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Tippens Fisica 7e Soluciones 10
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Tippens Fisica 7e Soluciones 10
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Manuel Cartagena
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!
tan !
v
2
=
gR
tan !
tan !
v
2
=
(11.1 m/s) 2 =
gR
v
(9.8 m/s2 )(96 m)
2
=
(12 m/s) 2 =
gR
(9.8 m/s2 )(0.30 m)
!
tan !
v
=
v
2
=
gR
; v
=
gR tan !
v 2! fR; f 2! R =
=
(9.8 m/s 2 )(0.173 m)( tan 60 0 )
1.71 m/s =
2! (0.173 m)
!
v
tan !
2
=
gR
sen!
;
v
R =
=
gR tan !
R =
0.4 m
L
=
(9.8 m/s 2 )(0.30 m) tan 30 0
" R # T$ % & 0.4 m '
! =
4!
2
2
f mR
"
cos!
(2 kg)(9.8 m/s2 )
mg =
=
56.1 N
T
!
m
1.5 lb =
32 ft/s
sin !
R =
0.0469 slug R
=
L
=
0.5 ft "
" R # % & 0.5 ft '
T$
=
4!
2
f 2 mR
cos!
!
(0.0469 slug)(32 ft/s2 )
mg =
=
2.57 lb
T
!
!
tan !
v
=
2
=
gR
;
v
=
gR tan !
2
0
(9.8 m/s )(7 m) tan 30
=
tan !
v
v
v
2
=
gR
2! fR;
;
v
=
gR tan !
v f 2! R =
v
=
6.33 m/s =
2! (7.695 m)
(9.8 m/s 2 )(7.695 m) tan 280
T vc
T vc
+
mg =
=
+
gR
mg =
=
gR
mv 2 R =
(9.8 m/s2 )(0.7 m)
mv 2 R =
(9.8 m/s2 )(0.7 m)
T
T
+
(1.2 kg)(8 m/s) 2 =
(0.9 m)
mg =
T
=
(0.9 m)
R
2
T
mv =
R
2
! mg
! (1.2 kg)(9.8 m/s2 )
T ! mg
(1.2 kg)(8 m/s) 2
mv
+
mv =
R
2
T
=
mv
(1.2 kg)(9.8 m/s2 )
R
2
+
mg
a
v
2
=
(620 ft/s) 2 =
R
N
(2800 ft)
! mg =
N =
mv
2
R
N =
;
(5 slugs)(620 ft/s) 2 (2800 ft)
+
mv
2 +
R
mg
160 lb N
a
v
2
=
=
R
7g;
v
7 gR
=
=
7(9.8 m/s2 )(1000 m)
N
T
T
(3 kg)(16 m/s)2 =
(8 m) vc
+
mg =
N
mv
2
R
T
mv =
! (3 kg)(9.8 m/s2 )
=
gR
=
(9.8 m/s2 )(8 m)
R
2
! mg
8m
cos !
=
20 m
? mv 2
=
;
mgh;
!
v
=
=
66.4
0
2 gh
2(9.8 m/s2 )(12 m)
=
T ! mg
T
=
(36 kg)(15.34 m/s)2 (20 m)
+
mv
2
=
R
T
=
mv
2
R
+
mg
(36 kg)(9.8 m/s2 )
#
m
1
F
(2 ton)(2000 lb/ton) =
=
32 ft/s 2 Gm1m2 R
F
=
Gm1m2 R
2
=
2
;
(6.67 =
R
=
125 slugs;
Gm1m2
m
2
(3 ton)(2000 lb/ton) =
=
187.5 slugs
(3.44 x 10-8 lb ft 2 /slug 2 )(125 slug)(187.5 slug) =
0.0004 lb
F
!
32 ft/s 2
10-11 N m2 /kg 2 )(4 kg)(2 kg) 0.08 m #
F 3
F 6
=
=
Gm3 m2 R
2
Gm6 m2 R
2
(6.67 x 10-11 N m2 /kg2 )(3 kg)(2 kg) =
(0.05 m)2 (6.67 x 10-11 N m2 /kg2 )(6 kg)(2 kg)
=
(0.05 m)2
#
#
#
# #
mg
Gmm p =
R 2
;
m p
gR 2 =
(5.00 m/s2 )(4560 m)2 =
G
6.67 x 10-11 N m2 / kg2 #
mg m g m g e
=
Gmmm Rm2 2
=
mm Re
2
me Rm
=
y g m =
Gmm
mm (4 Rm )
81mm Rm2
Rm2 2
mge
=
g m
9.8 m/s
2
Gmme Re2 =
y g e =
0.1975
Gme Re2
Gm2 m '
(10 ! x)
2
=
x
Gm6 m ' x
2
60 kg
(10 ! x)
6
2
m
(10 ! x)
m =
x
=
20 kg
m
2
=
2
6
=
m
2
1.732
#
mv
2
Gmme =
R
v
(6.67
!
