wong@Glacier.ARPA (Man Wong) (07/02/85)
What is mass? Mass is force divided by acceleration. What is force? Force is mass multiplied by acceleration. Something is definitely not right here. So exactly what are force and mass? What is the content of Newton's Second Law? Is it a definition? Can definitions be called physical laws? Please help!
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/05/85)
> What is mass? Mass is force divided by acceleration. > > What is force? Force is mass multiplied by acceleration. > > Something is definitely not right here. So exactly what are force and mass? > What is the content of Newton's Second Law? Is it a definition? Can definitions > be called physical laws? You should read "Concepts of Mass" and "Concepts of Force" by Max Jammer (also author of "Concepts of Space") if you want to see various attempts through history to nail down these concepts. Before discussing physics, I want to object to the implicit idea that a "definition" is an arbitrary setting of a term equal to some combination of other terms. A proper definition must capture the ESSENCE of a concept. This may, indeed, amount to a physical statement. Sticking strictly to Newtonian physics for purposes of discussion, force would be better defined as the gradient of energy, i.e. how much work per unit distance has to be exerted to change position. (Since energy is a conserved quantity in Newtonian physics, it is "more fundamental" than force.) Mass has two meanings. It is the amount of "inertia" a body has, and it is also the amount of a source of gravitation. The equality of these two characteristics is unexplained in Newtonian physics. Your question is about the inertial aspect of mass. The amount of mass in an object can be obtained by adding the masses of its constituent pieces, all the way down to the atomic level (there is a very small discrepancy due to mass associated with binding energy, but this is a relativistic detail). The preceding sentence states a fundamental physical property of what is called "mass", such that mass appears to be a measure of the "amount" of material in an object. This is the intuitive meaning that people used all along; Newton provided a mathematical theory relating mass to other things. Newton's First Law is a special case of his Second; the reason it was separately stated was probably to emphasize that the "natural" state of things (free motion) is different from what was previously believed (e.g. Aristotle claimed that an object would stop moving if not continually subjected to a force). A better statement of the Second law would be A body's momentum (mass * velocity) changes at a rate equal to the applied force (gradient of work). This is really a vector (3-D) statement. The reason that this is a better statement of the law is that an object's mass can change under some circumstances (e.g., a rocket in flight loses mass as it consumes fuel). In general, a physical theory consists of a number of properties (mass, energy, position, force, charge, etc.) and a number of formulas that give quantitative relationships among the primitive properties. Besides these purely formal aspects, there must also be a method of relating the elements of the theory to what is actually observed in the physical world. Sometimes there are implicit assumptions that are not considered (due to lack of omniscience), as the Euclidean nature of 3-D space in Newtonian physics. The whole package making up a complete physical theory normally takes considerable study to comprehend, especially since most of the primitive quantities can only be measured by applying some consequences of the theory itself. This does not necessarily indicate a "vicious circle" of self-reference, but perhaps just an internal self-consistency. This helps show why alternative theories are possible, though. To feel better about the relationship between mass and force, practice working Newtonian mechanics problems and eventually gravitational and electromagnetic particle problems. The concepts work out pretty well, although if pressed too hard one has to give up Newtonian physics for relativistic or quantum theories.
fred@mnetor.UUCP (Fred Williams) (07/05/85)
In article <9255@Glacier.ARPA> wong@Glacier.ARPA (Man Wong) writes: >What is the content of Newton's Second Law? Is it a definition? Can definitions >be called physical laws? > >Please help! Newton's second law really defines a relationship between mass, force, and the "time rate of change of momentum". I believe Newton himself expressed it as; dp F = ---- dt It is interesting to note that this holds true even when relativistic effects are taken into account. It resolves to "ma" when the mass is constant. I do not mean to imply that Newton anticipated Einstein, merely that he knew well the calculus which he invented and it's implications in the real world. If you are looking for the definitions of "mass" and "force", check any good physics text. Cheers, Fred Williams
carlc@tektronix.UUCP (Carl Clawson) (07/08/85)
In article <9255@Glacier.ARPA> wong@Glacier.ARPA (Man Wong) writes: > What is mass? ... What is force? >> (several followups, which don't answer the questions, follow). This is a serious question that most students probably don't bother to think about. I'll give my favorite thought experiment for answering it. Let's play Newton. Take some objects of different weights to experiment with, and get a spring scale to measure how hard we pull on an object. We will call the reading of the spring scale "force." For starters, we put two marks on our scale, which correspond to forces F1 and F2. This is the definition of forces F1 and F2. We have not yet assigned a NUMBER to either F1 or F2, just marks on a scale. Now we pull on some objects and measure the accelerations. (I'm assuming that time and distance have already been suitably defined.) The first thing we notice is that the acceleration is determined by the force, i.e., it is constant as long as the force is constant. We're on to something! Two objects are pulled with the same force when the spring scale gives the same reading. By pulling with the same force F1 on a number of objects we get different accelerations for different objects. Now pull with force F2 on the same objects. Being clever scientists, we notice that although each object is accelerated at a different rate than when we pulled with F1, the ratios between the different objects are the same. If object A has twice the acceleration of object B under force F1, then it will also have twice the acceleration of B under F2. Thus there is a property of objects that governs this proportionality. We call this property "mass," and we can define ratios of masses by pulling different objects with the same force and taking the inverse ratio of the accelerations. To define mass absolutely, you need a standard from which other masses can be measured by taking ratios. A hunk of metal in France will do for now. Now we want to calibrate our force scale. We have so far not assigned numbers to forces, we've just put marks on our scale so we can reproduce them. Let's do the simplest thing and make force proportional to acceleration. Now we can sit back, have a beer, and declare Newton's Second Law, F=ma. (We could just as well have calibrated our scale differently, in which case the second law would be f(F)=ma where f is some calibration function.) Summary: Mass is defined by ratios of accelerations under a given force. The essence of Newton's second law is that these ratios are independent of the force used. Force is defined operationally as the reading of a scale, and calibrated to give the simplest proportionality. -- Carl, who is not a historian and doesn't claim that this is what Newton actually did.
alan@sdcrdcf.UUCP (Alan Algustyniak) (07/08/85)
In article <1182@mnetor.UUCP> fred@mnetor.UUCP (Fred Williams) writes: > > Newton's second law really defines a relationship between mass, >force, and the "time rate of change of momentum". I believe Newton >himself expressed it as; > > dp > F = ---- > dt > I wrote that it was a great day, When Newton said,"F is ma." Alas, he did not; He said."F is p-dot." And my doctorate drifted away. Josef Solomon (In a letter in a very old issue of "Physics Today")