Презентация Work, energy and power. Conservation of energy. Linear momentum. Collisions онлайн

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Слайды и текст к этой презентации:

№1 слайд

Содержание слайда: Physics 1 Voronkov Vladimir Vasilyevich

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

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

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Содержание слайда: 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).

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Содержание слайда: Work done by a varying force

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Содержание слайда: 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

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

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Содержание слайда: 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:

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Содержание слайда: 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

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Содержание слайда: 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.

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Содержание слайда: 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.

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

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Содержание слайда: Gravity is a conservative force: Gravity is a conservative force:

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Содержание слайда: Friction is a nonconcervative force:

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

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Содержание слайда: 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.

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Содержание слайда: Potential Energy of Gravity

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Содержание слайда: 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.

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

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

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Содержание слайда: 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:

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Содержание слайда: 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.

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Содержание слайда: 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.

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Содержание слайда: 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.

№30 слайд

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

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Содержание слайда: 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.

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