Work Energy Theorem
Energy is a scalar valve
↳
gain 1 loss
work: Transfer of
energy
"
Energy Value
"
: steerable of work in a system
Analogy
-
money as
energy
:
System
-
= bank account
work = transfers in the account
-
↳e debit I withdraw
-
g -
vs .
Deposit
cross $) (gain $)
final balance
'
- .
Energy = in account
Mathematical definition Of work
'
. W = EX SI
work -
in Joules
E -
force causing displacement IN)
Dd -
displacement of Object Lm)
work is dot product Of E 3
.
Dot
↳ Scalar product of 2 Vectors
↳ direction not important
↳ cross product : product of 2 Vectors that produce a third vector
↳
product of magnitude give magnitude of vector
↳ another rule gives directionality
Unit J= N
analysis
: -
m
J=
kgm
-
SZ
, Graph: work is calculated as area of F vs Sd graph
if Eqn = W= E. sat
↳ The force is
}
F <
constant
↳
highly unrealistic
↳ work
derivative
actually integral 1 Anti
Of a E vs Sot
•
Implication of eqn
Ad is evidence that W was
successfully transferred to
the system b/c it
give pic of change that can be created by an
application of force which can result in the transfer of
energy
i. A force does transfer
acting on a system not
energy unless it
successfully causes displacement
push
-
against Wall : using energy → there is force
↳ there is 0 work → was an attempt
↳ O → transfer
Force =
to attempt to
energy
Note: newtons law still applies
↳ F
causing 1 affecting
Sot must be in same axis
Derivation of Eg
if W= F bot-
and W= Ez -
E,
W -
-
DE
L h3
← he Then Ez E ,
-
= E. sat
a hi
- Where the minimum amnt Of force
to lift I
required move an object is
Fg
↳ just a little > to
Fg accelerate
↳ F-
mg -7 Ez -
E, =
mg .
Dot then back to
Fg to keep constant
motion
Energy is a scalar valve
↳
gain 1 loss
work: Transfer of
energy
"
Energy Value
"
: steerable of work in a system
Analogy
-
money as
energy
:
System
-
= bank account
work = transfers in the account
-
↳e debit I withdraw
-
g -
vs .
Deposit
cross $) (gain $)
final balance
'
- .
Energy = in account
Mathematical definition Of work
'
. W = EX SI
work -
in Joules
E -
force causing displacement IN)
Dd -
displacement of Object Lm)
work is dot product Of E 3
.
Dot
↳ Scalar product of 2 Vectors
↳ direction not important
↳ cross product : product of 2 Vectors that produce a third vector
↳
product of magnitude give magnitude of vector
↳ another rule gives directionality
Unit J= N
analysis
: -
m
J=
kgm
-
SZ
, Graph: work is calculated as area of F vs Sd graph
if Eqn = W= E. sat
↳ The force is
}
F <
constant
↳
highly unrealistic
↳ work
derivative
actually integral 1 Anti
Of a E vs Sot
•
Implication of eqn
Ad is evidence that W was
successfully transferred to
the system b/c it
give pic of change that can be created by an
application of force which can result in the transfer of
energy
i. A force does transfer
acting on a system not
energy unless it
successfully causes displacement
push
-
against Wall : using energy → there is force
↳ there is 0 work → was an attempt
↳ O → transfer
Force =
to attempt to
energy
Note: newtons law still applies
↳ F
causing 1 affecting
Sot must be in same axis
Derivation of Eg
if W= F bot-
and W= Ez -
E,
W -
-
DE
L h3
← he Then Ez E ,
-
= E. sat
a hi
- Where the minimum amnt Of force
to lift I
required move an object is
Fg
↳ just a little > to
Fg accelerate
↳ F-
mg -7 Ez -
E, =
mg .
Dot then back to
Fg to keep constant
motion
