Questions from Fundamentals of physics 8th editon-Friction

[luthien09]

Does anyone knows how to solve problem 8 on page 130??

Homework Statement

>> In fig. a horizontal force of 100N is to be applied to a 10kg slab that is initially stationary on a frictionless floor, to accelerate the slab. A 10kg block lies on top of the slab;
the coeffitiont of the friction (mu) between the block and the slab is not known,
and the block might slip

(a) considering that possibility, what is the possible range of values for the magnitude
of the slab's acceleration?

(b) what is the possible range for the magnitude a of the block's acceleration?

Homework Equations

F=(mu)*Normal Force
F=ma


3. The Attempt at a Solution



>>I thought like... when the net force of the block is less than the fiction,
the block and the slab move together...
so (a) slab's acc. is ..

F= (M+m)a (when moving together)
a=5m/s^2

F-f(friction)=m(slab's mass)a
100-(mu)*(blockmass)*(g)=ma


answer: 5<a<(100-mu*blockmass*g/m) ?

(b)
block's acceleration
5m/s^2 (when moving together)
f(friction)=ma
a=mu*g

mu*g<a<5??




I'm totally stuck in this problem ...
can anyone help me?
** picture included

 

[Doc Al]

Your solutions look OK to me. It's not clear if they want a numerical range or a range in terms of the unknown μ. I would have answered with a numerical range.

For the slab: As you found, the minimum acceleration will be when the block sticks to it. To get the maximum acceleration, assume there's no friction at all.

For the block, the reasoning is reversed: The maximum acceleration will be when it sticks to the slab; the minimum will be if there were no friction at all.