Section 12 1 .
Newtons law of Universal Gravitation ;
Fgrav .
= Em , me
r2
↳ distance between their centers
Nm2
G = 6 67. x 10- "
1g2
this force acts between every pair of objects
this force is always
Gravity :
we know Eg =
-may
Only vertical displacement gives work
·
nonzero
if we let
lay) = h , then IWg) mgh :
-
moving down Eg and by are parallel ,
and Eg does positive work :
Wg togh =
When an object is lifted or lowered ,
the applied force does work too .
·
if
object starts &-
ends at rest , then work from applied Force is equal in magnitude , opposite in
sign , to from .
work
gravity
Section 5 5 .
if the force varies as position changes ,
work is given by
W= S"Fx x)dx
Xy
for 2D 3D motion we
or
get
·
,
Way =
F dr .
A
·
this integral follows from A to i
path taken point point
Section 5 . 6 :
recall that Esp = -KX (if Xo is equilibrium position
if from
you hang a mass a spring, gravity has effect of
shifting equilibrium position , so we can still
consider just the spring.
* kx (Fsp)
>
work done by a
spring is
Wsp kx
-
=
=
neg cause spring is trying
it is to
get back to equilibrium K 63 5 N
=
1450 NIm
·
. =
EX : Solved Problem 5 2 .
0 0435m
.
F 63 5N
=
.
,
1X = 0 0435m
.
,
M= 0 .
075kg ,
Vo = Omis k =
+muz
1450 : E (0 875) v .
V =
Newtons law of Universal Gravitation ;
Fgrav .
= Em , me
r2
↳ distance between their centers
Nm2
G = 6 67. x 10- "
1g2
this force acts between every pair of objects
this force is always
Gravity :
we know Eg =
-may
Only vertical displacement gives work
·
nonzero
if we let
lay) = h , then IWg) mgh :
-
moving down Eg and by are parallel ,
and Eg does positive work :
Wg togh =
When an object is lifted or lowered ,
the applied force does work too .
·
if
object starts &-
ends at rest , then work from applied Force is equal in magnitude , opposite in
sign , to from .
work
gravity
Section 5 5 .
if the force varies as position changes ,
work is given by
W= S"Fx x)dx
Xy
for 2D 3D motion we
or
get
·
,
Way =
F dr .
A
·
this integral follows from A to i
path taken point point
Section 5 . 6 :
recall that Esp = -KX (if Xo is equilibrium position
if from
you hang a mass a spring, gravity has effect of
shifting equilibrium position , so we can still
consider just the spring.
* kx (Fsp)
>
work done by a
spring is
Wsp kx
-
=
=
neg cause spring is trying
it is to
get back to equilibrium K 63 5 N
=
1450 NIm
·
. =
EX : Solved Problem 5 2 .
0 0435m
.
F 63 5N
=
.
,
1X = 0 0435m
.
,
M= 0 .
075kg ,
Vo = Omis k =
+muz
1450 : E (0 875) v .
V =
