If we consider situations in which g → g → is a constant on Earth, we see that weight w → w → is directly proportional to mass m, since w → = m g →, w → = m g →, that is, the more massive an object is, the more it weighs. In addition, it is difficult to count and identify all of the atoms and molecules in an object, so mass is rarely determined in this manner. It is tempting to equate mass to weight, because most of our examples take place on Earth, where the weight of an object varies only a little with the location of the object. For example, a person closer to the center of Earth, at a low elevation such as New Orleans, weighs slightly more than a person who is located in the higher elevation of Denver, even though they may have the same mass. In contrast, weight is the gravitational force acting on an object, so it does vary depending on gravity. Because these numbers do not vary, in Newtonian physics, mass does not vary therefore, its response to an applied force does not vary. The quantity or amount of matter of an object is determined by the numbers of atoms and molecules of various types it contains. Mass is an intrinsic property of an object: It is a quantity of matter. We use the preceding definition of weight, force w → w → due to gravity acting on an object of mass m, and we make careful distinctions between free fall and actual weightlessness.īe aware that weight and mass are different physical quantities, although they are closely related. When they speak of “weightlessness” and “microgravity,” they are referring to the phenomenon we call “free fall” 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. This is the most common and useful definition of weight in physics. 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, or the Sun. A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.6 N on the Moon. On the Moon, for example, acceleration due to gravity is only 1.62 m/s 2 1.62 m/s 2. Weight varies dramatically if we leave Earth’s surface. However, when objects on Earth fall downward through the air, they are never truly in free fall because there is always some upward resistance force from the air acting on the object.Īcceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. 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 gravity. Substituting these into Newton’s second law gives us the following equations. We know that the acceleration of an object due to gravity is g →, g →, or a → = g → a → = g →. Newton’s second law says that the magnitude of the net external force on an object is F → net = m a →. It experiences only the downward force of gravity, which is the weight w → w →. Using Galileo’s result and Newton’s second law, we can derive an equation for weight.Ĭonsider an object with mass m falling toward Earth. Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g. Weight can be denoted as a vector because it has a direction down is, by definition, the direction of gravity, and hence, weight is a downward force. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight w → w →, or its force due to gravity acting on an object of mass m. Newton’s second law says that a net force on an object is responsible for its acceleration. When an object is dropped, it accelerates toward the center of Earth. Although 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.
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