WORK AND MECHANICAL ENERGY.
Energy is called a scalar physical quantity that is a common measure of the different forms of motion.
To mechanical energy is the energy associated with the forces of gravity, elastic deformation of the body and the energy associated with the motion of the body.
If the body under the force makes moving , a work force that is equal to the scalar product of the force on the motion vector. The work force is a scalar quantity
The work of the horizontal component of the force F - force equals Ftraction equal:
The work of the vertical component of the force F - lifting force is Fn:
Force whose direction is perpendicular to the direction of motion of the body, no work.
Force directed against the pull, and negative work force is called resistance. Force perpendicular to the displacement does not change the numerical value of the speed (this force causes the body to move in a circle - the centripetal force) and the work it is 0.
II The work force of gravity. Conservative forces.
Determine the work force of gravity when moving body of mass m on an inclined plane, whose length l, and the height h. The body of two forces: gravity, directed vertically downward and reaction force , directed perpendicular to the plane of the AC. Their net one does work to the body acceleration (force of friction is neglected).
b) Determine the work done by the force of gravity in free fall at the height of the body
A comparison of the work done by the force of gravity when driving on an inclined plane and the free fall shows that the work force of gravity does not depend on the length and shape of the path traversed by the body, and is determined by the product of the force of gravity at the height difference in the initial and final position.
Force, work which does not depend on the shape and length of the path, and is determined only by the initial and final positions of the body, called conservative.
The work of conservative forces in a closed path is zero. Examples of conservative forces: gravity, the force of the spring, and the strength of the electrostatic interaction.
Dissipative forces are called force, the total work is in any movement of a closed system is always negative. Example: the force of friction and the resistance movement of bodies in liquids and gases. As a result of the dissipative forces the mechanical energy is transformed into other forms of energy.
IV Work variable force.
A complete work on all moving from point 1 to point 2 is
or, passing to the limit,
The work variable force is:
The work of the elastic force, given that
The work of the elastic force of a closed path 1-2-1
elastic force – conservative.
V Kinetic energy.
If elementary moving written as
According to II Newton's law
Value Wk equal to is the kinetic energy
The work of the resultant of all the forces acting on the particle is equal to the change in kinetic energy.
or other record
If A > 0, the WK increases (falls)
If A > 0, then decreases WK (throwing).
Moving bodies have the ability to do the job and in the event that no force on the part of other bodies do not act on them. If the body is moving with constant velocity, - the sum of all the forces acting on a body is equal to 0 and the work is not done. If the body is to act with some force in the direction of the body to another, then it can do the work. According to III rd Newton's law a moving body will be attached to the same magnitude force, but in opposite directions. Due to the action of this force will decrease the speed of the body until it stops. WK energy due to the movement of the body is called kinetic energy. Completely stop the body can not make work. WK depends on the speed and weight. Changing the direction of the velocity does not affect the kinetic energy.
If you press the spring on the value of X2 = X (X1 = 0), then return to its original state deformed spring is able to perform the work
Consequently, these bodies have stored energy, which arises due to the interaction of bodies with one another. This energy is called potential energy. Potential energy is called energy, which depends on the relative positions of the particles of the system.
If a body falls from a certain height h1do height h2, the potential energy changes from
Perfect for this work is
i.e. work performed by the bodies to which action conservative forces equals the change in potential energy of the opposite sign.
Thus, when a falling body performs positive work, his Wp decreases. If the body is lifted up, the force of gravity and makes a negative work Wp increases.
VII. Total energy.