What physics concepts support the observation of the book and paper falling together?

Question

you place a sheet of paper on a book, it falls with it rather than being separated & slowed by air resistance. What physics concepts support the observation of the book and paper falling together?

Answer 1

If you place the book on the desk and a piece of paper on it, if there is no wind turbulence it will stay there until the cleaning lady comes.

Why? because the gravitational force keeps it there, and in addition frictional forces, i.e. electromagnetic interactions between the paper molecules and book molecules . This would be true in vacuum too. Atmospheric pressure on top of the paper and "vacuum", i.e. displacement of air between the book and paper contact surface adds to the stability.

When both fall, unless a turbulence lifts a side of the paper and air enters underneath, they will fall together. If falling from a great enough height, turbulence will separate them inevitably. Just needs some air to intervene between the two surfaces.

Answer 2

Concepts

Assume the projected area, $A$, of the book is about equal to the projected area of the paper as they both fall towards the earth. The fundamental principles are

(1) Different gravitational force, $F_m=mg$, that acts on each object's mass, m

(2) Similar opposing drag forces, $F_d=-(1/2)C_d A \rho v^2 $ which act on each object in air

(3) Different terminal velocities in air determined by setting $F_d = F_m$ and solving for $v_{book}$ and $v_{paper}$ in each case. The book's terminal velocity is faster than the paper's since the mass is greater.

(4) The lack of a terminal velocity in vacuum and the same acceleration rate of each object as they fall. This is because the drag force goes to zero and there are no other forces to oppose acceleration. An alternate scenario: if the paper falls together with (on top of) the book it is sheltered by the drag forces that would normally slow it down, and so in this case they both accelerate at the same rate until the book reaches terminal velocity.

An easier and more dramatic demonstration of the latter is a feather and a cup.

Answer 3

Due to Newton's 2nd Law, F=ma for both the book and the paper that is on top of the book. Since the force on the paper and the book is just the force due to gravity, that force is their weight, so you also get F=mg for both the book and the paper. This leads to ma=mg. Divide this final equation by m to eliminate it, and observe that the acceleration of each object is g, and is independent of their masses.