Linear momentum

GENERALIZED CONSERVATION OF ENERGY

Thus far we have taken a rather limited view of energy. We have considered only macroscopic (bulk) kinetic and potential energies. In effect all objects were treated as particles without structure. However, consider a block that slides to a stop on a rough surface. What happens to its kinetic energy? The work done by the force of friction on the block transforms the bulk kinetic energy of the block into internal kinetic and potential energies associated with the random motion of the atoms. This added thermal energy is manifested as a rise in temperature of the block. After a while, the block cools down. The extra thermal energy is removed by heat, which is a transfer of energy associated with the temperature difference between the warm block and the cooler surroundings.

Around 1845, several scientists independently concluded that all natural pro­cesses are subject to an important constraint called the principle of the conserva­tion of energy:

Energy can change its form, but it can neither be created nor destroyed.

The formulation of this principle required the identification of heat as a form of energy. The fact that the internal energy of a system can be changed by the performance of work or by the transfer of heat is the essence of the first law of thermodynamics.

In general, one can regard the relation between work and energy as follows: Work is a mode of energy transfer from one body to another in which a force moves through a displacement. If the work done by object A on object В is positive, energy is transferred from A to B. If it is negative, energy is transferred from В to A. Work is also a measure of the transformation of one form of energy into another. For example, the work done by our muscles in pulling a block represents a transformation of chemical energy into kinetic energy.

Linear momentum of a particle is the product of a particle's mass and its velocity. For some reason which escapes me at the moment, the symbol p is customarily used to designate momentum. Since it is the product of a vector and a scalar, it is a vector quantity:

Linear momentum p = m v.

The rate of change of momentum with respect to time, taking mass to be constant, is p' = m v', where v ' is the vector acceleration of the particle. Remember that we are using the ' symbol to represent the rate of change with respect to time. From our expression of Newton's second law, we know that m v ' is the force on a particle so p' = F. A modern statement of Newton's second law is

F = d p / dt (5.7)

The net force acting on a particle is equal to the time rate of change of its linear momentum.

For a system of particles, the linear momentum is just the vector sum of that of each of the particles individually.

Дата добавления: 2014-01-05