 |
Business | Industries | Finance | Tax |
| Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
|
|||||
| First Prev [ 1 2 3 ] Next Last |
Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. It is a central concept of classical mechanics and related subjects.
Strictly speaking, there are two different quantities called mass:
Although inertial and gravitational mass are conceptually distinct, no experiment performed to date has ever managed to find a difference between the two. One of the consequences of this is the fact, famously demonstrated by Galileo Galilei, that objects with different masses fall at the same rate, assuming factors like air resistance are negligible. The theory of general relativity, the most accurate theory of gravitation known to physics, rests on the assumption that inertial and gravitational mass are completely equivalent. This is known as the equivalence principle.
In the SI system of units, mass is measured in kilograms (kg). Physicists sometimes find it more convenient to work with other units of mass. For instance, it is common in particle physics to measure mass in terms of electron volts (eV), a unit of energyThis article is about the scientific concept. Energy use by humans is discussed in other articles''. Energy generally and qualitatively speaking, is the property (or the quantity of the property) of doing things or supplying power. The expressions energy. One electron volt is about 1.602 × 10−19To help compare different orders of magnitude we list here energies between 10−19 joules and 10−18 joules (0. Weaker energies 1. 602 × 10−19 J 1 electron volt (eV) 1. 602 × 10−19 J Average kinetic energy of a molecule at 11300 ° C JThe joule (symbol J also called newton metre or coulomb volt is the SI unit of energy and work. The unit is pronounced to rhyme with "tool", and is named in honour of the physicist James Prescott Joule (1818-1889). 1 joule 1 N · 1 m 1 newton · 1 metre 1 k. This is related to mass using the relativistic connection between mass and (rest) energy, E = mc˛ (see below .) One electron volt is thus equivalent to 1.783 × 10-36 kg. For more information on the different units of mass, see Orders of magnitude (mass)See also SI SI prefix SI base unit Physical unit Mass Orders of magnitude Conversion of units orders of magnitude (length) orders of magnitude (area) orders of magnitude (volume) orders of magnitude (time) List of energies in joules Planck units size comp.
To understand what the inertial mass of a body is, one begins with classical mechanics and Newton's Laws of Motion. Later on, we will see how our classical definition of mass must be altered if we take into consideration the theory of special relativitySpecial relativity (SR or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. It replaced Newtonian notions of space and time, and incorporated electromagnetism as represented by Maxwell's equations. The theory is, which is more accurate than classical mechanics. However, the implications of special relativity will not change the meaning of "mass" in any essential way.
According to Newton's second law, we say that a body has a mass m if, at any instant of time, it obeys the equation of motion
where F is the force acting on the body and v is its velocityVelocity (symbol: v is a vector measurement of the rate and direction of motion. The scalar absolute value ( magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement, depending on. For the moment, we will put aside the question of what "force acting on the body" actually means.
Now, suppose that the mass of the body in question is a constant. This assumption, known as the conservation of mass, rests on the ideas that (i) mass is a measure of the amount of matter contained in a body, and (ii) matter can never be created or destroyed, only split up or recombined. These are very reasonable assumptions for everyday objects, though, as we will see, the situation gets more complicated when we take special relativity into account. Another point to note is that, even in classical mechanics, it is sometimes useful to treat the mass of an object as changing with time. For example, the mass of a rocket decreases as the rocket fires. However, this is an approximation, based on ignoring pieces of matter which enter or leave the system. In the case of the rocket, these pieces correspond to the ejected propellent; if we were to measure the total mass of the rocket and its propellent, we would find that it is conserved.
When the mass of a body is constant, Newton's second law becomes
where a denotes the acceleration of the body.
This equation illustrates how mass relates to the inertia of a body. Consider two objects with different masses. If we apply an identical force to each, the object with a bigger mass will experience a smaller acceleration, and the object with a smaller mass will experience a bigger acceleration. We might say that the larger mass exerts a greater "resistance" to changing its state of motion in response to the force.
However, this notion of applying "identical" forces to different objects brings us back to the fact that we have not really defined what a force is. We can sidestep this difficulty with the help of Newton's third law, which states that if one object exerts a force on a second object, it will experience an equal and opposite force. To be precise, suppose we have two objects A and B, with constant inertial masses mA and mB. We isolate the two objects from all other physical influences, so that the only forces present are the force exerted on A by B, which we denote FAB, and the force exerted on B by A, which we denote FBA. As we have seen, Newton's second law states that
where aA and aB are the accelerations of A and B respectively. Suppose that these accelerations are non-zero, so that the forces between the two objects are non-zero. This occurs, for example, if the two objects are in the process of colliding with one another. Newton's third law then states that
Substituting this into the previous equations, we obtain
Note that our requirement that aB be non-zero ensures that the fraction is well-defined.
This is, in principle, how we would measure the inertial mass of an object. We choose a "reference" object and define its mass mB as (say) 1 kilogram. Then we can measure the mass of every other object in the universe by colliding it with the reference object and measuring the accelerations.
| Politics | Business | Finance |
 |
 |
 |
|