Does weight/mass really have no effect on the rate that objects fall?

[John Salerno]

I know the lesson that if you were to drop a book and a sheet of paper, the book hits the ground first, not because of its weight or its mass, but because of air resistance. So I was reading this website that attempts to explain it: http://www.physicscl...wtlaws/efar.cfm

 

and was a little confused by this paragraph, with the relevant phrase bolded:

 

In fact, objects will continue to accelerate (gain speed) until the air resistance force increases to a large enough value to balance the downward force of gravity. Since the elephant has more mass, it weighs more and experiences a greater downward force of gravity. The elephant will have to accelerate (gain speed) for a longer period of time before their is sufficient upward air resistance to balance the large downward force of gravity.

 

Now, I understand the very basics behind how two objects will fall at the same rate in a vacuum, regardless of weight or mass. But when we are not speaking in terms of a vacuum, I thought it was still wrong to say that the reason the book falls faster is because of its weight or mass. However, the above quote seems to directly implicate weight and mass as factors for why the elephant falls faster than the feather.

 

So what is correct? Is it really wrong to say that a book hits the ground before the sheet of paper because of its weight or mass? Doesn't that have *anything* to do with it? If not, what does the above quote mean? Is the website wrong or am I just misunderstanding?

 

Thanks.

Edited November 7, 2010 by John Salerno

[Cap'n Refsmmat]

Consider two objects with the same shape and size, so they have exactly the same air resistance when dropped, but one of the objects is twice as heavy as the other.

 

Because of that extra weight, it will fall slightly faster. The force of gravity acting upon it will be stronger, but the air resistance acting on it will be no different, so it will fall slightly faster.

 

Now, it'll eventually reach a speed -- the terminal velocity -- at which the air resistance equals the force of gravity, and the object stops accelerating and merely falls at a constant velocity. The object with a higher weight will have a higher terminal velocity.

[timo]

I know the lesson that if you were to drop a book and a sheet of paper, the book hits the ground first, not because of its weight or its mass, but because of air resistance.

That is a tricky statement because the acceleration due to air resistance depends on the mass

It is also correct that an object with more mass experiences a larger gravitational force; only the acceleration due to gravity is the same for all objects.

 

I thought it was still wrong to say that the reason the book falls faster is because of its weight or mass. However, the above quote seems to directly implicate weight and mass as factors for why the elephant falls faster than the feather.

 

So what is correct? Is it really wrong to say that a book hits the ground before the sheet of paper because of its weight or mass?

It is, in my opinion, absolutely correct to say that a book falls faster than a sheet of paper due to its larger mass. But beware that you are comparing books with papersheets here! A feather pillow might have more mass than a rifle bullet but I doubt it will fall down faster. Mass is not the only factor determining the speed of falling.

 

You might be interested in reading this thread where I put a similar statement into a slightly more scientific form: http://www.scienceforums.net/topic/26055-galileos-expements/

[John Salerno]

It is, in my opinion, absolutely correct to say that a book falls faster than a sheet of paper due to its larger mass.

 

Hmm, that's interesting. I mean, I understand that mass isn't the *only* factor, but this seems like one of those things where the "smart" answer is to say "The mass of the objects has nothing to do with why the book falls faster than the paper." In other words, it's the example given to people to prove to them that mass *doesn't* affect the rate at which an object falls, or to show them something neat about physics that goes against their natural assumption.

 

In a way, are you saying that the "over-corrected" answer is actually wrong as well, and a person's intuitive assumption that the mass does matter is actually right?

Edited November 7, 2010 by John Salerno

[timo]

It is (again in my opinion) absolutely wrong to say that mass has no effect on how fast something falls (in the presence of friction). Assume two bodies with the same shape but different densities, and a friction force which only depends on the objects' shape and velocity (the latter should serve as a very good approximation for many cases). In this case, the object with the greater mass will fall faster.

 

My statement about "depends on many things" is much more involved than you might think at first glance. Perhaps forget about it (in which case the "in my opinion" parts become "that's how it is") and just focus on the two example in the previous paragraph and the little calculation I quoted above - and possibly the thread I linked. There, it is clear that an object with larger mass will fall faster when air resistance is non-negligible. If you are seriously interested in understanding it, I strongly advice to understand the calculation steps, why I showed them, and what they do mean (there is a bit more to it than a simple rearrangement of terms). Also, try to first understand in terms of equations why all objects fall at the same rate when there is no friction.

[ewmon]

Let's look at the basics.

 

Time of flight (ie, regarding which object "lands first") is inversely related to velocity, and velocity is the integral of the acceleration, which is caused by the sum of the forces, which in turn, is the force of gravity minus the drag. For all intents and purposes, the force of gravity is a constant depending on the object's mass (although it does vary by extremely small amounts depending on its altitude).

 

Traditionally,

 

D = ½·C_D·p·V²·S

 

D is drag

C_D is the coefficient of drag (due to its shape)

p (rho) = air density

V = velocity

S = cross-sectional area

 

The drag is a function of the object's shape, velocity and cross-sectional area (although the density of the air does change by extremely small amounts depending on the altitude). With shape, area and air density remaining the same, drag becomes a function of velocity, and velocity is an integral of the sum of the forces. So, for relatively small drops in altitude, the time of flight is a function of the object's mass (–), shape (±) and cross-sectional area (+), where the sign in parentheses shows the variable's correlation to the time of flight.

 

Terminal velocity occurs when the force of drag perfectly counteracts the force of gravity (ie, the sum of forces equals zero, and no further acceleration occurs). Technically speaking, a falling object will approach but never attain its terminal velocity. Computing the time of flight involves integrating it through the drop as the velocity increases.

Edited November 8, 2010 by ewmon

[Skaffen]

Objects fall to Earth at a rate of approx 10m/s/s due to its gravitational field - elephants or paper sheets have negligible gravitational attraction. Air resistance increases with velocity until balanced (terminal)

 

Mass = Gravity, and determines rate of fall, however it is only significant when considering massive objects like stars, planets and moons.

[Edtharan]

It has to do with inertia.

 

More massive objects are indeed more strongly pulled by gravity, however, more massive objects have a greater inertia and so requier a greater force to achieve the same rate of acceleration.

 

As it is the mass of an object that governs both the force felt by gravity and inertia, then as the mass increases the force felt and the amount of inertia both increase.

 

It just so happens that these two influeces increase at the exact same rate. That is the force requiered to reach a certain rate of acceleration (inertia) matches the amount of force provided by gravity.

 

But, when you have a situation where the is an extra effect, say air resistance, then the two effects start to diverge and we get a different rate of acceleration for objects of different masses.