I.E.P. “DOSCIENTAS MILLAS PERUANAS”
VII. TRABAJO MECÁNICO (CONTINUACIÓN)
4. POTENCIA 4.1. CONCEPTO
E! (' t,% ,('/+% (* + &*/++ +( t/(3%. P = W t
P = F .V
4.2. UNIDADES SI Wtt! "W# = $%&'( S()&*+%
4.3. OTRAS UNIDADES UNIDADES DE POTENCIA 1 4/'%5tt
= 1 4W = 10 6 W
1 M() 5tt
= 1 MW = 10 7 W
1 C''% +( F&(,
= 1 %,!( P%5(, = 1 P = 9:; W
1 C''% C''% V3%, V3%,
= 1 C.V. C.V. = 96; W
PROBLEMAS RESUELTOS 1#.- U* &t% 3%, /?* +( &* @&(, @&(, +( :; N. D(t(, D(t(,/* /* !& 3%t(*/ Solució! P = F . V = :; . 2: = 1080 Wtt! 2#.- C'&' ' 3%t(*/ +( &* %t%, B&( ,(' ,('/ / &* t, t, % % +( :;00 :;00 $%&' $%&'( ( +&,*t( 600 !()&*+%!. Solució! P = Wt P = :;00600 = 1; Wtt!
FÍSICA
6#.- C&' (! ' 3%t(*/ 3%t(*/ +( &* %t%, B&( (@(t (@(t &* t,% t,% +( 180 000 $%&'( (* 20 /*&t%! Solució! P = 180 000 20 70
# :; 45 +# 8; 45
P = 1;0 Wtt!. :#.:#.- U* &t%
1.- C&' (! ' 3%t(*/ +( &* %t%, B&( (@(t &* t,% +( ;: 000 $%&'( (* 0.2; G%,! # ;: W (# 9; 5
# 70 W
2.- U* &t%?
# 2: 45 (# 12 45
# 10 45
6.- C&' (! ' 3%t(*/ +( &* %t%, B&( (@(t (@(t &* t,% t,% +( ;: 000 $ (* &* G%,. #1; W +# :; W
# 1: W (# 2; 5
# 10 W
:.-U* :.-U* &t% &t% ''(< ''(< &* <('%/+ <('%/++ + +( H0 4G. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 700 N. #1; 45 +# ;; 45
# 1: 45 (# 2;00 W
# 7; 45 (# 80 45
# 70 45
7.- C&' (! ' 3%t(*/ +( &* %t%, B&( (@(t &* t,% +( 67 4 $%&'( (* 2; /*&t%! #6; W +# ;; W
# 2: W (# 9; 5
# 70 W
9.- U* &t%?
PRÁCTICA DIRI"IDA N# 1$
#1; W +# ;; W
;.- U* &t%
# 60 45
#1; 45 +# 6; 45
# 2: 45 (# 12 45
# 10 45
8.- C&' (! ' 3%t(*/ +( &* %t%, B&( (@(t &* t,% t,% +( 67000 $ (* (+/ G%,. # 20 W # 60 W # 10 W +# 18 W (# 2; 5 H.- U* &t% ''(< &* <('%/++ <('%/++ +( :; !. C& C&'' (! ' 3%t( 3%t(* */ / +( !& %t% %t%,, !/ +(!,,%'' &* @&(, +( 700 N. # 1; 45 +# ;; 45
# 1: 45 (# 18 45
# 29 45
10.- U* &t%
# 7; 45 (# 80 45
# 29 45
11.- L 3%t(*/ +( &* B&/* (! 2>: P. P. (3,(! +/G 3%t(*/ (* Wtt!. # 6:; W # 1988 W # 1070 W +# 18;; W (# 199; W 12.12.- L 3%t(*/ 3%t(*/ +( &* %t%, %t%, (! 170 Wtt Wtt!> !> !/ ,('/ ,('/ &* t, t,% % +( 7:0 $%&'(!. '' (' t/(3% (3'(+%.
