ACTIVIDAD ENTREGABLE N° 3 NOMBRE: Semblantes Ponce Daniel Alejandro EJERCICIO N° 24 1.- Un piloto !"#$i%! &n' t$'(!#to$i' #i$#&l'$ ! $'io R !n &n pl'no )!$ti#'l #on &n' $'pi!* #on"t'nt! ). ). El piloto ti!n!n &n' +'"' + ( ll!)' &n' %,"#&l' !n !l '"i!nto ' /#&,nto +'$#'$, l' %,"#&l' !n lo" p&nto" +," 'lto ( +," %'0o ! l' t$'(!#to$i' % /& )!lo#i' !%!$, ll!)'$ !l piloto p'$' &! l' %,"#&l' +'$&! #!$o !n !l p&nto +," 'lto # /& )!lo#i' !%!$, ll!)'$ !l piloto ( !n & po"i#i5n p'$' !6p!$i+!nt'$ in7$')i!* Ec + ep=0 1 2
2
m v + m∗g∗h= 0
'
∑ Fy =m∗a 2
m∗ v N − W = R 2
v N = m + m∗g R
∑ Fy =m∗a 2
v N = m ∗m∗g R 2
v N = m ( − g ) R
2
v N = m ( + g ) R
# 8'$' &! 9'(' in7$')i!* !%! !"t'$ !n "& p&nto +," 'lto. 2
v N = m ( + g ) R 2
v = g R V = √ gR gR
2.- L' #'$7' ! +'"' + &! )' ' "!$ t$'n"po$t'' !n &n %&&! "! %'l'n#!' !n &n #'%l! ! '#!$o ' +'n!$' ! &n pn&lo "i+pl!. L' &!$*' ! $!"i"t!n#i' ' l' $ot&$' !l #'%l! !" !&i)'l!nt! 'l o%l! !l p!"o ' l' #'$7'. /C&,l "!$, !l +'(o$ ,n7&lo &! p&!! o$+'$ l' #&!$' #on l' )!$ti#'l "in $o+p!$"!
∑ Fy =0
1 Tcosθ − P= 0
2 T =2 P θ
;2 !n ;1 2 Pcosθ
= P
cosθ =
1 2
θ= 60 °
8 3.- Un o%0!to ! 2 <7. D! +'"' p'$t! !l $!po"o !n l' po"i#i5n ;1 ( !"li*' "o%$! l' "&p!$=#i! li"' 9'"t' l' po"i#i5n ;2 #ontin&'no "& +o)i+i!nto 9'"t' l' po"i#i5n ;3 on! =n'l+!nt! &!' !n $!po"o. D!"! ;2 9'"t' ;3 l' p'$t>#&l' "! +&!)! "o%$! &n' "&p!$=#i! 9o$i*ont'l &! ti!n! &n #o!=#i!nt! ! $i##i5n U# ? @.@. i ( ? + !t!$+in! !l )'lo$ ! l' i"t'n#i' 6.
1
p
2
3 x=?
D'to" M =2 kg Fr =0.80
R!"ol&#i5n E1= E 2 1
E1=U =mgy 1
E2= E C = m v 2
mgy = m v 2
2
v =√ 2 gy
2
v =√ 2 ( 10)( 5 ) v =10 m / s
∑ Fy =0
E2= E 3 E2= E C
−mg+ N =0
E3=W FNC
fr = μmg = 0.8 ( 2 ) ( 10 )=16 N
1 2
1 2
2
m v =fr∗ x
2
( 2 ) (10 ) =16 x
X =6.25 m
4.- Un #&!$po ! <7 ! +'"' "! !"li*' "o%$! &n' +ont'' $&"' ! o$+' &! l' &!$*' !0!$#i' po$ l' "&p!$=#i! "o%$! !l #&!$po !" "i!+p$! p!$p!ni#&l'$ ' l' "&p!$=#i! ( ' l' i$!##i5n !l +o)i+i!nto !l #&!$po. D!t!$+in'$ !l t$'%'0o $!'li*'o po$ !l #'+po 7$')it'#ion'l "o%$! !l #&!$po #&'no "t! "! !n#&!nt$' ' l'" po"i#ion!" ;2 ( ;3 /C&,nto #o+p$i+i$, + 'l $!"o$t! "i l' #on"t'nt! !l,"ti#' < !l $!"o$t! !" 1@@ N+ To'" l'" "&p!$=#i!" #'$!#!n ! $i##i5n. 1
2 3 +
D'to" m =5 kg
R!"ol&#i5n
1@+
y 1 =10 m
ω 1− ω 2= Eg 1− Eg 2
y 2 =5 m ω 1− ω 2=( m∗g∗ y 1 )−( m∗g∗ y 2 ) y 3 =1 m ω 1− ω 2=( 5∗9.8∗10 )−( 5∗9.8∗5 ) T 2=2
ω 1− ω 2=245
! =1500 N / m μ=0
ω 2− ω 3=( m ∗g∗ y 2 )−( m ∗g∗ y 3 )
ω 2− ω 3=( 5∗9.8∗5 ) −( 5∗9.8∗1 ) ω 2− ω 3=196
Eω" =( ω 1− ω 2 )+( ω 2 −ω 3 ) Eω" =245 + 196 E ω" = 441
1
T = ! x
2
2
x =√ 2∗44 4 / 1500 x =0.8 m
.- Un o%0!to ! <7 ! +'"' "! !"pl'*' !n #ont$' ! &n' &!$*' &! "! $!"i"t! ' "& +o)i+i!nto ! t'l +'n!$' &! #$!#!
