# Density affects Acceleration?

1. Dec 16, 2012

### HenryKhais

Hello,

I was conducting some experiments with toilet paper.
I tore off 2 sheets of square paper, each measuring 0.5g.

I began dropping them from equal levels at approximately the same exact time.
They each landed equally (obviously), however, as I began to crumble one of the sheets into a ball, I observed that it reached the surface much faster than the other sheet that remained flat.
I also observed that the denser I made the ball (the smaller I shaped it), the faster it dropped.

Why is this?
Does this have to do with less Force going against the denser object because it's smaller (aerodynamically)?

I have read people say that density does not affect acceleration, yet the experiment showed that the more compact you made it, the faster it accelerated.

My Current Theory:
Equal masses, regardless of the matter (be it toilet paper, notebook paper, or an eraser), have equal Maximum Velocities (under equal gravity).
The density, however, affect how fast the sample of matter will reach it's maximum velocity, before falling at an equal rate.

Please keep in mind, I am very new to Physics, apologies if I sound dumb!

Thank You!

Last edited: Dec 16, 2012
2. Dec 16, 2012

### Drakkith

Staff Emeritus
The answer to this is also the answer to why a feather and a hammer don't reach the ground at the same time when dropped at the same time. Air resistance. The feather, and your flat piece of paper both have large amounts of air resistance relative to their mass. The hammer and crumpled up paper have much less air resistance relative to their mass, so they accelerate faster and reach the ground faster.

If you drop these in a vacuum they do in fact hit the ground at the same time.

See here:

Last edited by a moderator: Sep 25, 2014
3. Dec 16, 2012

### Staff: Mentor

It isn't the density of the object that matters. The drag force is a function of the geometric shape and size of the object, and of the velocity of the object through the air. The drag force does not depend on the density of the falling object.

4. Dec 17, 2012

### HenryKhais

Fascinating video!
It seems to me that Resistance plays a very large role in the every day world, causing lots of variation. However, in a vacuum tube or on the moon, where there is no resistance, does the gravitational force determine how fast objects will fall?

5. Dec 17, 2012

### sophiecentaur

If you were an insect, you would notice that even more. The relative effects of electric and gravitational forces are very much subject to scale. They say that a mouse, thrown off the Empire State Building would survive the landing but not a cat that would have the same density.

6. Dec 17, 2012

### A.T.

The scaling factor (lower mass / cross-section ratio) lowering terminal velocity, when falling in air. It also reduces the internal stresses occurring during the high acceleration on impact.

Last edited: Dec 17, 2012
7. Dec 17, 2012

### Studiot

Hello Henry,

First let me congratulate you on a clear precise experiment and report.

You investigated the effect of varying some parameter (density), whilst controlling another parameter (total weight of falling object) and subjecting them to the same acceleration regime.

It is unfortunate that the conclusion was wrong because there was another uncontrolled effect at work - that of air resistance as already noted. This is of course due to the difference in shape of the objects.

So keep at the good work but learn to be aware that unforseen effects may occur and unforseen agents may act.