Does normal force equal gravity?

Question

like if a box is not moving at all on a flat surface, the force of gravity is = to normal force right?

what are some cases when these two forces are not equal?

Answer 1

Yes, you are right in the first case. That's when gravity and normal vectors are 180deg form each other. Sometimes one may pull up with some force, like pulling a sled with a rope at an angle. In this case, you are helping out the normal force and you + normal = gravity. In another case, a block sitting on a slope does not experience the same normal force as gravitational force. It's normal force is a fraction of gravitational depending on the angle included in F= mg xcos(@), and trigonometry. However, in most cases, yes, normal force is equal and opposite to gravitational force (that's why it doesn't move up or down when sitting on the table).

Answer 2

If a box is not moving on a flat surface, then the magnitude of the normal force is equal to the force of gravity, but the direction is exactly opposite; gravity pushes down, the floor pushes up. Thus the net force on the box is zero. If the normal force was in the same direction as gravity, the net force would be non zero, and the box would accelerate, falling through the floor.

What we call the normal force, exerted by a surface on an object, is just the equal and opposite of the force exerted by the object on the surface, as required by Newton's third law. So, if you were to push on the box with your hand the normal force would increase -- it would now have magnitude equal to the force of gravity + the force of your hand. Another case where the normal force is not equal to force of gravity is on an inclined plane. Gravity still acts directly downwards, but now the normal force acts at an angle (the normal force always acts perpendicular to the plane of the surface -- normal is just another word for perpendicular). On an inclined plane only part of force of gravity goes into pushing the box against the surface, the rest goes into moving the box down the plane. So, the normal force is less than the total force of gravity.