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PPT – Potential energy , and conservation of energy Chap 8 PowerPoint presentation | free to download - id: 166017-ZDc1Z

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Potential energy ??, ?? and conservation of

energy (Chap 8)

Potential energy is the energy associated with

the arrangement of the objects in a system. It is

like the energy stored in the system.

- When throwing a tomato upward, the gravitational

force does a negative work, i.e. it gains energy.

Here it means the tomato-Earth system. - Then energy, gravitational potential energy, is

stored in the tomato-Earth system (or it can be

said that the energy is stored in the

gravitational field). - kinetic energy of tomato reduced
- when the tomato falls back, gravitational force

does positive work, the system loses energy - the tomato gains energy and speeds up

Another example

- (a) the work done by the spring is negative.
- therefore energy is stored in the block-spring

system, elastic ?? potential energy. - when the block moves to the left, energy

released. - energy from potential energy to kinetic energy.

Conservative and nonconservative forces

- in the previous examples, the work done

(negative) by the force is stored in the terms of

potential energy and is able to transfer back to

the kinetic energy

- in this situation, the force is called

conservative force ??? gravitational force,

spring force. - other situations where certain amount of energy

is lost and cannot be transferred back, the force

is nonconservative, like frictional force and

drag force.

Path independence of conservative force

(1) For a conservative force, the total work done

around a closed path is zero.

- on the other hand, since the force is

conservative, then

(2) the work done by a conservative force is

independent of the path taken

No, F is nonconservative because the work done

depends on the path.

Wh0

Wvmgh

Because the gravitational force is conservative,

its work done on any paths are the same.

Relation between potential energy and

conservative force.

The potential energy gain is simply the negative

of work done by the conservative force

Gravitational potential energy

Note that only the difference in U is important,

i.e. the energy change relative to a reference

point.

Elastic potential energy

take xi 0

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(3), (1), (2)

Conservation of mechanical energy ???

Mechanical energy the sum of kinetic energy and

potential energy.

- Assumptions
- the system concerned is isolated, i.e. no

external force acting on the system - there is only conservative force.

Since we have

and by definition the potential energy is the

negative of work

No change in mechanical energy

Or in other form

This is called the principle of conservation of

mechanical energy

A typical example

The mechanical energy of the pendulum is always

the same.

spring

An experiment done by Galileo Galileo discovered

that when the swing of a pendulum was interrupted

by a peg, the bob still rose to its initial level.

It is because of the conservation of mechanical

energy.

Application

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Fmax is determined using the conservation of

mechanical energy

Gravitation potential energy of the climber

elastic potential energy of the rope.

A quadratic equation of d

The solution of d is

Only take the positive solution

Fmax is then given by

The factor 2H/L is important here

Put in the numbers we have for (a) Fmax4.7x103N

and for (c) Fmax5.3x103N

The situation in (c) is more dangerous.

Potential energy curve

We have learned previously how to find the

potential energy by integrating a conservative

force

But we can also do reverse, find the force by

differentiate the potential

- For example
- Spring potential
- Gravitational potential

Since K?0, so the particle cannot move beyond the

turning point where K0.

Consider a general potential

Given a mechanical energy Emec, the kinetic

energy K is just the difference between the line

of Emec and the curve U(x).

- Equilibrium point is the location where the force

is zero, i.e. the slope of U(x) is 0. - If it is a minimum in U(x), then it is a stable

equilibrium point. - If it is a maximum, then it is a unstable

equilibrium a small derivation will cause the

particle moves away from the point.

For different mechanical energies

In this case, if Emec lt 4, the particle moves

back and forth within a region.

- Another example a typical potential curve of a

molecule (e.g. H2). - the molecule has an energy less than U0, then it

is bounded (it forms a molecule), otherwise the

two atoms can move apart. - the equilibrium point is located at r0.
- the potential is huge when two atoms move too

close to each other.

Work done by external force

The work done by the external force will be the

same as the change in mechanical work of the

system

The change in mechanical work must equal to the

total change in kinetic and potential energy.

If friction is involved, work done by the

frictional force should also be considered

Therefore total work done on the system is now

Work done by internal force

- for an isolated system, the total energy must

conserve, i.e. total work done on the system is

zero

Change in internal energy

- in this example, force F does no work on the

skater. There is no energy transfer from the rail

to the skater. - but the skaters kinetic energy does change

(increases), the energy comes from her

bio-chemical energy (internal energy).

Initial energy Final energy

Conservation of energy tells us that

Assume it stops at a distance d from the left

edge

Initial potential energy

Heat lost due to friction

Since d is larger than L, so the particle has

enough energy to climb the right curved portion

Problems 5, 22, 23, 51, 135

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