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

• Serbiwni
In summary, the conversation discusses the concept of static friction and its role in preventing motion between surfaces. The correction shows a different direction for the static force, leading to confusion about who is right. The conversation also explains how static friction affects the motion of the table and the books.
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
.
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.

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

PeroK said:
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 ?

Serbiwni said:
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.

## 1. What is Newton's 2nd Law?

Newton's 2nd Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

## 2. How does Newton's 2nd Law apply to a pile of books on a table being moved?

In this scenario, the books have a mass and are being acted upon by a net force, which is the force exerted by the person moving them. According to Newton's 2nd Law, the acceleration of the books will be directly proportional to the net force and inversely proportional to their mass.

## 3. What factors affect the acceleration of the books?

The acceleration of the books will be affected by the amount of force being applied to them and their mass. The greater the force and the lesser the mass, the greater the acceleration will be.

## 4. What happens if the net force acting on the books is increased?

If the net force acting on the books is increased, their acceleration will also increase. This means that they will move faster and cover more distance in the same amount of time.

## 5. How does the mass of the books affect their acceleration?

The mass of the books has an inverse relationship with their acceleration. This means that if the mass of the books is increased, their acceleration will decrease, and if the mass is decreased, their acceleration will increase.

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