When would the normal force not equal the weight?

[gungo]

Homework Statement

I know that on a horizontal surface. if the net force is 0 in the y direction the weight of object=the normal force, but wouldn't the normal force always equal the magnitude of gravity on an object, just in opposite directions? Because if the weight is stronger than the normal force or vice versa, the object would move in the y direction, but objects don't fall through the ground or randomly or start floating so I'm kind of confused.

Homework Equations

Fg=mg

The Attempt at a Solution

N/A

 

[TJGilb]

Assuming a statics situation $\sum \mathbf F = 0$, there are conceivable situations in which the normal force wouldn't equal the force of gravity. One example is if you were applying a light upward force on the object from a hand or string or something that isn't strong enough to actually pick it up. In this case, the normal force would equal the force of gravity minus the applied upward force.

 

[haruspex]

Homework Statement

I know that on a horizontal surface. if the net force is 0 in the y direction the weight of object=the normal force, but wouldn't the normal force always equal the magnitude of gravity on an object, just in opposite directions? Because if the weight is stronger than the normal force or vice versa, the object would move in the y direction, but objects don't fall through the ground or randomly or start floating so I'm kind of confused.

Homework Equations

Fg=mg

The Attempt at a Solution

N/A

Normal force between two surfaces is the minimum magnitude force which prevents their interpenetration. Thus, it is always normal to the contact plane.
If an object is placed on a frictionless slope, the normal force only has to counter the component of gravity normal to the plane. The other component leads the object to slide down.

See also https://www.physicsforums.com/insights/frequently-made-errors-vectors-elementary-use and https://www.physicsforums.com/insights/frequently-made-errors-mechanics-friction/

 

[Buffu]

When would the normal force not equal the weight?

When there is more force acting in y-direction than just gravity.
Two books kept on top each other is one example. Here weight of the top book is also acting on the bottom book.

one more example :-
https://www.physicsforums.com/threads/pulley-system-on-rough-surface.890142/