Transcript Kinetic energy

Chapter 8
Potential Energy and Conservation of
Energy
8-6 Conservation of Energy Wext = ΔE
8-1 Work and Potential Energy
8-2 Path Independence of Conservative Forces
8-3 Determining Potential Energy Values
8-4 Conservation of Mechanical Energy
8-5 Work Done on a System by an External Force and
Thermal Energy due to Friction
Kariapper
Ch9-page 1
8-6 Conservation of Energy
Energy of a System
Work Kinetic Energy Theorem
For a Single Object:
W = ΔK
Conservation of Energy Principle
For a system of objects
W = ΔE
Change in
Kinetic energy
Work done by an (external)
force on the object/system
Change in
Kinetic energy
Change in
Energy
ΔE = ΔK + ΔU  ΔEth + ΔEint
Change in
Change in
Potential energy thermal energy
Change in
internal energy
However we will not worry about DEint
in phys101, and we’ll deal only with situation where DEint =0
Kariapper
Ch9-page 2
8-6 Conservation of Energy
Energy of a System
A particle-earth system
A spring-block system
Fext
F
g
Fg is not an external force
Fext
Fs
Fs is not an external force
If we choose our system to be a particle or a block only,
then Fg and Fs will be an external force to our system
(which is a single body now)
Kariapper
Ch9-page 3
8-2 Work and Potential Energy
Gravitational Potential Energy
A particle-earth system
F
F
g
g
initial
W = ΔK + ...?...
final
If Fext = 0 for this system then W = 0, but we know that DK is not
zero as the ball falls.. So where is the energy coming from to
increase its kinetic energy?
We associate what is called a Potential Energy Ug with the
configuration of the earth particle system, the change of which is
the negative of the work done by gravitational force: DUg = -Wg
Kariapper
Ch9-page 4
8-3 Path Independence of Conservative Forces
Conservative Forces
Work done by a conservative force does not depend on the path
between the initial and final point.
W1
W1=W2
W2
In another words:
The net work done by a conservative force on a
particle moving around any closed path is zero.
W=0
Conservative
Force
Gravitational Force Frictional Force
Spring Force
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Non-Conservative
Force
Drag force
Ch9-page 5
8-3 Path Independence of Conservative Forces
Non-Conservative Forces
Non-Conservative Force
Work depends on the path
Example:
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Ch9-page 6
8-3 Determining Potential Energy Values
Definition of Potential Energy
It is defined for a system of two or more objects
It is defined only for conservative forces
xf
DU c  W c    F dx
Gravitational Potential Energy, Ug
xi
yf
DU g    Fg dy  W g   mg Dy
yi
Elastic Potential Energy, Us
xf
1
2
2
DU s    Fs dx  W s  k  x f  x i 
2
xi
Kariapper
Ch9-page 7
8-3 Determining Potential Energy Values
Checkpoint
Checkpoint:
A particle moves from x =0 to x=1, under the influence of a conservative
force as shown. Rank according to DU, most positive first (descending
order).
Kariapper
Ch9-page 8
8-3 Determining Potential Energy Values
Example
What is the U of the sloth-earth system if our reference point is
• at the ground
• at a balcony floor that is 3.0 m above the ground
• at the limb
• 1 meter above the limb?
Kariapper
Ch9-page 9
8-4 Conservation of Mechanical Energy
Mechanical Energy
Emech = K+U
Mechanical
energy
Kinetic
energy
Potential
energy
If there is no external acting on a system (W = 0) and its thermal
energy is constant (no non-conservative forces such as friction,
DEth = 0), then its mechanical energy is conserved.
0 = DK+DU
OR
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Mechanical Energy is
conserved
Kf+Uf= Ki+Ui=constant
Ch9-page 10
8-4 Conservation of Mechanical Energy
Checkpoint
Rank according to speed at point B. Ball sliding on a Frictionless
Ramp
Kariapper
Ch9-page 11
8-4 Work Done on a System
No friction involved
We have a block-floor-earth system. The applied force F is external to
the our system. The law of conservation of energy states that the work
done by external force on a system is equal to the change of energy
W = DE
0 same height
Fd= DK+DU
Kariapper
Ch9-page 12
8-4 Work Done on a System
friction involved
We have a block-floor-earth system, this time there is friction. The friction
force is now an internal force. However as a result of the friction force,
there will be a loss in the kinetic energy which appear as an increase in
the thermal energy (converted to heat) of the system.
W = DE
W = DEmech+DEth
0
F d= DK+DU+DEth
It can be shown that the change in thermal energy
is equal to the negative of the work done by the
friction force: DEth= fk d = - Wf
Therefore the conservation of energy principle can
also be stated in the form: W + Wf = DEmech
fk d
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Ch9-page 13
8-4 Work Done on a System
Example
By what distance d is the spring compressed when the block stops?
W = DEmech+DEth
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OR
W + Wf = DEmech
DEth = - Wf = fk d
Ch9-page 14