lin!'l+!nt! ' $'*5n ! 1@ nFton!" po$ #'' 2 +!t$o" &! l' +'"' "! +&!)!. i l' &!$*' #$!#! !"! #!$o ' /C&,l !" !l +o!lo +'t!+,ti#o ! l' &!$*' % G$'=&! l' &n#i5n !n#ont$'' !n !l in#i"o 'nt!$io$ # /C&,nt' !n!$7>' #inti#' "! pi!$! !n l' i"t'n#i' ! o" +!t$o"
10 N # 2 m
'
%
F # x
F(N)
F =kx
20 10
= k (2 )
10
k =5
2
F =5 x
0
4 x(m)
1
# Ec per$%$a = 2 ( 2− 0 ) ( 10 ) Ec per$%$a = 10
.- En !l H$i*o ! l' +&!$t! &! "! +&!"t$' !n l' =7&$' /C&,l !" !l )'lo$ ! !n t$+ino" ! R p'$' &! l' p'$t>#&l' + #o+pl!t! !6'#t'+!nt! !l $i*o ;"in !"p!7'$"! ! l' pi"t' Con"i!$! !l #'"o i!'l on! to'" l'" "&p!$=#i!" "on li"'" /K& o#&$$i$, "i 2.R /( "i 2.R
v &= 0
A B R
B E ' = E & E ' =mg(
2R
1
2
E& = m v & + mg ( 2 R ) 2
1
2
mg( = v & + 2 mgR 2
1
g( = gR + 2 gR 2
1
( = R + 2 R 2
( =2.5 R
Rpt': ' "i 2.R l' p'$t>#&l' #o+pl!t' l' t$'(!#to$i'. % "i 2.R l' p'$t>#&l' no #o+pl!t' l' t$'(!#to$i'.
.- Un o%0!to ! @.3 <7 &! )i'0' #on )!lo#i' 9o$i*ont'l "! in#$&"t' !n l' +'"' ! 1 <7 ! &n pn&lo i!'l ! 1 + ! lon7it& !n $!po"o. T$'" !l #9o&! !l pn&lo ( !l o%0!to "! +&!)!n #on )!lo#i' 9o$i*ont'l ! 2.14 +" ' 9'"t' &! ' lt&$' '"#i!n! !l "i"t!+' % !n "& )i'0! ! $!7$!"o #&'l !" l' t!n"i5n !n l' #&!$' !n !l p&nto +," %'0o ! "& t$'(!#to$i'. 1
2
3
4
T
=0 m2
!≠0
m1
E2
E3
D'to" T
m1
y
m1
+'C m DCL ;4
= 2"14 m#s m1 = 0"$ %& m2 = 1' %&
? m&
∑ Fy =m a
E2= E 3
c
1
E2= Ec = m v 2
2
T −mg =m ac
E3= mgy 1 2
T =m ( g + a c ) 2
2
m v =mgy
ac =
( 2.14 ) 1
= 4.6 m / s
2
2
( 2.14 ) v = y = 2g 2 ( 10 )
T =15.3 ( 10 + 4.6 )
y =0.23 m
T =220 N
2
.- L' p'$t>#&l' + p'$t! !l $!po"o !n l' po"i#i5n A ( "i7&! l' t$'(!#to$i' "in&o"' "in $i##i5n &! +&!"t$' l' =7&$' 33 /L' p'$t>#&l' + "! !"p$!n! ! l' pi"t' !n l' po"i#i5n C o #ontin&'$, ' lo l'$7o ! l' t$'(!#to$i' /K& +'$#'$>' &n' %'l'n*' ! $!"o$t!" ;%,"#&l' #&'no + p'"! po$ l'" po"i#ion!" B ( C Lo" p&nto" B ( C "on p'$t! ! "!+i#i$#&n!$!n#i'" ! $'io" 1@ + ( 4@ + $!"p!#ti)'+!nt!
