Explain the difference in between mass and also weightExplain why falling objects on earth are never truly in free fallDescribe the concept of weightlessness

Mass and also weight are often used interchangeably in day-to-day conversation. Because that example, our medical records often show our load in kilograms however never in the correct devices of newtons. In physics, however, over there is crucial distinction. Load is the traction of earth on one object. It counts on the distance from the center of Earth. Unlike weight, massive does not vary through location. The massive of things is the same on Earth, in orbit, or ~ above the surface ar of the Moon.

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Units of Force

The equation F_ extnet=ma is used to define net pressure in terms of mass, length, and time. As described earlier, the SI unit of pressure is the newton. Since F_ extnet=ma,

Although practically the entire people uses the newton for the unit the force, in the joined States, the most familiar unit of pressure is the lb (lb), wherein 1 N = 0.225 lb. Thus, a 225-lb person weighs 1000 N.

Weight and also Gravitational Force

When an item is dropped, it speeds up toward the center of Earth. Newton’s 2nd law claims that a net pressure on an object is responsible because that its acceleration. If waiting resistance is negligible, the net pressure on a falling thing is the gravitational force, generally called that weight overset o w , or that force due to gravity exhilaration on things of massive m. Weight deserve to be denoted as a vector due to the fact that it has actually a direction; down is, by definition, the direction the gravity, and also hence, load is a bottom force. The size of load is denoted together w. Galileo was critical in mirroring that, in the absence of waiting resistance, every objects fall with the same acceleration g. Utilizing Galileo’s an outcome and Newton’s second law, we deserve to derive one equation because that weight.

Consider things with massive m falling towards Earth. The experiences only the downward force of gravity, which is the weight overset o w . Newton’s second law states that the size of the net outside force on things is overset o F_ extnet=moverset o a. We know that the acceleration of an object due to gravity is overset o g, or overset o a=overset o g . Substituting these into Newton’s 2nd law provides us the complying with equations.

Weight

The gravitational force on a mass is that weight. We can write this in vector form, where overset o w is weight and also m is mass, as

overset o w=moverset o g.

In scalar form, we deserve to write

w=mg.

Since g=9.80, extm/s^2 ~ above Earth, the load of a 1.00-kg object on planet is 9.80 N:

w=mg=(1.00, extkg)(9.80, extm/s^2)=9.80, extN.

When the net exterior force on things is that is weight, us say the it is in free fall, that is, the only pressure acting top top the thing is gravity. However, when objects on earth fall downward, castle are never truly in totally free fall since there is constantly some upward resistance pressure from the air exhilaration on the object.

Acceleration due to gravity g different slightly over the surface of Earth, therefore the load of an object depends on its location and is no an intrinsic residential or commercial property of the object. Load varies drastically if we leave earth surface. ~ above the Moon, because that example, acceleration because of gravity is only 1.67, extm/s^2 . A 1.0-kg mass thus has actually a load of 9.8 N on Earth and also only around 1.7 N top top the Moon.

The broadest meaning of weight in this sense is the the weight of an item is the gravitational force on that from the nearest huge body, such as Earth, the Moon, or the Sun. This is the many common and also useful meaning of weight in physics. It differs dramatically, however, indigenous the definition of weight used by NASA and also the renowned media in relationship to an are travel and also exploration. Once they speak the “weightlessness” and “microgravity,” they room referring come the phenomenon we contact “free fall” in physics. We use the preceding an interpretation of weight, pressure overset o w because of gravity exhilaration on an object of mass m, and we make cautious distinctions between totally free fall and also actual weightlessness.

Be mindful that weight and also mass are different physical quantities, although castle are closely related. Mass is an intrinsic residential or commercial property of an object: the is a amount of matter. The quantity or quantity of matter of things is figured out by the number of atoms and molecules of various species it contains. Because these numbers do not vary, in Newtonian physics, massive does no vary; therefore, its solution to an used force does no vary. In contrast, weight is the gravitational force acting on an object, so the does vary relying on gravity. For example, a human closer to the center of Earth, at a low elevation such as new Orleans, weighs slightly an ext than a human who is situated in the greater elevation the Denver, even though castle may have the exact same mass.

It is tempting come equate mass come weight, due to the fact that most that our examples take ar on Earth, where the load of an object varies only a tiny with the location of the object. In addition, it is an overwhelming to count and also identify all of the atoms and also molecules in one object, so mass is rarely determined in this manner. If us consider cases in i m sorry overset o g is a consistent on Earth, we watch that load overset o w is directly proportional come mass m, since overset o w=moverset o g, that is, the an ext massive an object is, the more it weighs. Operationally, the masses the objects are figured out by comparison with the typical kilogram, together we discussed in Units and Measurement. However by comparing an object on planet with one on the Moon, we can conveniently see a sport in weight but not in mass. For instance, top top Earth, a 5.0-kg object weighs 49 N; top top the Moon, wherein g is 1.67, extm/s^2 , the thing weighs 8.4 N. However, the massive of the object is quiet 5.0 kg top top the Moon.

Example

Clearing a Field

A farmer is lifting part moderately hefty rocks native a field to plant crops. He lifts a rock that weighs 40.0 lb. (about 180 N). What force does he use if the stone accelerates in ~ a rate of 1.5, extm/s^2?

Strategy

We were given the load of the stone, i m sorry we use in recognize the net force on the stone. However, we likewise need to understand its massive to apply Newton’s 2nd law, so us must use the equation because that weight, w=mg , to determine the mass.

Solution

No forces act in the horizontal direction, for this reason we have the right to concentrate on vertical forces, as displayed in the following free-body diagram. We label the acceleration come the side; technically, the is not part of the free-body diagram, yet it helps to remind united state that the object accelerates upward (so the net pressure is upward).

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eginarrayccchfill w& =hfill & mghfill \ hfill m& =hfill & fracwg=frac180, extN9.8, extm/s^2=18, extkghfill \ hfill sum F& =hfill & mahfill \ hfill F-w& =hfill & mahfill \ hfill F-180, extN& =hfill & (18, extkg)(1.5, extm/s^2)hfill \ hfill F-180, extN& =hfill & 27, extNhfill \ hfill F& =hfill & 207, extN=210, extN to two far-reaching figureshfill endarray

Significance

To apply Newton’s 2nd law as the primary equation in solving a problem, we sometimes need to rely on various other equations, such as the one for weight or one of the kinematic equations, to finish the solution.