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

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2. Lecture 3 Work, energy and powerConservation of energy Linear momentum. Collisions.
3. Work A force acting on an object can
4. When an object is displaced on
5. Work Units
6. Work done by a varying force
8. Work done by a springIf the spring
11. Work of a springSo the work done
12. Kinetic energyWork is a mechanism for transferring
13. And finally:This equation was generated for the
14. Work-energy theorem:
15. Conservative and Nonconcervative ForcesForces for which the
16. ExamplesConservative Forces: Springcentral forcesGravityElectrostatic forcesNonconcervative Forces:Various kinds of Friction
17. Gravity is a conservative force: An object
18. Friction is a nonconcervative force:
19. PowerPower P is the rate at which work is done:
20. Potential EnergyPotential energy is the energy possessed
22. Potential Energy of Gravity
23. Conservation of mechanical energyE = K +
24. Linear momentumLet’s consider two interacting particles: and their accelerations are:using definition of acceleration:masses are constant:
25. So the total sum of quantities mv
26. General form for Newton’s second law:It means
27. The law of linear momentum conservationThe sum
28. Impulse-momentum theoremThe impulse of the force F
29. CollisionsLet’s study the following types of collisions:Perfectly
30. Perfectly elastic collisions
31. DenotingWe can obtain from (5)Here Ui and
32. Perfectly inelastic collisions
33. Energy loss in perfectly inelastic collisions
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Lecture 3 Work, energy and powerConservation of energy Linear momentum. Collisions.

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

Lecture 3 Work, energy and powerConservation of energy Linear momentum. Collisions.

Work A force acting on an object can do work on the object

When an object is displaced on a frictionless, horizontal surface, the

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

Work done by a springIf the spring is either stretched or compressed

Work of a springSo the work done by a spring from one

Kinetic energyWork is a mechanism for transferring energy into a system. One

And finally:This equation was generated for the specific situation of one-dimensional motion,

Conservative and Nonconcervative ForcesForces for which the work is independent of the

ExamplesConservative Forces: Springcentral forcesGravityElectrostatic forcesNonconcervative Forces:Various kinds of Friction

Gravity is a conservative force: An object of moves from point A

PowerPower P is the rate at which work is done:

Potential EnergyPotential energy is the energy possessed by a system by virtue

Conservation of mechanical energyE = K + U(x) = ½ mv2 +

Linear momentumLet’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

General form for Newton’s second law:It means that the time rate of

The law of linear momentum conservationThe sum of the linear momenta of

Impulse-momentum theoremThe impulse of the force F acting on a particle equals

CollisionsLet’s study the following types of collisions:Perfectly elastic collisions: no mass transfer

DenotingWe can obtain from (5)Here Ui and Uf are initial and final

Energy loss in perfectly inelastic collisions

Units in SIWork,Energy W,E J=N*m=kg*m2/s2 Power P J/s=kg*m2/s3Linear momentum p kg*m/s

Слайды презентации

Слайд 2 Lecture 3
Work, energy and power
Conservation of energy
Linear

momentum.
Collisions.

Слайд 3 Work
A force acting on an object can do

Work A force acting on an object can do work on the

work on the object when the object moves.

Слайд 4
When an object is displaced on a

When an object is displaced on a frictionless, horizontal surface,

frictionless, horizontal surface, the normal force n and the

gravitational force mg do no work on the object. In the situation shown here, F is the only force doing work on the object.

Слайд 6 Work done by a varying force

Слайд 8 Work done by a spring
If the spring is

Work done by a springIf the spring is either stretched or

either stretched or compressed a small distance from its

unstretched (equilibrium) configuration, it exerts on the block a force that can be expressed as

Слайд 11 Work of a spring
So the work done by

Work of a springSo the work done by a spring from

a spring from one arbitrary position to another is:

Слайд 12 Kinetic energy
Work is a mechanism for transferring energy

Kinetic energyWork is a mechanism for transferring energy into a system.

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:

Слайд 13

And finally:

This equation was generated for the specific

And finally:This equation was generated for the specific situation of one-dimensional

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

Слайд 14 Work-energy theorem:

Слайд 15 Conservative and Nonconcervative Forces
Forces for which the work

Conservative and Nonconcervative ForcesForces for which the work is independent of

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.

Слайд 16 Examples
Conservative Forces:
Spring
central forces
Gravity
Electrostatic forces
Nonconcervative Forces:
Various kinds of

Friction

Слайд 17 Gravity is a conservative force:
An object of

Gravity is a conservative force: An object of moves from point

moves from point A to point B on an

inclined plane under the intluence of gravity. Gravity does positive (or negative) work on the object as it move down (or up) the plane.

The object now moves from point A to point B by a different path: a vertical motion from point A to point C followed by a horizontal movement from C to B. The work done by gravity is exactly the same as in part (a).

Слайд 18 Friction is a nonconcervative force:

Слайд 19 Power
Power P is the rate at which work

is done:

Слайд 20 Potential Energy
Potential energy is the energy possessed by

Potential EnergyPotential energy is the energy possessed by a system 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.

Слайд 21

Слайд 22 Potential Energy of Gravity

Слайд 23 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.

Слайд 24 Linear momentum
Let’s consider two interacting particles:

and their accelerations

are:

using definition of acceleration:

masses are constant:

Слайд 25

So the total sum of quantities mv for

So the total sum of quantities mv for an isolated system

an isolated system is conserved – independent of time.
This

quantity is called linear momentum.

Слайд 26
General form for Newton’s second law:

It means that

General form for Newton’s second law:It means that the time rate

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:

Слайд 27 The law of linear momentum conservation
The sum of

The law of linear momentum conservationThe sum of the linear momenta

the linear momenta of an isolated system of objects

is a constant, no matter what forces act between the objects making up the system.

Слайд 28 Impulse-momentum theorem

The impulse of the force F acting

Impulse-momentum theoremThe impulse of the force F acting on a particle

on a particle equals the change in the momentum

of the particle.
Quantity is called the impulse of the force F.

Слайд 29 Collisions

Let’s study the following types of collisions:
Perfectly elastic

CollisionsLet’s study the following types of collisions:Perfectly elastic collisions: no mass

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.