Energy - PowerPoint PPT Presentation

PPT – Energy PowerPoint presentation | free to download - id: 772524-OWFlY

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

Energy

Description:

Energy - Wikispaces ... Energy – PowerPoint PPT presentation

Number of Views:114
Avg rating:3.0/5.0
Slides: 38
Provided by: Robert2386
Category:
Tags:
Transcript and Presenter's Notes

Title: Energy

1
Energy
2
• Analyzing the motion of an object can often get
to be very complicated and tedious requiring
detailed knowledge of the path, frictional
forces, etc.
• There has to be an easier way
• It turns out that there is it is done by
analyzing the objects energy.

3
Energy
• The something that enables an object to do work
is energy.
• Energy is measured in Joules (J).
• Forms of Energy
• Mechanical (kinetic and potential)
• Thermal (heat)
• Electromagnetic (light)
• Nuclear
• Chemical

4
(No Transcript)
5
Mechanical Energy
• Mechanical energy is the form of energy due to
the position or the movement of a mass.

6
Kinetic Energy
• Kinetic energy is the energy of motion it is
associated with the state of motion of an object.
• The faster an object is moving, the greater its
kinetic energy an object at rest has zero
kinetic energy.
• For an object of mass m, we will define kinetic
energy as
• The SI unit of kinetic energy is the Joule (J).

7
Kinetic Energy
• If we do positive work on an object by pushing on
it with some force, we can increase the objects
kinetic energy (and thereby increasing its
speed).
• We can account for the change in kinetic energy
by saying that the force transferred energy from
you to the object.
• If we do negative work on an object by pushing on
it with some force in the direction opposite to
the direction of motion, we can decrease the
objects kinetic energy (and decrease its
speed).
• We can account for the change in kinetic energy
by saying that the force transferred energy from
the object to you.

8
Kinetic Energy
• Whenever we have a transfer of energy via a
force, we say that work is done on the object by
the force.
• Work W is energy transferred to or from an object
by means of a force acting on that object.
• Energy transferred to the object is positive
work.
• Energy transferred from the object is negative
work.
• Work is nothing more than transferred energy it
therefore has the same units as energy and is
also a scalar quantity.
• Note that nothing material is transferred.
• Think of it like the balance in two bank
accounts when money is transferred the number
for one account goes down by some amount and the
number for the other account goes up by the same
amount.

9
Work-Energy Theorem
• Suppose we have an bead which is constrained to
move only along the length of a frictionless
wire.
• We then supply a constant force F on the bead at
some angle ? to the wire.
• Because the force is constant, we know that the
acceleration will also be constant.

10
Work-Energy Theorem
• But because of the constraint, only the force in
the x direction matters, thus Fx max where m
• We can relate the beads velocity at some
distance down the wire to the acceleration using

11
Work-Energy Theorem
• Solving for ax, substituting into the Fx
equation, multiplying both sides by d, and
distributing the ½m throughout the equation

12
Work-Energy Theorem
• But we can see that the right side of the
equation is no more than the kinetic energy after
the force has been applied minus the kinetic
energy before the force was appliedand that
by definition is the work done

13
Work-Energy Theorem
• When calculating the work done on an object by a
force during a displacement, use only the
component of the force that is parallel to the
objects displacement.
• where ? is the angle between the force F and the
horizontal.
• The force component perpendicular to the
displacement does no work.

14
Work-Energy Theorem
• Work-Energy Theorem the net work done on an
object is equal to the change in kinetic energy
of the object.
• W Kf Ki Fd 0.5m(vf2 - vi2)
• A net force causes an object to change its
kinetic energy because a net force causes an
object to accelerate, and acceleration means a
change in velocity, and if velocity changes,
kinetic energy changes.

15
(No Transcript)
16
(No Transcript)
17
Gravitational Potential Energy
• Potential energy (U) an object may store energy
because of its position. Energy that is stored
is called potential energy because in the stored
state it has the potential to do work.
• Work is required to lift objects against Earths
gravity.
• Potential energy due to elevated positions is
gravitational potential energy.
• The amount of gravitational potential energy
possessed by an elevated object is equal to the
work done against gravity in lifting it.
• Ug Fwh mgh

18
Work and Potential Energy
• When we throw a tomato up in the air, negative
work is being done on the tomato which causes it
to slow down during its ascent.
• As a result, the kinetic energy of the tomato is
reduced eventually to zero at the highest
point.
• But where did that energy go???