# 6 ! +# ; !
# 7 ! (# 8 !
# : !
16.- L 3%t(* 3%t(*/ / +( &* %t%, %t%, (! 6; Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 1:00 $%&'(!. '' (' t/(3% (3'(+%. # 60 ! +# 2; !
# 70 ! (# :8!
# :0 !
1:.1:.- L 3%t(*/ 3%t(*/ +( &* %t%, (! 600 Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( :;000 $%&'(!. '' (' t/(3% (3'(+%. # 1:6 ! +# 1;0 !
# 172 ! (# 280 !
# 1;: !
1;.1;.- L 3%t(*/ 3%t(*/ +( &* %t%, (! :;0 Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 18000 $%&'(!. '' (' t/(3% (3'(+%. # 60 ! +# 1; !
# 27! (# 28!
# :0 !
17.- U* &t% ''(< &* <('%/++ +( 29 4G. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 700 N. # 8>; 45 +# ;>; 45
# 1>: 45 (# 1>8 45
# :>; 45
19.- U* &t% ''(< &* <('%/++ +( 76 4G. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 700 N. # 10>; 10>; 45 +# ;>; 45
# 11>: 1>: 45 (# 18>H 45
#10 #10>8 >8 45
18.- U* &t% ''(< &* <('%/++ +( 20 !. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( :2;>; N. # 7>1 7>1; 45 +# 8>;1 45
# 7>:2 7>:2 45 (# :>2; 45
#2 #2>78 >78 45
I.E.P. “DOSCIENTAS MILLAS PERUANAS” 1H.- U* &t% ''(< ''(< &* <('%/++ +( ;8>; !. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 800 N. # 1;> 1;>H 45 +# ;; 45
# :7> :7>8 45 (# 18 45
# 29 45
20.- E' t,% B&( ,('/ &* % (! +( 790; $%&'(!> +&,*t( 7 !()&*+%!. C&' (! ' 3%t(*/ +( !& %t%, (* P # 1>; P +# 0.; P
# 1>: P (# 1.8 P
# 2>9 P
21.- L 3%t(*/ +( &* B&/* (! 6>: P. P. (3,(! +/G 3%t(*/ (* Wtt!. # 6:; W +# 18;; W
# 2;66 W (# 199; W
# 1070 W
22.22.- L 3%t(*/ 3%t(*/ +( &* %t%, %t%, (! 180 Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 1080 $%&'(!. '' (' t/(3% (3'(+%. # 6 ! +# ; !
# : ! (# 8 !
# 7 !
# 70 ! (# :8!
# ;0 !
2:.2:.- L 3%t(*/ 3%t(*/ +( &* %t%, %t%, (! :00 Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 7:000 $%&'(!. '' (' t/(3% (3'(+%. # 1:6 ! +# 170 !
# 172 ! (# 280 !
# 1;: !
2;.2;.- L 3%t(*/ 3%t(*/ +( &* %t%, %t%, (! :80 Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 2:000 $%&'(!. '' (' t/(3% (3'(+%. # 60 ! +# 1; !
# 27! (# 28!
27.- U* &t% ''(< &* <('%/++ +( ;: 4G. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 800 N # 8; 45 +# ;; 45
# ;0 !
# 1: 45 (# 18 45
# :6>2 45
29.- U* &t% ''(< &* <('%/++ +( 81 4G. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 900 N. # 1;>9 1;>9; ; 45 +# ;>; 45
# 11>: 1>: 45 (# 18>H 45
#10 #10>8 >8 45
28.- U* &t% ''(< &* <('%/++ +( 60 !. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( 72;>; N.
PROBLEMAS RESUELTOS
VIII. ENER"%A 1.
CONCEPTO
E!t& E!t&+/ +/, ,( (%! %! '%! '%! t/3% t/3%!! +( (*(, (*(,) ) (*/ B&( )%/(,** '%! &(,3%! +(3(*+/(*+% +( ' 3%!//?* (* B&( !( (!t* (!t&+/*+%> (! +(/, t%*+% (* &(*t &* */<(' +( ,(@(,(*/.
