Physics
posted by Sophie on .
I push a stack of six books (each weighting 4 kg) horizontally across a table to the right with a kinetic coefficient of friction uk = 0.5. I apply a force of 120 N.
a) What is the acceleration of the books?
b) what is the force of the rightmost book on its neighbor?
Next, I stack the books vertically and push them horizontally across a table to the right by applying a force only to the bottom book.. The kinetic coefficient of friction of the books with the table is uk=0.5 and the static coefficient of friction between the books is us=0.3.
c) What is the maximum force I can apply to the bottom book to move the books as a single unit, before books starts to fall off the stack?
I solved for a) and b) already. For a) I got 5 m/s^2 and for b) I got 40N.
But I am stuck on part c.
I don't really understand how to start because I know that the normal force would be constantly changing, but I don't know how does the kinetic friction and static friction plays in for finding the maximum force that I can apply to the books.
Can someone please explain to me how to finish the problem? Thank you.

How fast can the stack accelerate without the books above the first one slipping?
weight down on bottom book = 5 * 4 kg * g
maximum static friction force between top 5 and bottom book = 5 * 4 * g * 0.3
so max force = mass of top 5 * a
5*4*g*.3 = 5*4 * a
so
a = .3 g
that gives us the maximum acceleration before we get a slip
now what force gave that acceleration?
F = m a
F = 6 * 4 * a
F = 24 * .3 g
if g = 9.81 m/s^2
F = 70.6 Newtons 
shouldn't you take into consideration the kinetic friction, the less force you need according to this method you would need more force if you have 100 books.