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3.5.1: Normal Force

  • Page ID
    472526
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    Learning Objectives
    • Define normal force.
    • Explain the relationship between normal force and apparent weight.

    Weight (also called force of gravity) is a pervasive force that acts at all times and must be counteracted to keep an object from falling. You definitely notice that you must support the weight of a heavy object by pushing up on it when you hold it stationary, as illustrated in Figure \(\PageIndex{1}\)(a). But how do inanimate objects like a table support the weight of a mass placed on them, such as shown in Figure \(\PageIndex{1}\)(b)? When the bag of dog food is placed on the table, the table actually sags slightly under the load. This would be noticeable if the load were placed on a card table, but even rigid objects deform when a force is applied to them. Unless the object is deformed beyond its limit, it will exert a restoring force much like a deformed spring (or trampoline or diving board). The greater the deformation, the greater the restoring force. So when the load is placed on the table, the table sags until the restoring force becomes as large as the weight of the load. At this point the net external force on the load is zero. That is the situation when the load is stationary on the table. The table sags quickly, and the sag is slight so we do not notice it. But it is similar to the sagging of a trampoline when you climb onto it.

    fig-ch01_patchfile_01.jpg
    Figure \(\PageIndex{1}\): (a) The person holding the bag of dog food must supply an upward force \(\boldsymbol{F}_{\text {hand }}\) equal in magnitude and opposite in direction to the weight of the food \(w\). (b) The card table sags when the dog food is placed on it, much like a stiff trampoline. Elastic restoring forces in the table grow as it sags until they supply a force N equal in magnitude and opposite in direction to the weight of the load.

    We must conclude that whatever supports a load, be it animate or not, must supply an upward force equal to the weight of the load, as we assumed in a few of the previous examples. The force supporting a load is perpendicular to the surface of contact between the load and its support, and this force is called a normal force, often indicated with symbol N (Please do not confuse this with the abbreviation for newton, the unit of force, N). The word normal means perpendicular to a surface. The normal force is not always equal to the object's weight, if there are other forces acting on the object, or if the object is accelerating, so that the net force is not zero.

    Normal force also goes by another name, apparent weight. This is because all the forces you feel, especially your sensation of weight, are directly attributed to contact forces, such as the normal force. When NASA astronauts are weightlessly floating in the International Space Station, their actual weight (gravitational force on them by the Earth) is not zero, but their apparent weight (sensation of weight due to contact forces) is zero.

    Section Summary

    • When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts perpendicular to and away from the surface. It is called a normal force, and it also goes by the name "apparent weight."

    Glossary

    normal force
    the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the object rests

    Contributors

    Curated from resources found in Introduction to Physics published by OpenStax.

    apparent weight
    sensation of weight due to contact forces; usually the same as normal force

    This page titled 3.5.1: Normal Force is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jamie MacArthur.

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