# Homework Help: Downward acceleration greater than g

1. Jan 21, 2004

### mmfoley

Hello,

I am taking a Natural and Physical Sciences course. As math and sciences aren't my strongest subjects, I am really struggling, reading things over and over again, and they are just not sinking in. For example, I understand the acceleration of gravity - g. I think that something can have a downward acceleration greater than g, - at least I think this is correct based on my notes, but I do not understand exactly how.

Would the following be accurate? – When an object first falls it is unbalanced, until the force of air resistance is large enough to balance the acceleration of gravity. So until it balances out, it is falling faster g. Since the object is falling down, this would mean that while unbalanced it has a downward acceleration greater than g.

Help!!

Thank you!
mmfoley

2. Jan 21, 2004

### HallsofIvy

No, you are confusing speed with acceleration!

If there were no air resistance, the object would fall with acceleration g.

With air resistance, its acceleration is always less than g.

Since air resistance is proportional to speed, initially there will be very little resistance. The acceleration will be close to g, only very slightly less. As speed increases, so will air resistance so acceleration will go down. When speed is high enough that air resistance, upward, is equal to gravitational force, downward, (weight), the acceleration is 0,not g. The speed is now constant, not the acceleration.

Acceleration of a body falling through the air is initially g, then decreases to 0. It's speed is initially 0, then increases to it "terminal velocity".

3. Jan 21, 2004

### HallsofIvy

It is, of course, possible, to go downward with acceleration greater than g but not "falling". An airplane, diving downward with its engine force added to the force of gravity, would have acceleration greater than g.

4. Jan 21, 2004

### mmfoley

Thank you - one more question

Thank you for the help. Here is another question:

How do the mass and weight of an object at the earth's center compare with their values at the earth's surface?

I believe that as you move closer to the earth's center you get the gravitational attraction effect, but that is about where my knowledge runs out on this topic.

5. Jan 22, 2004

### HallsofIvy

You posted this as a separate thread and got very good answers there but I'll reply here.

As you move down into the earth, you are attracted only by the mass below you. It's a complicated calculation but it is possible to show that the gravitational attraction of the mass above you level cancels. Yes, since gravity depends on 1/R2, as you get closer to a mass gravitational pull (of that mass) increases but since volume (and so mass) below you depends on R3 the total gravitational pull (weight) depends on R3/R2= R. When R= 0, gravitational pull is 0.

The total gravitational pull at the center of the earth is 0 because you are pulled equally in all directions. Your "weight" will be 0. Of course, your "mass" stays the same.

6. Jan 22, 2004

### mmfoley

Thank you

Thank you for the quick response and help!

mmfoley