Gravity and falling objects

Gravity pulls harder on objects with more mass, correct? So why doesn't a heavier object fall faster than a lighter object? Is the extra force of gravity countered by the extra inertia that resists the acceleration of the heavier object? What is the relation of gravity to mass? Why DOES the earth pull harder on objects with more mass? How does it know which objects have more mass and which objects have less mass?

 

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Do you remember the hammer, feather experiment done by Commander David Scott on the Moon in Apollo 15?
On Earth the hammer would have hit the ground first because air resistance was slowing the feather.

 

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Gravity increases an objects downward velocity at 9.81 m/s...... it accelerates everything at exactly the same rate.

By the same token gravity needs to pull harder on heavier objects than lighter objects to attract them both by similar amounts.
On Earth though, we have air resistance affecting that.

 

Right. However, it will not accelerate any object faster than the gravitational gradient (in our case, 9.8 m/s2.)

In air it does. At terminal velocity (i.e. neither accelerating nor decelerating) then a heavier object will have more force on it. So if you have two identically sized bodies falling at terminal velocity in air, then the heavier one will fall faster.

However, in a vacuum, there is no terminal velocity. Thus the fastest you can accelerate due to gravity (at least on Earth) is 9.8 m/s2

It doesn't. The gravitational gradient affects all mass equally. However, if you oppose that force, then heavier objects, having more mass, will generate more force.

 

Why is there terminal velocity? Isn't gravity increasing as the object falls closer to earth? Isn't it still "pulling" on the object? Let's say it falls into a hole to the center of the earth. The gravity exerted on the object would increase, but it wouldn't fall faster? What is keeping it from doing that?

 

No, not so you'd notice. At the surface gravity is 9.81m/s2, at 10,000 feet (about where we usually jump from) it's 9.80 m/s2. The bigger change is the density of the atmosphere - it is less as you go higher. So in fact terminal velocity is LOWER near the surface.

It is always pulling on it with the same force per kg.

No. As you go below the surface then the mass above you starts to attract you as well, and gravity decreases. Gravity reaches zero as you get to the center of the Earth. (And of course air pressure would increase, slowing a terminal-velocity descent.)

 

At terminal velocity, what pulling is even necessary? Say I take a rope and pull a car at 20 mph. When it reaches terminal velocity, the rope is no longer pulling. It is slack, and the natural momentum of the car has taken over at least for a short while. Now if the rope pulls again, it will speed the car up. In what sense is gravity still pulling on the object when the object is simply resisting change in motion due to Newton's law? In what sense is there pulling when there is no resultant acceleration?

 

That demonstrates same-acceleration, not same-force.

F = m a

 

Incorrect. The rope is now pulling just enough to overcome rolling friction and air friction. If you cut the rope the car would slow down and eventually stop.

It is pulling on it the same way that rope is still pulling on the car - enough to overcome drag. If there were no gravity, the falling object would slow down and stop.

 

Then let's say I am pulling a rock thru a perfect vacuum of empty extraterrestrial space. At the point the rock reaches 20 mph, I am no longer pulling. Likewise with gravity. We say gravity is still pulling an object in a vacuum. But what counterforce is it overcoming?

See vacuum example above. Gravity is still pulling an object in a vacuum. But there is no drag to pull against. There would only be the inertia of resisting acceleration. In which case there WOULD BE acceleration from being pulled.

 

I think rpenner's point is the best way to look at this. Force = mass x acceleration.

To start with, gravity exerts a force which we call "weight", proportional to the mass of the object. This will cause the object to accelerate. So, if you take a 1kg mass and a 10kg mass at the Earth's surface, the force on the first is 9.8N and on the other is 98N.

But the acceleration is Force/mass. (F=ma => a = F/m, right? ) So the resulting acceleration of the first is 9.8/1 = 9.8 m/sec², while on the second it is 98/10 = 9.8 m/sec² . The same! The force on the more massive object is more, but then it takes a bigger force to give it a given acceleration - and, as my example shows, it happens that the two things exactly cancel out, with the effect that all objects have the same acceleration due to gravity.

This applies in vacuo: if there are other forces acting, due to air resistance for example, which is not proportional to mass, then there will be deviations from this behaviour.

 

OK. Then yes, if you cut the rope at that point, then there is no additional acceleration or deceleration

None, actually. From its perspective, and anything near it, there are no forces on the object; it is freely falling. However, in that region space itself is warped, and thus to an outside observer it looks like some thrust is accelerating the object. Once the object hits something that limits its motion (like the surface of a planet) that warping is seen as a force proportional to mass; we call this force "weight."

There's a famous thought experiment which asks is someone in a box can tell if they under a 1G acceleration in a rocket or on the surface of the Earth. And the answer (with one very minor exception) is no - they experience the same thing. Same thing for someone in a box in orbit around the Earth (with almost 1G of gravity acting on them) or in deep space with no gravity. Again, they can't tell the difference.

Inertia really doesn't apply; inertia keeps the object in free-fall, which in warped space means acceleration towards the gravitational source. In other words there's no combination of weights you could come up with to make inertia overcome gravity or vice versa.

 

So you're saying its only an illusion that there is a force pulling on the object in a vaccum? That gravity has ceased to act upon that object as it continues moving due to momentum?

 

Well, the force itself is not an illusion since it can be measured. However, that force appears due to the object's presence in the warped space rather than a true external force acting on the object.

Gravity "acts" on it by creating the warped spacetime in which the object moves. So it's always acting on it.

 

Wouldn't gravity have to be a force already if it warps spacetime? Or is it mass that warps spacetime, creating gravity?

 

I think you are getting off track, so back to this:

Yes, inertia. So yes, in space the acceleration due to gravity is always there and there is no terminal velocity because there is no counterforce but that from inertia.

 

It is generally considered a force, yes. However, not all forces act like the normal force (the force caused by "pushing" something, as in with a rocket or a stick.)

That is a common way to describe the effects of gravity, yes.

 

Duplicate

 

I think the views of Einstein and Newton are getting confused a bit. Read the page I linked to above.