FACULTAD DE INGENIERÍA GEOLÓGICA MINERA METALÚRGICA METALÚRGICA Y GEOGRÁFICA ESCUELA ACADEMICO PROFESIONAL DE INGENIERIA CIVIL
EJERCICIOS PROPUESTOS DE SÓLIDO RÍGIDO ASIGANTURA: DINÁMICA
DOCENTE: IVAN CONISLLA
ALUMNO: LAURENTE ROMERO PAUL MARTIN
1) El bloq! A"CD #! $!%! &! '(l $(!*( q! !l +'o " #,-! ( *!.'( %!*',.(l #ob*! l( +(*!&/ 0 A #! $!%! ( lo l(*-o &! ( *!.'( o*,2o'(l +!*+!&,.l(* ( l( +(*!&3 C(&o 45678 !l +'o A #! $!%! .o ( %!lo.,&(& &! 9$# (.,( l( ,2q,!*&( 0 .o ( (.!l!*(.,; &! 19$#9 (.,( l( &!*!.(3 D!'!*$,! l( %!lo.,&(& 0 (.!l!*(.,; &!l +'o E +(*( !#'( +o#,.,; &!l bloq! *!.'(-l(*3 9, $# <19, $#
*"A5 <13=9, > 1? $
@ VA5
*E"5 736, > o3B9? $
@ (A5
9
•
*EA5 <73, > 13B9? $
V"5 VA > A" *"A V" ?5 9, <13=6A" ? <A", 75 9 <A" A"5 9 *(&# V"5 <63B? $#
•
VE5 VA > AE *EA 5 V" > E" *E" 9, H73AE ? <13B9AE, 5 <63B? >736E" ? <73B9E", E"5 9 *(&# VE5 <139, <13B? $# AE5 9 *(&#
•
("5 (A > A" *"A > A" A" *"A) (" ?5 <19, <13=6A" ? HA", >B39, <? 75 <19 <A" >B39 A"5
•
(E5 (A > AE *EA > AE AE *EA) 5 (" > E" *E" > E" E" *E") <19, <73AE ? <13B9AE, >639, 736E" ? <73B9E", <63=9, <93? ,): <3 <13B9AE 5 <73B9E" <63=9 ?): <73AE 736E" E"5
9) &!'!*$,(* l( (.!l!*(.,; &! A #, ab =1.5 m / s 2 (.,( l( &!*!.( 0 l( %!lo.,&(& (-l(* &! AC !# &! 9 *(&# .o'*(*,( ( l(# $(!.,ll(# &!l *!lo? 0 &!.*!.! ( *(2; &! *(	
&('o# : a B=1.5 m / s
2
w AC = 2 rad / s 2
α AC =−4 rad / s
A+l,.($o# l( ;*$l( +(*( (ll(* l( (.!l!*(.,; a A =a⃗ B + α AB x r A / B + w AB x w AB x r A / B ⃗ a A =( 1.5 , 0 )− 4 k^ x ( 0.3 √ 2 ,− 0.3 √ 2 ) + 2 k^ x 2 k^ x ( 0.3 √ 2 ,− 0.3 √ 2 ) ⃗ a A =( 1.5 , 0 ) + (−1.2 √ 2 ,− 1.2 √ 2 )+ (−1.2 √ 2 , 1.2 √ 2 ) ⃗ a A =(−1.894 , 0 ) m / s ⃗
2
6) E l( +o#,.,; q! #! $!#'*( ! l( -*(/ l( b(**( A" ',!! !# o*,2o'(l 0 !l &,#.o ',!! ( %!lo.,&(& (-l(* .o#'('! .o'*(*,( ( l(# $(!.,ll(# &!l *!lo? &! 67 *( (ll(*: () L( %!lo.,&(& &! " b) L( (.!l!*(.,; &! "
W AB= 30 K ⃗
rad s
⃗ V =30 K × ( 0.3 , 0.3 √ 3) ⃗
A
V B =V A + W AB × r B / A
⃗
( V b , V b )=( −9 √ 3 , 9 ) +W K × ( 1.8 , 0 ) ⃗
W AB=13.657 K rad / s V B =(−15.548 , −15.548 ) m / s ⃗