2.
TIPOS DE ENER"%A MECÁNICA
&'. ENER"%A CIN)TICA (E*' E! B&('' (*(,) B&( 3%!((* '%! &(,3%! (* %
1#.1#.- S/ &* 3('%t 3('%t (! '*+ '*+ %* &* ,3/+( ,3/+( +( 10!. C'&' !& (*(,) (*(,) /*t/ !/(*+% !& ! =2J). Solució ! S(%! B&( V=10!
#12> #12>78 78 45
D%*+(
2H.- U* &t% ''(< &* <('%/++ +( 78>; !. C&' (! ' 3%t(*/ +( !& %t%, !/ +(!,,%'' &* @&(, +( H00 N. # 90> 90>7; 45 (# 18 45
# 29 45
60.- E' t,% B&( ,('/ &* % (! +( 1119; 1119; $%&'(!> +&,*t( ; !()&*+%!. C&' (! ' 3%t(*/ +( !& %t%, (* P # 6 P +# : P
# : P (# 8 P
EJ = K V 2
UNIDAD "S.I# = ! EJ $%&'(! "$# V = ,3/+( +'. ENER"%A POTENCIAL (E,' E! B&('' (*(,) B&( 3%!((* '%! &(,3%! &*+% !( (*&(*t,* &* /(,t 't&, +(' */<(' +( ,(@(,(*/. "N.R# R(!3(t% t/(,,
# 9 P
EJ =
D%*+(
2# (
6#
:#
;# (
7#
9# (
8#
H#
10#
11#
12#
16#
1:#+
1;#
17#
19#
18#+
1H#
20#
21#
22#
26#
2:#+
2;#
27#
29#
28#+
2H#
60#
"2#"10#2 = 100J
2#.- S/ &* (t !( (*&(*t, ; +(' !&('%> !&('%> '&' '&' !& (*(,) (*(,) 3%t(* 3%t(*/' /' ,(!3(t% ' !&('% !/ !& ! (! +( 2J). 2 ")=10! #. Solució ! S(%! B&( ;
)
= ! +(' &(,3%"J)# = 't&, "# ) = ('(,/?* (,/?* +( ' ),<(++ T/(,, "N.R#
E3 = )G
T/(,, "N.R#
E3 = )
)
CLAVES DE RESPUESTAS 1#
1 2
V0=0
EJ = K V 2
L&()%
V
# 17>1 17>1; ; 45 # 17>: 17>:2 2 45 +# 18>9 18>97; 7; 45 (# 1:>2 1:>2; ; 45 45
# 1;> 1;>H 45 +# ;; 45
26.- L 3%t(* 3%t(*/ / +( &* %t%, %t%, (! ;; Wtt!> Wtt!> !/ ,('/ ,('/ &* t,% t,% +( 29;0 $%&'(!. '' (' t/(3% (3'(+%. # 60 ! +# 2; !
FÍSICA
) = 10! 2
OBSERVACI-NOBSERVACI-N - L (*(,) (*(,) (*/ (*/ (! ' !& +( ' (*(,) (*(,) /*t/ ! ' (*(,) 3%t(*/'.
EM EC / EP
L&()% E3) = 2 10 ; E p = 100J
6#.- S/ &* 3,t/+ 3,t/+% % +( @t%' @t%' &* &)+%, &)+%, '* &* ,(t( ' ,% %* &* ,3/+( +( 20!. S/ ' ! +(' '?* (! +( ;00),. ;00),. C'&' C'&' !& (*(,) (*(,) /*t/ /*t/ (* (!( /*!t*t(. Solució ! V = 20!
S(%!
I.E.P. “DOSCIENTAS MILLAS PERUANAS” EJ =
1
FÍSICA
V2
EJ =
= ;00), 2 P(,% P(,% ' ! ! “” “” +(( +(( (!t (!t, , (3,(!+ (* J)> (*t%*(!
