# Physics

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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.

• Physics -

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

• Physics -

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.

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