Work, energy and power. Conservation of energy. Linear momentum. Collisions презентация

Physics 1 Voronkov Vladimir Vasilyevich

Lecture 3 Work, energy and power Conservation of energy Linear momentum. Collisions.

Work A force acting on an object can do work on the object when the object moves.

Work Units Work is a scalar quantity, and its units are force multiplied by length. Therefore, the SI unit of work is the newton • meter (N • m). This combination of units is used so frequently that it has been given a name of its own: the joule ( J).

Work done by a varying force

Work done by a spring If the spring is either stretched or compressed a small distance from its unstretched (equilibrium) configuration, it exerts on the block a force that can be expressed as

Work of a spring So the work done by a spring from one arbitrary position to another is:

Kinetic energy Work is a mechanism for transferring energy into a system. One of the possible outcomes of doing work on a system is that the system changes its speed. Let’s take a body and a force acting upon it: Using Newton’s second law, we can substitute for the magnitude of the net force and then perform the following chain-rule manipulations on the integrand:

And finally: This equation was generated for the specific situation of one-dimensional motion, but it is a general result. It tells us that the work done by the net force on a particle of mass m is equal to the difference between the initial and final values of a quantity

Work-energy theorem: In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system. This theorem is valid only for the case when there is no friction.

Conservative and Nonconcervative Forces Forces for which the work is independent of the path are called conservative forces. Forces for which the work depends on the path are called nonconservative forces The work done by a conservative force in moving an object along any closed path is zero.

Examples Conservative Forces: Spring central forces Gravity Electrostatic forces Nonconcervative Forces: Various kinds of Friction

Gravity is a conservative force: Gravity is a conservative force:

Friction is a nonconcervative force:

Power Power P is the rate at which work is done:

Potential Energy Potential energy is the energy possessed by a system by virtue of position or condition. We call the particular function U for any given conservative force the potential energy for that force. Remember the minus in the formula above.

Potential Energy of Gravity

Conservation of mechanical energy E = K + U(x) = ½ mv2 + U(x) is called total mechanical energy If a system is isolated (no energy transfer across its boundaries) having no nonconservative forces within then the mechanical energy of such a system is constant.

Linear momentum Let’s consider two interacting particles: and their accelerations are: using definition of acceleration: masses are constant:

So the total sum of quantities mv for an isolated system is conserved – independent of time. This quantity is called linear momentum.

General form for Newton’s second law: It means that the time rate of change of the linear momentum of a particle is equal to the net for force acting on the particle. The kinetic energy of an object can also be expressed in terms of the momentum:

The law of linear momentum conservation The sum of the linear momenta of an isolated system of objects is a constant, no matter what forces act between the objects making up the system.

Impulse-momentum theorem The impulse of the force F acting on a particle equals the change in the momentum of the particle. Quantity is called the impulse of the force F.

Collisions Let’s study the following types of collisions: Perfectly elastic collisions: no mass transfer from one object to another Kinetic energy conserves (all the kinetic energy before collision goes to the kinetic energy after collision) Perfectly inelastic collisions: two objects merge into one. Maximum kinetic loss.

Perfectly elastic collisions We can write momentum and energy conservation equations: (1) (2) (1)=> (3) (2)=> (4) (4)/(3): (5)

Denoting We can obtain from (5) Here Ui and Uf are initial and final relative velocities. So the last equation says that when the collision is elastic, the relative velocity of the colliding objects changes sign but does not change magnitude.

Perfectly inelastic collisions

Energy loss in perfectly inelastic collisions

Units in SI Work,Energy W,E J=N*m=kg*m2/s2 Power P J/s=kg*m2/s3 Linear momentum p kg*m/s