How many books can you lift?

We know from Newton's second law that every book being acted upon by 120 N of force will also react with 120 N. This means that every book in the stack is being compressed by 120 N from each side, which makes everything symmetrical with respect to any book.

The first thing to notice is the two different coefficients of static friction: between hands and books is 0.6, and between just books is 0.4. We already realized that there are 120 N of force in the normal (in this case, horizontal) direction at every interface. Static friction is proportional to normal force, and provides a reaction against gravity up to its maximum limit. The formula is: $F_{f} ≤ µF_{N}$ where µ is the coefficient of static friction.

The stack of books falls apart when any book slips; that is, the force of gravity becomes greater than the maximum possible force of friction. This means we only have to worry about the interfaces with the lowest coefficient of static friction: between two books. If the stack were heavy enough to slip out of Jason's hands, it would have already fallen apart.

Using the given data, we find the frictional force between two books: $F_{f} = 0.4 \times 120 N = 48 N$

Each book is touching two other books (except for the ones on the ends - hold onto that thought for later) so the total upward force from friction is 96 N. We can also calculate the gravitational force on one book: $F_{g} = mg = 0.960 kg \times 10 m/s^{2} = 9.6 N$

Because each book is exerting downward force on its neighbors, the weights of the books add up, and each interface must use friction to support the weight of all the books combined. Knowing that the maximum force from friction is 96 N, we can divide by the weight of each book to find out how many can be supported: $\frac{96 N}{9.6 N} = 10 books$

Don't forget about the books on the very ends, though! Those can't slip out because they're touching Jason's hands, which provide more friction. So, we add one extra book on either side to obtain the answer: 12 books.