A
+ C c≠0
R?1@@+ R?4@+
R?1@+ RB?1@+
)
RC?4@+ B E ' = EC
;C
E ' =mg R ' 1
2
EC = mgRC + m v c 2
1
2
mgR ' =mgR C + mv c 2
No E6i"t!
NC?@
R
¿
' −¿ R C 2 g¿
∑ Fy =m a
v C =√ 2 ( 10 )( 100 −40 )
N − mg =m ac
v C =34.64 m / s
N = m ( g + ac )
C
¿
2
v ac = r E ' = E &
N = m ( 10 + 220 ) 1
2
mgR ' =mgR & + m v &
N =23 mg
2
R
¿
' −¿ R & 2g ¿
¿
v &=√ 2 (10 ) [ 100 −( −10 ) ]
v &= 46.9 m/ s
.- Un #&$"o$ ! 2 <7 ! +'"' +ont'o "o%$! &n' %'$$' li"' ( &nio ' &n p&nto =0o C +!i'nt! &n $!"o$t! ! P?2@@ N+ ( 2 + ! lon7it&. Un' &!$*' !6t!$n' #on"t'nt! Q ? L i '#t' !n !l #&$"o$ ( l! #o+&ni#' !n A &n' )!lo#i' ! +". E"t! "! !"pl'*' "o%$! l' %'$$' "in $o*'+i!nto 9'"t' !l p&nto B !n on! "! !ti!n!. D!t!$+in'$ l' lon7it& &! $!#o$$! !l #&$"o$.
A
L
D'to" B
m = 2 %& = 200 N#m *0 = 2 m
2+
a = ' m#s F = '#* i
C
EC = E PE 1 2
L
1
2
mv = kx
2
2
2
x =v
x =5
√
√
m k
2
2.
2 200
1
x = = 0.5 m 2
) =) o + x ) =2 + 0.5 =2.5 m *=√ ( 2.5 ) −( 2 ) 2
2
*=√ 2.25 *=1.5 m
[email protected] L' 7$,=#' ! l' =7&$' 3 +&!"t$' #5+o )'$>' l' &!$*' &! '#t' "o%$! &n #&!$po ! +'"' 2 <7 !n &n#i5n ! "& po"i#i5n. D!t!$+in'$: ' El t$'%'0o $!'li*'o po$ l' &!$*' #&'no !l #&!$po !"t, !n l' po"i#i5n 2@ + % !l t$'%'0o $!'li*'o po$ l' &!$*' 'l p'"'$ !l #&!$po !"! l' po"i#i5n 6?3@ + # l' )!lo#i' !l #&!$po 'l p'"'$ po$ l' po"i#i5n 6?3@ + "i p'$ti5 !l $!po"o l' po"i#i5n !nt$! @ ( 3@ + on! !l #&!$po 'l#'n*' l' +,6i+' )!lo#i' ! "i !n 6?@ + l' )!lo#i' !$' ! 2 +" $!p$!"!nt'$ 7$,=#'+!nt! l' )'$i'#i5n ! l' !n!$7>' #inti#' E # !l #&!$po !n t$+ino" ! l' po"i#i5n '0 6 !n !l int!$)'lo ;@3@ +!t$o". El #&!$po "! +&!)! "i!+p$! !n &n pl'no 9o$i*ont'l.
20
$0
'
T Fo− 20=+ F ∗ + x T Fo− 20 =(50 )( 20 ) T Fo− 20=1000
%
+ F ∗ + x
T 20− 30=
T 20− 30=
2
( 50 )( 30 −20 ) 2
T 20−30=250
#
T Fo−30=+ EC T Fo−30+ T F 20−30= EC − EC 30
Donde
0
1
T Fo− 30+ T F 20− 30= ∗m∗v 30 2
v 30=
√
v 30=
√
2
( T Fo− + T F
)
m
(
2 1000
+ 250 )
2
v 30=25 √ 2
20 −30
20
2
m , 35.36 m / s s
T Fo− 20=+ E C T Fo−20= EC
− E C
20
T Fo−20=
v 20=
√
2
1 2
∗m∗v
20
( T Fo− ) 20
m
Donde EC = 0 o
0
2
E C = 0 0
v 20=
√
(
2 1000
)
2
v 20=10 √ 10
m , 31.62 m / s s
- v 30 > v ∈( v 0 . v 30 ) ∴ E) c/erpoa)ca01a s/ mayor rap%$e1e2 x
=30 m
