The normal force is not always mg

Gideon's book lies on a desk. The book weighs 40 N, and the desk supplies a 40 N normal force. The two balance exactly.

Then Gideon presses down on the cover. What does the normal force do?

The normal force is a response, not a fixed property of the book. The surface supplies whatever force the perpendicular balance requires. That is not always mg.

Here is the book alone. Its weight is 40 N down, and nothing else acts on it perpendicular to the desk. The desk supplies 40 N up, so here N = w.

The book alone: the desk balances only the weight, so N = 40 N.

Now Gideon presses down on the book with 20 N. The desk must now balance 60 N of downward force. The normal force rises to 60 N.

Gideon presses down with 20 N: the desk now balances 60 N, so N rises to 60 N.

A 50 N box rests on a table while Lotte presses down on it with 30 N. Enter the normal force on the box in N.

Now a string applies a 15 N upward force to the same book instead. The string carries part of the weight, so the desk supplies only the rest. The normal force drops to 25 N.

A string lifts 15 N of the load: the desk supplies only 25 N.

One book, three normal forces: 40 N, 60 N, and 25 N. The surface answers the perpendicular balance each time.

So the normal force equals mg only when the weight and the normal force are the only perpendicular forces.

Before you use N in any later calculation, check the perpendicular direction first: what else presses down, and what else lifts up?

June says the normal force on a box always equals the box's weight. Is June correct?

Casper's crate rests on a level floor. Nothing touches the crate except the floor. Casper says the normal force on the crate equals the crate's weight. Is Casper correct?

The normal force takes whatever value the perpendicular balance requires. It equals mg only when the weight and the normal force are the only perpendicular forces.

A 70 N crate rests on a floor while a worker presses down on it with 25 N. Calculate the normal force on the crate.

Write down the values in the question:

w = 70 N

downward applied force = 25 N

N = ?

The floor balances every downward force:

N = w + downward applied force

Substitute in the values:

N = 70 + 25

Simplify:

N = 95 N

The normal force on the crate is 95 N.

A 150 N crate rests on a floor while a rope applies a 60 N upward force to it. Calculate the normal force on the crate.

Write down the values in the question:

w = 150 N

upward rope force = 60 N

N = ?

The rope carries part of the weight, and the floor supplies the rest:

N = w − upward rope force

Substitute in the values:

N = 150 − 60

Simplify:

N = 90 N

The normal force on the crate is 90 N.

Your turn

A 120 N crate rests on a dock while a cable applies a 45 N upward force to it. Enter the normal force on the crate in N.

A box rests on a level floor. In which of the following cases is the normal force on the box BIGGER than the box's weight?

A 90 N toolbox rests on a bench while a clamp presses down on it with 25 N. Enter the normal force on the toolbox in N.