1 2
V2 ..."1#
/# C'&'% +( V
1J) =;00), . = 0>;), 1000),
# 2;$ +# 70$
V@ = = V/ ).t V = 0 10 2
R((3'*+% (* "1# 1
EJ =
2 1
EJ =
V = 20!
"0>;# "20#2 ."
2
1 2
E* "1#
# ":00#
:#.- U* 3/(+, (! '*+ G/ ,,/ +(!+( t/(,,> !/ *t(! +( /*//, (' ,(t%,*% ,(%,,/? &* 't&, +( 10. C'&' !& (*(,) 3%t(*/' ,(!3(t% t/(,, !/ !& ! (! +( 1J). ")=10! 2# Solució ! S(%! B&( E3 = ) E3 = 1 10 10
)
10
E pB = 100J
V/ "N.R#
;#.- S/ &* 3('%t 3('%t (! !%'t+ !%'t+ +(!+( /(,t 't&,. C'&' !& (*(,) /*t/ '&()% +( 2! +( + '/,( !/ !& ! (! +( 2J) ")=10!2#. Solució ! V/=0
A
) 2!
1 "2# "202#2 2
E K KB = 400J
PRÁCTICA DIRI"IDA N# 11
E = 100J
V@ =0
EJ=
N%! 3/+(*
1#.- C'&' ' (*(,) /*t/ +(' '%B&( +( 1J) !/ !& ,3/+( (! +( :!. # :$ +# 10$
# 7$ (# 12$
# 80$ (# 170$
# 100$
6#.6#.- S/ &* 3('%t 3('%t (! '*+ '*+ %* &* ,3/+( ,3/+( +( 7!. 7!. C'&' C'&' !& (*(,) (*(,) /*t/ !/ !& ! (! /)&' 2J). # 7$ +# 2:$
# 12$ (# 67$
# 18$
:#.:#.- S/ &* (t (t !( (*&(* (*&(*t, t, (* ' %t( +( &* (+/@//%> '&' !& (*(,) 3%t(* 3%t(*/' /' !/ !( (*&(* (*&(*t, t, 10 10 +( 't&, Q !& ! (! /)&' (+/% J/'%. ")=10!2# # ;0$ +# 120$
# 9;$ (# 1;0$
# 6;$ (# ;0$
7#.- S/ &* 3('%t +( t(*%3%, (! !%!t(*/+ 3%, 3%, &* G/'% G/'% +( &* t(G t(G% % (' &' &' !( (*&(*t, 20 +( 't&,> !/ ' 3('%t/t t/(*( &* ! +( 0>2J). C'&' !& (*(,) 3%t(*/'. ")=10! 2# # 20$ +# ;0$
# 60$ (# 70$
# :0$
9#.- S/ &* (!,/t%,/% (! (3&+% %* &* ,3/+( ,3/+( +( ;!. ;!. C'&' C'&' !& (*(,) (*(,) /*t/ !/ !& ! (! /)&' 20J). # 2;$ +# 200$
# 12;$ (# 2;0$
# 17;$
# 100$
8#.- S/ &* 3('%t (! '*+% G/ ,,/ %* 10!. C'&' !& (*(,) /*t/ !/ !& ! (! /)&' 0>1 J). # ;0$ +# 10$
# 2;$ (# ;$
# 20$
# 10$ (# 2>;$
# 1;$
# ;0$ # 9;$ # 100$ +# 12;$ (# 1;0$
7!
A
) =;
12#.- C'&' ' (*(,) (*/ +( ' 3('%t/t +( ! 100), (* (' /*!t*t( %!t,+%. ")=10! 2# +(!+( t/(,,. :!