R
2
v
;
#
Gme =
R
10-11 N m2 / kg2 )(5.98
=
#
!
1024 kg)
7.18 x 106 m
#
# #
#
#
#
mv
v
=
R + h
=
(6.67
!
10-11 )(1.9
1.315
!
!
1027 kg)
108 m
Gmme =
R
Gme
2
R
2
;
#
mv
2
Gmme =
R
v
(6.67
!
R
2
v
;
#
Gme =
R
10-11 Nm2 /kg2 )(5.98
=
7.58
!
#
!
1024 kg)
106 m
#
mg
Gmmm
=
2
Rm
2
;
mm
=
gRm
(1.63 m/s2 )(1.74 x 106 m)2 =
6.67 x 10-11 N m2 /kg2
G
#
#
#
#
T
2
T
=
" 4! 2 # 3 % &R Gm e ( ' 3.82
=
!
4! 2 (7.28 $ 106 ) 3 =
7
10
-11
2
T
R
=
" 4! 2 # 3 % &R ; Gm e ( '
3 =
1.03
!
s
R
23
24
(6.67 $ 10 N m /kg )(5.98 $ 10 kg)
;
2
T
= 3.82 $ 107 s 2
2
#
2
2
GmeT
3
=
3
10 m
4! 2
# 2
(6.67 $ 10 -11Nm 2 /kg 2 )(5.98 $ 10 24kg)(1.02 $ 1010s 2) =
4! 2 #
#
ac
T
=
=
ac
2
2
4! f R;
mac
v
=
2
=
=
(12 ft/s2 )
ac 2
4! R
=
2
4! (3 ft)
; f
=
0.1013 s -2
! 6 lb " 2 # 32 ft/s 2 $ (12 ft/s ) % &
(15 m/s) 2 =
R
f
2
(0.300 m)
#
mv
2
Gmme =
R
v
R
2
(6.67 =
!
;
v
Gme
R
=
R
=
10-11 N m2 / kg2 )(5.98 8.047
!
6
10 m
2.64
!
#
7
! 0.3048 m " % & 1 ft '
10 ft $
1024 kg)
=
8.047
#
6
10 m
T
+
vc
mg =
=
gR
mv
2
R =
(9.8 m/s2 )(2.0 m)
T
T
(4 kg)(10 m/s) 2 =
(1.4 m)
+
mg =
T
f
=
(1.4 m)
1 =
2!
g h
1 =
2!
2
R
T
mv =
R
2
! mg
! (4 kg)(9.8 m/s 2 )
T ! mg
(4 kg)(10 m/s) 2
mv
+
mv
2
=
R
T
=
mv R
2
+
mg
(4 kg)(9.8 m/s2 )
9.8 m/s
2
0.125 m
!
vc
=
gR
=
(9.8 m/s2 )(6.0 m)
N + mg =
N
(210 kg)(12 m/s)2 =
(6 m)
mv
2
N
R
mv =
R
2
! mg
! (210 kg)(9.8 m/s2 ) N
tan !
tan !
v
2
=
gR
;
v
=
gR tan !
v
2
=
(66 ft/s) 2 =
gR
(9.8 m/s2 )(200 ft)
;
2
Fc
f
f 2
=
F c
2
2
4! R
=
=
µ s mg
2
0.557 rev/s;
2
4! (0.557 rev/s)
50 rev
=
35 s
µ s g
4!
2
R
F
2
4! f 2 mR2
(0.6)(9.8 m/s 2 )
=
=
4! (0.12 m)
=
2
=
f
2
1.114 rev/s =
2
4! f mR
(0.6)(9.8 m/s2 )
µ s g
=
R2
f
2
4! f mR; F s =µ s mg ;
=
2
1.429 rev/s
Fc
=
4!
2
f 2 mR
4! 2 (1.429 rev/s) 2 (0.4 kg)(0.14 m)
=
µ s mg ;
R2
=
µ s g 2
2
4! f 2
F c
mv =
R
2 mv 1 1
=
2
;
2 m v 2 2
;
2 v 2
2 1 1
mv =
=
m
2
v
2
(400 g)v12
=
(500 g)
=
(400 g)v12 (500 g)
0.894 v1
mv
2
1 1
F c
R2
=
4! 2 (1.3 rev/s) 2 (0.000625 slug)(0.333 ft)
(4 in) =
2
=
2 in
=
m v 2
2
2
#
#
#
g j
Gm j =
tan !
(6.67
!
=
2
v
10-11N m 2 /kg 2 )(1.914 (7.018
R j
mg j
#
!
!
Gmm j =
R j2
10 27kg)
10 7 m)2
2
=
gR
; v
=
gR tan !
f
T
cos !
(1.19 m/s)
v =
2! R
=
2! (0.25 m)
(2 kg)(9.8 m/s2 )
mg =
(9.8 m/s 2 )(0.25 m) tan(30 0 )
=
=
cos 300
!
F vc
=
µ s gR
=
(0.4)(9.8 m/s2 )(86 m)
F
F F
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