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Units of force

F net = m a size 12{F rSub { size 8{"net"} } =ma} {} is used to define the units of force in terms of the three basic units for mass, length, and time. The SI unit of force is called the newton (abbreviated N) and is the force needed to accelerate a 1-kg system at the rate of 1 m/s 2 size 12{1" m/s" rSup { size 8{2} } } {} . That is, since F net = m a size 12{F rSub { size 8{"net"} } =ma} {} ,

1 N = 1 kg m/s 2 size 12{"1 N "=" 1 kg" cdot "m/s^2"} {} .

While almost the entire world uses the newton for the unit of force, in the United States the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb.

Weight and the gravitational force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law states that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight     w size 12{w} {} . Weight can be denoted as a vector w size 12{w} {} because it has a direction; down is, by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as w size 12{w} {} . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g size 12{g} {} . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m size 12{m} {} falling downward toward Earth. It experiences only the downward force of gravity, which has magnitude w size 12{w} {} . Newton’s second law states that the magnitude of the net external force on an object is F net = ma size 12{F rSub { size 8{"net"} } = ital "ma"} {} .

Since the object experiences only the downward force of gravity, F net = w size 12{F rSub { size 8{"net"} } =w} {} . We know that the acceleration of an object due to gravity is g , or a = g size 12{a=g} {} . Substituting these into Newton’s second law gives

Weight

This is the equation for weight —the gravitational force on a mass m size 12{m} {} :

w = mg size 12{w= ital "mg"} {} .

Since g = 9.80 m/s 2 size 12{g=9 "." "80"" m/s" rSup { size 8{2} } } {} on Earth, the weight of a 1.0 kg object on Earth is 9.8 N, as we see:

w = mg = ( 1 . 0 kg ) ( 9.80 m/s 2 ) = 9.8 N size 12{w= ital "mg"= \( 1 "." "0 kg" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) =9 "." 8" N"} {} .

Recall that g size 12{g} {} can take a positive or negative value, depending on the positive direction in the coordinate system. Be sure to take this into consideration when solving problems with weight.

When the net external force on an object is its weight, we say that it is in free-fall    . That is, the only force acting on the object is the force of gravity. In the real world, when objects fall downward toward Earth, they are never truly in free-fall because there is always some upward force from the air acting on the object.

The acceleration due to gravity g size 12{g} {} varies slightly over the surface of Earth, so that the weight of an object depends on location and is not an intrinsic property of the object. Weight varies dramatically if one leaves Earth’s surface. On the Moon, for example, the acceleration due to gravity is only 1.67 m/s 2 size 12{1 "." "67"" m/s" rSup { size 8{2} } } {} . A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

The broadest definition of weight in this sense is that the weight of an object is the gravitational force on it from the nearest large body , such as Earth, the Moon, the Sun, and so on. This is the most common and useful definition of weight in physics. It differs dramatically, however, from the definition of weight used by NASA and the popular media in relation to space travel and exploration. When they speak of “weightlessness” and “microgravity,” they are really referring to the phenomenon we call “free-fall” in physics. We shall use the above definition of weight, and we will make careful distinctions between free-fall and actual weightlessness.

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Source:  OpenStax, Physics 110 at une. OpenStax CNX. Aug 29, 2013 Download for free at http://legacy.cnx.org/content/col11566/1.1
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