normal force
Summary
The normal force is the contact force a surface exerts on an object, directed perpendicular to the surface and pushing the object away from it. Its size depends on the other forces and on any acceleration perpendicular to the surface. It equals mg for a block at rest on level ground but mg cosθ on a simple incline.
Detail
Meaning: The normal force (N) is the component of a surface's contact force that is perpendicular to the surface. It arises because the surface deforms slightly, like a compressed spring, and pushes back. Its magnitude adjusts to whatever value keeps the object from moving into the surface.
Equation: N − mg cosθ = 0, so N = mg cosθ, where N is the normal force (N), m is mass (kg), g is 9.8 m/s², and θ is the incline angle from the horizontal (degrees or radians). On level ground with no other vertical forces and no vertical acceleration, θ = 0 and N = mg.
On the MCAT: Expect free-body diagrams and incline problems. A push or pull at an angle changes N, and so does an elevator accelerating (N = m(g + a) for upward acceleration a). N matters because friction depends on it: fs ≤ μsN and fk = μkN. A larger N gives a larger maximum static friction. In vertical circular motion, N and gravity together supply the centripetal force.
Common confusion: Students set N = mg automatically. Instead, write Newton's second law along the axis perpendicular to the surface and solve for N. Also, N and weight are not a Newton's third-law pair, even when they are equal in size. The third-law partner of the weight is the object's gravitational pull on Earth.
Sources
- Physics (Giancoli)
- University Physics (Young and Freedman)
- Fundamentals of Physics (Halliday, Resnick, and Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.