# 20$ # 28$ # 8$ +# 60$ (# 2:$
1J) =2
t/(,,
16#.- S/ &* &+(,*% +( 0>1J) (! !%'t+% +(!+( +(!+( &* 't&, 't&, +( ;. C'&' C'&' !& (*(,) 3%t(*/' (* (!( /*!t*t(
# :$
1:#.- D%! &t%! 3%!((* ! +( 2J) Q :J) Q !&! ,3/+((! !%* +( :! Q 2! ,(!3( ,(!3(t/< t/<( (*t( *t(.. C'&' C'&' ' (*(,) (*(,) /*t/ +(' 3,/(, &t%. # 12$ (# 2:$
# 17$
1;#.1;#.- C%* '%! +t%! +(' 3,%. *t(,/ *t(,/%, %, '&' ' (*(,) /*t/ +(' (*%,. # 7$ +# 17$
2!
0
t/(,,
# 8$ +# 18$
10#. 10#.-- E* ' @/)& @/)&, , ' '&' &' ' (*(, (*(,) ) /*t/ +(' '%B&( +( 1J) (* '%! 3&*t%! A” Q “”. # 2$ 18$ # 2$ H$ # 1$ H$ +# 2$ 67$
11#.- C'&' ' EP) +(' '%B&( ,(!3(t% ' t/(,,. ")=10!2# =2J)
# 2>;$ +# ;$
H#.- C%* '%! +t%! +(' 3,%'( *t(,/%,> '&' ' (*(,) 3%t(*/' !/ '* &* 't&, +( 2. ")=10! 2# # 2$ +# ;$
(# N.A.
# :;$
# 8$
2#.- S/ &* 3('%t !( (*&(*t, 10. D( 't&,. C'&' !& (*(,) 3%t(*/' !/ !& ! (! +( 1J). ")=10! 2# # ;0$ +# 10$
;#.- U* 3('%t +( 3/*)-3%*) (! '*+% %* &* ,3/+( +( 60!. C'&' !& (*(,) /*t/ !/ !& ! (! /)&' 1J).
# 8$ (# 18$
# 12$
17#.- D%! D%! 3('%t! 3('%t! +( 0>1J) 0>1J) Q 0>2J) !%* !%'t+%! +(!+( 't&,! +( 20 Q 10
I.E.P. “DOSCIENTAS MILLAS PERUANAS” ,(!3(t/< ,(!3(t/<(*t(. (*t(. &/(* &/(* t(*+, t(*+, Q%, (*(,) 3%t(*/'. ")=10! 2# # L L 3,/ 3,/(, (, # A!
# L L !()& !()&*+ *+ +# F F't* + +t%!
(# N. N.A.
19#.- S/ +%! ?;J) 3%!((* ,3/+((! +( :! Q : 2 . &/(* &/(* t(*+, t(*+, Q%, Q%, (*(,) (*(,) /*t/. # +# F.D
# A Q (# N.A.
# A
18#.- S/ &* !/'' +( 1J) (! !%'t+% +(!+( &* 't&, +( 10. C'&' !& (*(,) 3%t(* 3%t(*/' /' (* (!( /*!t* /*!t*t( t( ,(!3( ,(!3(t% t% t/(,,. ")=10!2# # ;0$ +# 2;$
# 9;$ (# 12;$
# 100$
1H#.1H#.- C%* '%! +t%! +t%! +(' 3,%. 3,%. *t(,/ *t(,/%, %,>> '&' !& (*(,) /*t/ &*+% ''() t/(,, !/ '% G( %* &* ,3/+( +( 8!. # 7:$ +# 17$
# :8$ (# 128$
# 62$
20#. 20#.-- E* ' @/)& @/)&, , ' '&' &' ' (*(, (*(,) ) (*/ (*/ +(' '%B&( '%B&( +( 2J) (* '%! 3&*t%! A Q ,(!3(t/<(*t(. 2! A
# :$ :0$ # 2$ 80$ # 8$ 120$ +# :$ 120$ (# :$ 8:$
)=10!2
=:
