Why Isn’t Normal Force Always Equal to Weight?

Maybe you learned this in physics:

(N=mg)

Then you found a problem where the normal force was not equal to the weight.

That can be confusing.

So, is normal force equal to weight or not?

Sometimes they have the same value. But they are different forces.

Here is a simple way to see why.

Think about $20

Imagine you have a $20 bill in one hand and $20 in coins in the other.

Both are money.

Both are worth exactly $20.

But they are not the same type of money.

The bill fits easily in your wallet. The coins are heavier and take up more space. You handle them in different ways.

They have the same value, but they are still different types of money.

Normal force and weight are like that.

Both are forces.

Sometimes they have the same value.

But they are different types of forces, so we have to treat them differently in physics.

Think about a book on a table

Put a book on a table.

Gravity pulls the book down. That pull is its weight.

The table pushes the book up. That push is the normal force.

The book is just sitting there.

In this case, the two forces have the same value:

(N=mg)

But that does not make them the same force.

Think about the money again.

A $20 bill and $20 in coins can have the same value without being the same type of money.

Normal force and weight can have the same value without being the same type of force.

Now change the situation

Now imagine someone pushes down on the book.

Did the book's weight change?

No.

Gravity is still pulling down on the same book.

But now there is another downward force: the person's push.

The table has to push up harder.

So the normal force gets bigger while the weight of the book stays the same.

Now you can see why normal force is not always equal to weight.

The idea to remember

Weight comes from gravity.

Normal force comes from a surface pushing on an object.

They are different forces.

Sometimes they have the same value.

Sometimes they do not.

So when you see

(N=mg)

remember the $20 bill and $20 in coins.

Both are money. They can have the same value, but they are different types of money.

Normal force and weight are both forces. They can have the same value, but they are different types of forces.

Same value does not mean same thing.

And that is why normal force can equal weight in one situation but not in another.

Want to go deeper?

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