Tippens Fisica 7e Soluciones 10

!

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