21#. 21#.-- S/ &* &t% &t% 3,t 3,t( ( +(' +(' ,(3% ,(3%!% !% ('(,*+% ('(,*+% %*!t*t( %*!t*t((*t( (*t( +( %+% B&( '&()% +( /(,t% t/(3% !& ,3/+( (! 10!. C'&' !& (*(,) /*t/ !/ !& ! (! +( 100J). # ;00$
# ;0$
# 1000$
FÍSICA
+# ;000$
(# 9;0$
22#.- S/ &* 3('%t (! /3&'!+ +(!+( (' ,(3%!% ('(,*+% %* 2! 2. C'&' !& (*(,) /*t/ '&()% +( ;! !/ !& ! (! 1J). # 100$ # ;0$ # 2;$ +# 12;$ (# 9;$ 26#.- S/ &* 3('%t ( +(!+( &* 't&, +( 80. C'&' C'&' !& (*(,) (*(,) 3%t(*/' ),-;J) (! '*+ G/ G/ ,,/ ,,/ '* '**+ *+% % &* 't&, 't&, / / +( 20. 20. C'&' C'&' !& (*(,) (*(,) 3%t(*/' 3%t(*/' ),
# 9;$ (# 2;$
# 100$
29#.- S/ &* (t (! !%'t+ +(!+( &* 't&, 't&, +( 100. L&()% L&()% +( :!> &' !(, !& (*(, (*(,) ) /* /*t/ t/ ")=1 ")=10 0! !2#. C%*!/+(, !& ! +( 0>;J). # 200$ +# 100$
# 600$ (# 800$
# :00$
28#.28#.- C%* '%! +t%! +(' 3,%. *t(,/%, *t(,/%, '&' '&' (* (!( /*!t* /*!t*t( t( !& (*(,) (*(,)
3%t(*/' 3%t(*/' ),
# 9;$ (# 2;0$
# 100$
2H#.- S/ &* ,% +( 20J) (!t 20 +( 't&, 't&,.. C'&' C'&' !& (*(,) (*(,) 3%t(* 3%t(*/' /' ),< ),
# 200$ (# :000$
# 800$
60#.- S/ &* )%'%*+,/* )%'%*+,/* !( (*&(*t, (*&(*t, 10 +( 't&, Q
# ;0$ (# ;:$
# 17$
61#.- E* (' /*!t*t( /*!t*t( %!t,+% %!t,+% '&' '&' ' (*(,) (*/ +(' '%B&( ,(!3(t% t/(,,. = 21),> 21),> =10 ")=10!2# # 100$ # 1;0$ # 200$ +# ;0$ (# 0$
# 2! # 6! # :! +# ;! (# 7! 6:#. 6:#.-- S/ ' E M (* (' /*!t*t( /*!t*t( %!t,+% %!t,+% ,(!3(t% t/(,, (! 262$. C'&' “”. =:J). V=7!. # 1 # 2 # 6 +# : (# ;
V t/(,,
6;#.6;#.- C%* '%! +t%! +t%! +(' 3,%. 3,%. *t(,/ *t(,/%, %,>> '&' ' E4 +(' ?
# 18$ (# H0$
# ;:$
)
t/(,,
62#. 62#.-- E* ' @/)& @/)&, , ' '&' &' ' (*(, (*(,) ) (*/ (*/ ,(!3( ,(!3(t% t% t/(,, t/(,,.. =;J)> =;J)> =2 V=:!. # 100$ # ;0$ # 90$ +# 1:0$ (# 200$
V
)
CLAVES DE RESPUESTAS
t/(,,
66#.- S/ ' E M +(' '%B&( +( 2J) +( ! V C'&' (* (!( /*!t*t( /*!t*t( (! 12;$. 12;$. C'&' V. ")=10!2# R(!3(t% t/(,,. ) ;
1#
2#
6# (
:#
;#
7#
9# (
8# (
H#
10#
11#
12#
16#+
1:#
1;#
17#
19#
18#
1H#
20#(
21#+
22#
26#+
2:#
2;#
I.E.P. “DOSCIENTAS MILLAS PERUANAS” 27#+
29#
28#
2H#(
60#
61#
62#+
66#+
6:#+
6;#+
FÍSICA
