# Does pushing down on a book increase the Normal force?

## Main Question or Discussion Point

So, I know that there is a Normal force exerted on the book by the table, and, according to Newton's Third Law, the book exerts a force onto the table. However, I have two questions: if I were to push down on the book, would that Normal force increase? What "creates" the Normal force? Is it the weight of the book pushing down on the table, or something else? Thanks!

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Do the math and see for yourself. ;) Do a case without pushing it down. Draw a free body diagram, sum the forces and see what the normal force is. Do the same exercise with an extra force pushing it down. I suspect you already know the answer.

The normal force is usually the repulsion of atoms from each other do to their charges. It is a coulomb force. Recall how the formula works, the closer together the stronger the force. If the book is heavier then it will push the charges closer together resulting in a stronger repulsive force.

toboldlygo
Do the math and see for yourself. ;) Do a case without pushing it down. Draw a free body diagram, sum the forces and see what the normal force is. Do the same exercise with an extra force pushing it down. I suspect you already know the answer.

The normal force is usually the repulsion of atoms from each other do to their charges. It is a coulomb force. Recall how the formula works, the closer together the stronger the force. If the book is heavier then it will push the charges closer together resulting in a stronger repulsive force.
I'm thinking the Normal force has to increase to balance out the applied force, but I think I'm mostly confused about what exactly the Normal force is. I know that it's mgsin/cos(θ) (depending on which way the object is oriented and all that), but I also know that it's a reaction force from the contact surface. The internet (and my prof) is mostly saying, "It's the force perpendicular to the contact surface," which is great, but that doesn't really help me intuitively grasp what it actually represents. Thanks for clearing up where the Normal force originates!

However, another question: assuming there's static friction (this hypothetical book is now on an incline), would applying a force directly down on the book (assuming it's still at rest) increase the static friction because the Normal force increases? Or am I misusing the relationship between static friction and Normal force?

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I'm thinking the Normal force has to increase to balance out the applied force, but I think I'm mostly confused about what exactly the Normal force is. I know that it's mgsin(θ), but I also know that it's a reaction force from the contact surface. The internet (and my prof) is mostly saying, "It's the force perpendicular to the contact surface," which is great, but that doesn't really help me intuitively grasp what it actually represents. Thanks for clearing up where the Normal force originates!

However, another question: assuming there's static friction (this hypothetical book is now on an incline), would applying a force directly down on the book (assuming it's still at rest) increase the static friction because the Normal force increases? Or am I misusing the relationship between static friction and Normal force?
Correct. The normal force does increase due to Newton's third law.
The normal force (at the most fundamental level) is caused by electrostatic repulsion between the atoms in the table and the atoms in the book. The reason why you cant pass your hand through the book is becuase of this repulsion.
Pushing down harder on the book will increase the static friction. Its probably poor wording to say that static friction is increasing because the normal force is increasing, but rather its increasing because the downward force is increasing(even though its true). It is true that $f_{static}=\mu F_n$ but then ask your self what $F_n$ is: its $mgcos(\theta)$.

toboldlygo
Pushing down harder on the book will increase the static friction. Its probably poor wording to say that static friction is increasing because the normal force is increasing, but rather its increasing because the downward force is increasing(even though its true). It is true that f_static=μFn but then ask your self what Fn is: its mgcos(θ).
So normal force is mathematically dependent on gravity, theta, and an applied force, assuming there are no other forces acting on an object. Correct? And are there any situations in which I apply a downward force to an object and the normal force doesn't increase?

So normal force is mathematically dependent on gravity, theta, and an applied force, assuming there are no other forces acting on an object. Correct?
Well, say I pushed the book against the wall. Is the normal force dependent on gravity then?

Well, say I pushed the book against the wall. Is the normal force dependent on gravity then?
No; it'd just depend on on the applied force, right? So the rule of thumb for normal force is just, "Well, it depends." I guess I'm not going to be able to get out of drawing a free body diagram haha

And are there any situations in which I apply a downward force to an object and the normal force doesn't increase?
Sure, what if you push so hard you break the desk? Now the normal force disappears and when you draw your free body diagram and sum the forces you will find the acceleration is non-zero. You have pushed the charges so close together that they in turn push on the charges next to them so hard that the bonds between them break and the desk breaks.