Transcript energy

ENERGY
• ENERGY is present in the Universe in a
variety of forms, including mechanical,
chemical, electromagnetic, and nuclear
energy.
• Mechanical energy, is a sum of Kinetic
energy (the energy associated with
motion), and potential energy (the energy
associated with position)
• WORK-is done only if
an object is moved
through some
displacement while a
force is applied to it
• The WORK done on
an object by a
constant force F is
give by:
W = FΔx
F- the magnitude of the • SI unit:
joule (J)= newton meter
force
=Nm
Δx- magnitude of the
2/s2
=
kg
m
displacement
• Work is a scalar
quantity
• The work done by a
constant force F is
given by:
W= (F cosθ)Δx
F-is the magnitude force
• Work can be either
Δx – the magnitude of
positive or negative,
the object’s
depending on whether
displacement
cos θ is positive or
θ- the angle between
negative
the directions F and
Δx
• Wnet= Fnet Δx
=(m a) Δx
v2 =vo2 +2a Δx
aΔx = (v2-vo2)/2
W= m (v2-vo2)/2
W= ½ mv2-½ mvo2
The KINETIC ENERGY • The net work done on an
of an object of mass object:
m moving with a
Wnet= Kef –Kei =ΔKE
speed v is defined
where the change in the
kinetic energy is due
by:
entirely to the object’s
KE=1/2 mv2
change in speed
SI unit: (J)=kg m2/s2
• A force is
conservative if the
work it does moving
an object between
two points is the
same no matter
what path is taken
(ex gravity)
Nonconservative forces
don’t have this
propriety (ex friction
force)
• The Work – Energy theorem:
Wnet= Kef –Kei =ΔKE
Can be written in terms of the work done by
conservative forces (Wc) and the work
done by nonconservative forces (Wnc)
Wnet= Wnc +Wc =ΔKE
The work done by conservative forces is
called POTENTIAL ENERGY – a quantity
that depends obly in the beginning and
end points of a curve, not the path taken
• Gravity is a conservative
force, then a potential
energy can be found.
• If a book falls from height yi
to a height yf, we neglect
the force of air friction, so
the only force acting is
gravitation
• How much work is done?
Wg= F Δy cosθ
= mg (yi-yf) cos0o
= -mg (yf-yi)
Wnet = Wnc +Wg =ΔKE
Wnet = Wnc –mg (yf-yi) =ΔKE
Wnc =ΔKE +mg (yf-yi)
The gravitational potential energy of a
system consisting of the Earth and an
object of mass m near the Earth’s surface
is give by:
PE= mgy
SI unit : (J)- joule
g- acceleration of gravity
y – vertical position of the mass relative
the surface of Earth
Wg = - (PEf-Pei)
= - (mgyf-mgyi)
Wnc = (KEf- KEi) + (PEf –PFi)
The work done by nonconservative
forces, Wnc is equal to the change in
the energy plus the change in the
gravitational potential energy
!!! It is important to choose a location at
which to set that energy equal to zero
(y=0)
• Gravity and the Conservation of
Mechanical Energy
When a physical quantity is conserved
the numeric value of the quantity
remains the same throughout physical
process (final value is the same as its
initial value)
KEi + PEi = KEf +PEf
The sum of kinetic energy and the
gravitational potential energy remains
constant at all the times , is a
conserved quantity
• Total mechanical energy :
E = KE +PE
The total mechanical energy is conserved!
In any isolated system of objects
interacting only through conservatives
forces, the total mechanical energy E=
KE +PE, of the system, remains the
same all times