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Weight and normal force
Beginner
Weight pulls down; the surface pushes back perpendicular to it.
N = mgWeight W = mg pulls down. The normal force is the surface's push perpendicular to the contact, adjusting to whatever stops penetration. On a level surface at rest N = mg, but it changes on slopes and in accelerating lifts.
On a 30° slope a 10 kg block has N = 98 cos30° ≈ 85 N.
N isn't always equal to mg.
In more detail
Weight is the gravitational force on a mass, W = mg. The normal force is the contact force a surface exerts perpendicular to its surface, and it equals weight when there is no other vertical force.
Real-world uses
- A scale measures the normal force on its platform, which it converts into weight.
- A book on a table experiences a normal force from the table equal to its weight.
- A book resting on a table has a normal force equal to its weight, which is why the table does not collapse.
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Frequently asked questions
Is the normal force always equal to weight?
No. On a slope, in a lift accelerating up or down, or with a pulling force, the normal force differs.
Is weight the same as mass?
No. Weight is a force, measured in newtons, while mass is measured in kilograms.
Is the normal force always equal to the weight?
No. On a slope, a lift or a surface pushing down on a book, the normal force depends on the other forces and the acceleration.
Related topics in Newton's Laws & Forces
Newton's second law · Units of force · Newton's third law · Free-body diagrams · Net force and equilibrium · Tension