19
Work and Potential Energy
• Where it went was into an increase in the
gravitational potential energy of the tomato.
• The reverse happens when the tomato begins to
fall down.
• Now the positive work done by the gravitational
force causes the gravitational potential energy
to be reduced and the tomatos kinetic energy to
increase.

20
Work and Potential Energy
• From this we can see that for either the rise or
fall of the tomato, the change ?U in the
gravitational potential energy is the negative of
the work done on the tomato by the gravitational
force
• In equation form we get

21
• Only changes in potential energy have meaning it
is important that all heights be measured from
the same origin.
• In many problems, the ground is chosen as the
zero level for the determination of the height.
• As the ball falls from A to B, the potential
energy at A is converted to kinetic energy at B.
• The amount of potential energy of the ball at
point A will equal the amount of kinetic energy
of the ball at point B.

22
Elastic Potential Energy
• Stretching or compressing an elastic object
requires energy and this energy is stored in the
elastic object as elastic potential energy.
• The work required to stretch or compress a spring
is dependent on the force constant k.
• The force constant will not change for a
particular spring as long as the spring is not
permanently distorted (which occurs when the
elastic limit of the spring is exceeded).
• F kx

23
(No Transcript)
24
Elastic Potential Energy
• The force required to stretch/compress an elastic
object is not a constant force. The work needed
varies with the amount of stretch/compression.
• W 0.5kx2
• The potential energy of an elastic object is
equal to the work done on the elastic object.
• Ue 0.5kx2
• In actual practice, a small fraction of the work
in stretching/compressing an elastic object is
converted into heat energy in the spring.

25
Work and Elastic Potential Energy
• If we give the block a shove to the right, the
kinetic energy of the block is transferred into
elastic potential energy as the spring
compresses.
• The work done in compressing the spring is the
negative of the change in the blocks kinetic
energy.
• And of course the reverse happens when the spring
stretches back out potential energy gets
transformed back into kinetic energy.

26
Conservation of Mechanical Energy
• Conservative forces all the work done is stored
as energy and is available to do work later.
Example gravitational forces, elastic forces.
• Nonconservative (dissipative) forces the force
generally produces a form of energy that is not
mechanical.
• Friction is a nonconservative (dissipative) force
because it produces heat (thermal energy, not
mechanical).
• The total amount of energy in any closed system
remains constant.

27
Conservation of Mechanical Energy
• The sum of the potential and kinetic energy of a
system remains constant when no dissipative
forces (like friction) act on the system.
• Law of Conservation of Energy energy cannot be
created or destroyed it may be changed from one
form to another or transferred from one object to
another, but the total amount of energy never
changes.

28
Conservation of Mechanical Energy
• In a closed system in which gravitational
potential energy and kinetic energy are involved,
the potential energy at the highest point is
equal to the kinetic energy at the lowest point.
• mgh 0.5mv2

29
(No Transcript)
30
(No Transcript)
31
• Notice that the sum of the potential energy (PE)
and kinetic energy (KE) at every point is 40000
J. Energy is conserved.

32
• The velocity at the lowest point can be
determined by the height

33
Conservation of Mechanical Energy
• The change in velocity due to a change in height
can also be determined
• The height can be determined by the initial
velocity (vf 0 m/s)

34
Conservation of Mechanical Energy
• In a closed system in which elastic potential
energy and kinetic energy are involved, the
potential energy at the maximum distance of
stretch/compression is equal to the kinetic
energy at the equilibrium (rest) position.

35
Conservation of Mechanical Energy
• Conservation of Energy Equation
• W done (by applied force) Ugravitational before
Uelastic before K before Ugravitational
after Uelastic after K after W done
(usually by friction)
• Fappliedd m g hi 0.5 k xi2 0.5 m vi2
m g hf 0.5 k xf2 0.5 m vf2 FFd

36
• If there is no change in height m g hi and m
g hf drop out of the equation.
• If there is no spring or elastic object 0.5
k xi2 and 0.5 k xf2 drop out of the equation.
• If there is no change in velocity 0.5 m vi2
and 0.5 m vf2 drop out of the equation.
• If there is no applied force (a push/pull that
you supply) Fappliedd drops out of the
equation.
• If there is no friction FFd drops out of the
equation.

37