(ll($o# l( (.!l!*(.,; r A /O W OA × ¿ a A =a O + α AB × r A / O + W OA × ¿
⃗
⃗
⃗
⃗
⃗ ⃗
⃗
30 K × ( 0.3 , 0.3 √ 3 ) a A= 0 + 30 K × ¿ ⃗
⃗
⃗
a A =(−270 ,− 270 √ 3 ) m / s
2
⃗
r B/ A
⃗
W AB × ¿ ⃗
⃗
a B=a A + α AB × r B / A + W AB × ¿ ⃗
⃗
⃗ ⃗
a B=(−270 , −270 √ 3 )+ α AB K × ( 1.8 , 0 )+ 13.657 K × (13.657 K × ( 1.8 , 0 ) ) ⃗
(a
B
⃗
⃗
⃗
, aB ) =(−270 −335.724 ,− 270 √ 3 +1.8 ∝)
a B=(−605.725 ,−605.725 ) m / s
2
⃗
) El *o&,llo ! C #! $!%! ! ( -( %!*',.(l3 El !#l(b; A" ',!! ( %!lo.,&(& (-l(*/ ! !l #!',&o &! l(# $(!.,ll(# &!l *!lo? &! 1 *(&#/ 0 ( (.!l!*(.,; (-l(* &! ,-(l #!',&o &! 139*(] (ll(* l( (.!l!*(.,; &!l *o&,llo3
w AB=−1 k rad / s ∝ AB
=−1.2 k rad / s2
v B= v A + wx r B / A v B=−1 kx ( 1.5 j ) v B=1.5 i
m s
v C =v B + wx r C / B
( 0, v C ) =1.5 i + wBC x ( 3.6 i −1.5 j ) ( 0, v C ) =( 1.5 + 1.5 w BC , 3.6 w BC ) rad w BC =−1 k s
v C =−3.6
m s
a B=a A + ∝ AB x r B / A + wx ( wx r B / A ) a B=1.8 i − 1.5 j
aC =aB + ∝BC x r C / B + wx ( wx r C / B )
( 0, aC ) =( 1.8,−1.5 ) +
¿
∝
BC
kx (3.6, −1.5 ) + (−1 k ) x (−1 k ) x ¿ 63B/<
13K)
( 0, aC ) =( 1.8 + 1.5 =1.2 rad / s
∝BC
2
∝
−3.6, 3.6
BC
∝
)
BC
aC =( 0,4.32 ) m/ s
2
K) E !l $!.(,#$o &! !#l(bo!# $o#'*(&o ! -*( NQ 7K/ !l +'o ',!! ( %!lo.,&(& &! =397 $# (.,( l( &!*!.( 0 !l !#l(b; A" ',!! (.!l!*(.,; (-l(* &! K *(&# 9 .o'*(*,( ( l(# $(!.,ll(# &!l *!lo?/ .(&o !l $!.(,#$o !#' ! l( +o#,.,; $o#'*(&(/ &!'!*$,(*: (3 L( %!lo.,&(& (-l(* &!l !#l(b; A" b3 L( (.!l!*(.,; &!l +'o C Sol.,;: Co$!2(*!$o# &!'!*$,(&o l( %!lo.,&(& (-l(* &! CD:
Vc =0 + ω CD × ( 0 i −1.2 j ) rad ωCD = 6 k s
Ao*( (ll(*!$o# A" 0 "C ! b(#! ( V": V B =7.2 i + ω BC k ×−2.7 i V B =7.2 i − 2.7 ωBC j V B =0 + ω AB k × ( 1.8 i + 2.4 j ) → V B = 1.8 ω AB j −2.4 ω AB i ∴ ω AB
rad rad ω BC =2 k s s
=−3 k
L!-o: a B=0 + 5 k × ( 1.8 i + 2.4 j )−3 k × ( −3 k × (1.8 i + 2.4 j ) ) a B=−28.2 i −12.6 j
m 2
s
F,(l$!'!: •
aC =0 + α CD k × ( 0 i −1.2 j ) + 6 k × ( 6 k × ( 0 i − 1.2 j )) aC =1.2 α CD i + 43.2 j
•
aC =−28.2 i −12.6 j − 2.7 α BC + 10.8 i
∴
rad rad α CD =−14.5 k 2 , α BC =−20.667 k 2 s s
aC =−17.4 i + 43.2 j
RPTA:
rad ω AB =−3 k s
m s
2
aC =−17.4 i + 43.2 j
m s
2
