably smaller than it is at sea level, and those place to place variations are key to finding things like oil.

Whenever an object accelerates towards Earth, Earth accelerates towards that object at a rate directly proportional to the other object's mass, correct?
Yes, but this acceleration is immeasurably small.

Is this why the mass of the other object cancels out?
No. It cancels out because of the forms of Newton's law of gravitation, [itex]F=GmM/r^2[/itex], and Newton's second law, [itex]F=ma[/itex]. Via transitivity (if a=b and a=c, then b=c) we must have [itex]ma = GmM/r^2[/itex], or [itex]a=GM/r^2[/itex].
 
  • #10
D H said:
Acceleration due to Earth's gravity is approximately constant. It varies with latitude, with altitude, and even from place to place at the same latitude/altitude. Gravitational acceleration at the poles is about half a percent more than that at the equator, gravitational acceleration atop a high mountain measurably smaller than it is at sea level, and those place to place variations are key to finding things like oil.


Yes, but this acceleration is immeasurably small.


No. It cancels out because of the forms of Newton's law of gravitation, [itex]F=GmM/r^2[/itex], and Newton's second law, [itex]F=ma[/itex]. Via transitivity (if a=b and a=c, then b=c) we must have [itex]ma = GmM/r^2[/itex], or [itex]a=GM/r^2[/itex].

Is the acceleration approximately constant because the force of gravitational pull acts strongly on more massive objects and weaker on less massive objects? The mass of the attracted object has no bearing whatsoever on its acceleration?
 
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  • #11
nDever said:
Is the acceleration approximately constant because the force of gravitational pull acts strongly on more massive objects and weaker on less massive objects?
Yes. The gravitational force on an object is directly proportional to its mass. But the acceleration, given by Newton's 2nd law, is inversely proportional to its mass. Thus those two factors balance out, giving a constant acceleration regardless of mass.
 
  • #12
Doc Al said:
Yes. The gravitational force on an object is directly proportional to its mass. But the acceleration, given by Newton's 2nd law, is inversely proportional to its mass. Thus those two factors balance out, giving a constant acceleration regardless of mass.

I believe I understand.

If I were to push a 1 kg supermarket cart down an aisle with a constant force of 1 N, it would accelerate at 1 m/s/s. If I were to put more stuff in the cart such that it has 2 kg of mass and then I push it with the same 1 N of force, then the acceleration halves and it accelerates at .5 m/s/s. These are the effects of applied forces. Double the mass, half the acceleration. Triple the mass, one third the acceleration.

Now Gravity is just a different force where the magnitude of the force is directly proportional to the product of the two masses (lets ignore the distance, I understand that). So then, the force of gravity increases and decreases with the mass. Its the nature of gravity. If the mass is small, the force is small. If the mass is large, the force is large. So then if a small and large mass is dropped from the same height, gravity pushes lightly on the less massive object and heavily on the more massive object, thus the acceleration is the same.

In a sense, gravity acts like this.

Now I have two supermarket carts placed side by side, one with a bunch of stuff in it, the other with very little in it, and I get two people to push them at the same time. The cart with more in it gets pushed harder and the other with less items gets pushed lighter. Let them go, and they move at the same rate with respect to one another.

Do I have the right idea?
 
  • #13
nDever said:
Do I have the right idea?
I think you do.

For a more mathematical view, review D H's post #9 where he shows that the acceleration due to gravity does not depend on the mass of the object.
 
  • #14
Ah, I see. It has everything to do with the mathematical definition of acceleration in terms of force.

So then any two objects that are dropped from the same height within the gravitational field of any more massive body will fall at the same time. After gravity takes it's course, the only thing that the acceleration depends on is the mass of the larger body and the distance between it and the others. As altitude increases, g decreases.

The reason that Earth's g is about 9.8 m/s/s is only because of the way that the Earth's mass and our distance from its center works out. Because the Earth is large and we are relatively small, the everyday heights that we achieve allow us to average g out to be 9.8 m/s/s.

If this be the case, then it can be said that it is impossible for any two objects dropped from two different heights to land on the same point at the same time (with negligible air resistance). Is this sound?
 
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1. What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In other words, the more mass an object has, the more force is needed to accelerate it at a certain rate.

2. How does Newton's Second Law relate to gravity and weight?

Gravity is a force that pulls objects toward each other, and it is a result of mass. Newton's Second Law explains that the force of gravity acting on an object is directly proportional to its mass. This means that the more massive an object is, the greater its weight will be.

3. What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is constant, while weight can change depending on the strength of the gravitational force.

4. How does gravity affect objects of different masses?

Gravity affects all objects in the same way, regardless of their mass. However, objects with greater mass have a stronger gravitational pull, and therefore, require more force to accelerate them at the same rate as objects with less mass.

5. How does the distance between objects affect the force of gravity?

The force of gravity decreases as the distance between objects increases. This is known as the inverse square law, which means that the force of gravity is inversely proportional to the square of the distance between objects. This is why objects feel lighter when they are farther away from the Earth's surface.

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