Newton's 2nd Law: Pile of Books on a Table Being Moved

[Serbiwni]

Homework Statement

Carl tries to move a table, which has a pile of books sitting on it of total mass m_books. The dynamic coefficient of friction is μd (between the table and floor) and the static coefficient of friction between the table and books is μs . Determine the maximum force that Carl can apply to the table so that the books do not slide.
Assume the books do not slide with respect to each other.
Numerical application: μs = 0.75, μd = 0.5, m_books = 3 kg, m_table = 10 kg

1) Draw the free body diagram of the books.

Relevant Equations

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I drew a free body diagram for the books but it's not the same one in the correction. The static force Fs between the books and the table must be opposite to the motion but the correction does not the same and puts that vector in the same direction as the motion. Here's a drawing of the situation and also the free body diagram of the correction, as you can see its direction is also the motion's one.

 

[PeroK]

With static friction there is no motion between surfaces. Static friction acts to prevent motion between two surfaces.

 

[Serbiwni]

With static friction there is no motion between surfaces. Static friction acts to prevent motion between two surfaces.

So if the motion is to the right, the static friction must be to the left right ? But that's not what the correction says. Who is wrong ?

 

[PeroK]

So if the motion is to the right, the static friction must be to the left right ? But that's not what the correction says. Who is wrong ?

First, if there was no friction.

If the table is pushed to the right, the books would not move at all. Relative to the table the books would slide across the surface of the table.

Second, if there is static friction:

If the table is pushed to the right, the static friction will pull the books to the right also. And, by Newton's third law, the books will retard the motion of the table.

So, it depends how you look at. The force of static friction acting on the table will oppose the acceleration of the table. But, the static friction acting on the books will accelerate the books.