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  • Define normal and tension forces.
  • Apply Newton's laws of motion to solve problems involving a variety of forces.
  • Use trigonometric identities to resolve weight into components.

Forces are given many names, such as push, pull, thrust, lift, weight, friction, and tension. Traditionally, forces have been grouped into several categories and given names relating to their source, how they are transmitted, or their effects. The most important of these categories are discussed in this section, together with some interesting applications. Further examples of forces are discussed later in this text.

Normal force

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 [link] (a). But how do inanimate objects like a table support the weight of a mass placed on them, such as shown in [link] (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.

A person is holding a bag of dog food at some height from a table. He is exerting a force F sub hand, shown by a vector arrow in upward direction, and the weight W of the bag is acting downward, shown by a vector arrow having the same length as vector F sub hand. In a free-body diagram two forces are acting on the red point; one is F sub hand, shown by a vector arrow upward, and another is the weight W, shown by a vector arrow having the same length as vector F sub hand but pointing downward. (b) The bag of dog food is on the table, which deforms due to the weight W, shown by a vector arrow downward; the normal force N is shown by a vector arrow pointing upward having the same length as W. In the free-body diagram, vector W is shown by an arrow downward and vector N is shown by an arrow having the same length as vector W but pointing upward.
(a) The person holding the bag of dog food must supply an upward force F hand size 12{F rSub { size 8{"hand"} } } {} equal in magnitude and opposite in direction to the weight of the food w size 12{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 size 12{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. If the force supporting a load is perpendicular to the surface of contact between the load and its support, this force is defined to be a normal force     and here is given the symbol N size 12{N} {} . (This is not the unit for force N.) The word normal means perpendicular to a surface. The normal force can be less than the object’s weight if the object is on an incline, as you will see in the next example.

Common misconception: normal force (n) vs. newton (n)

In this section we have introduced the quantity normal force, which is represented by the variable N size 12{N} {} . This should not be confused with the symbol for the newton, which is also represented by the letter N. These symbols are particularly important to distinguish because the units of a normal force ( N size 12{N} {} ) happen to be newtons (N). For example, the normal force N size 12{N} {} that the floor exerts on a chair might be N = 100 N size 12{N="100"" N"} {} . One important difference is that normal force is a vector, while the newton is simply a unit. Be careful not to confuse these letters in your calculations! You will encounter more similarities among variables and units as you proceed in physics. Another example of this is the quantity work ( W size 12{W} {} ) and the unit watts (W).

Questions & Answers

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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