Why does a heavier book fall faster than a lighter sheet of paper?

[Jow]

I love physics, but I find that I am ignorant about some of the more basic concepts, so forgive me if this question may sound a bit foolish.
My teacher the other day demonstrated that all objects fall at the same rate on earth. The only reason things don't seem to follow this rules is because of air resistance. He showed that when flat, paper falls slower than a golf ball, but when crumpled to the size of the golfball they fall at the same rate.
I have two questions about this. I know that a book will fall faster than a piece of paper of the same shape and size. I tested at home to make sure. If it has nothing to do with weight than why does the book fall faster?
Also, shouldn't weight, or mass make a difference. If F = Gm1m2 / r^2, than surely the more massive something is than the faster it will fall. My textbook answers neither of these questions, so it would be much aporeciated if you could answer them. Thank you.

 

[emKhairol]

Hi Jow,

For your first question, you can't simply neglect the weight or the mass of the book because its already clear that F = ma.

Its already stated that mass is related to acceleration (gravity).

 

[A.T.]

but when crumpled to the size of the golfball they fall at the same rate.

That is not true. Two objects of exactly the same shape/size, but different mass fall at different rates in the atmosphere. Only in vacuum the acceleration is the same, because gravity is the only force acting and proportional to mass. But air resistance is not dependent of mass. At the same velocity the opposing air resistance is the same for both objects, but the weight is different. So the net force and acceleration are different. At low velocities the drag is low, and the difference is not noticeable which allows the teacher to fool the students.

 

[mfb]

If F = Gm1m2 / r^2, than surely the more massive something is than the faster it will fall. My textbook answers neither of these questions, so it would be much aporeciated if you could answer them. Thank you.

And F=m₁a. Combine both equations, and you get a = Gm₂/r^2, which depends on the mass of Earth but not on the mass of the falling object. If the falling object has a mass similar to earth, you would have to take the motion of Earth into account, but that can be neglected for any realistic experiment.

 

[jtbell]

https://www.physicsforums.com/showthread.php?t=511172