Constrained Motion of Connected Particles

4 One Degree of Freedom

XT a

X g b Thelength ofthe cableA ra

X 1274 zy 1242 bn ny r Y u try toy 1 TenthsYv v

L ra ri b constant

Bo x 2gO UAt2UB

0 54 2

O Aa12dB

IkoIZZ't 50kgd

50kg

EH EHIZZY 52211

BHooky

B Bcooky

2 Two Degree of Freedom

LA LA ya12yd1constant

dya O yia2y.io

a DYE in a O Efa1240a V YaYB YDLB LB YB yet c yo constantD

Yc A O y.BI2y.c y.ioa

dyaqO ijg 2jo ij

c26 2 3 4ge

O ga 12 3 4yc Ua12M 141 0

ijp igis 2geO ija 12 314g AA12dB1406 0

Example 2.15

A has a downwardvelocity of o 3msDetermine the velocity of B

A

YA L 2ya139 const

Yog V 0 29 3 3 Ja UA 0.3 v

O 2UAt3UB

UB 4gMA O.IMpA mm Ans

UH_0.3Mls

B

Example 216The tractorA is used to hoist73

with the pulley arrangement

A has a forward velocity UA

Determine an expressionfor upward VelocityUBXin terms of X

dhe

a tractoryV V B NAA

X

It 2Chyo il 2g s feted I dkdt dkdx.dkO XI 2g

L

f x4h dl1dx TxFH

UB y X VA I X dngdtf X4h d97thmmmm Ans X x

dxZhImn

mmmm

L SB 13Satconst

O UB13mA

i Ups 3NAAng

r

hM 1 2yts constant0 25 5Ans

be

A

L 3SA12SBtconst

o 3mA 2UBAnsf ne

H

f i

9 ul

D An

or

SB 1Sax constO UB 17UA

aa

Li XiF2y constte Xztkyzy.ptconst

r

p 1

9 251 0 y hiya

0 8212429.1 0

Xsty 1 12 0ya Xyz Ia Ana C

y

µµ I

f

e

M th

Mma