ENGR 3311: DYNAMICS SPRING 2018

NAME:

Exam 03: Chapters 16 and 17

INSTRUCTIONS • Solve each of the following problems to the best of your ability. • Read and follow the directions carefully. • Solve using the method required by the problem statement. • Show all your work. Work as neatly as you can. If you need additional paper, please be sure to staple all pages in the

proper order. • It is permissible to use your calculator or an online solver (like Wolframα) to perform derivatives or integrals. If you do,

state this explicitly. • Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units. • You must submit your exam paper no later than Wednesday, March 28. You should submit the paper to me directly, or, if

I am not in my office, please turn it in to Mrs. McDaniel in the department office (LSC 171), no later than 12:00PM. You may not slide the paper under my door. Late papers will not be accepted.

Yourworkwillbescoredaccordingtothefollowingpointstructure:

Problem 01: /15

Problem 02: /15

Problem 03: /15

Problem 04: /15

Problem 05: /15

Problem 06: /15

Problem 07: /15

Problem 08: /15

Problem 09: /15

Problem 10: /15

ENGR 3311: DYNAMICS SPRING 2018

Problem 01 16.3: Rotation About a Fixed Axis

Amillinatextileplantusesthebelt-and-pulleyarrangementshowntotransmitpower.Whent = 0anelectricmotoristurningpulleyAwithaninitialangularvelocityωo = 3rad/s.IfthispulleyissubjectedtoaconstantcounterclockwiseangularaccelerationαA = 1.5rad/s2,determinetheangularvelocityofpulleyBafterBturns5revolutions.ThehubatDisrigidlyconnectedtopulleyC andturnswithit.

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EXAM 03 PAGE !/!2 11

ωA, αA

ENGR 3311: DYNAMICS SPRING 2018

Problem 02 16.5: Relative Motion Analysis

IftheangularvelocityoflinkABisωA = 5rad/s,determinethevelocityoftheblockatCandtheangularvelocityωC oftheconnectinglinkCBattheinstantθ = 45°and𝜙= 30°.

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EXAM 03 PAGE !/!3 11

ωA = 5rad/s

vB

vB

vC

vC/B

ωB

ωA

ENGR 3311: DYNAMICS SPRING 2018

Problem 03 16.6: Instantaneous Center of Zero Velocity

IfthecollaratCismovingdownwardtotheleftatvC = 8m/s,determinetheangularvelocitiesωA andωCoflinksABandBCattheinstantshown.

EXAM 03 PAGE !/!4 11

vB

ωA

vC = 8m/s

vC

vB

ωC

60°45°

75°rBrC

ENGR 3311: DYNAMICS SPRING 2018

Problem 04 16.7: Relative Motion Analysis: Acceleration

Atagiveninstant,thegearhastheangularmotionshown.DeterminetheaccelerationsofpointsAandBonthelinkandthelink’sangularaccelerationatthisinstant.

EXAM 03 PAGE !/!5 11

.

..IC

O

ω

vA

.

.O

aA/O]t

aA/O]n

aO

ICα

vA

vB

aB

aA

αAB

ωAB

ENGR 3311: DYNAMICS SPRING 2018

Problem 05 16.8: Relative Motion Analysis Using Rotating Axes

CollarCmovesalongrodBAwithavelocityvC/B = 2m/sandanaccelerationaC/B = 0.5m/s2,bothdirectedfromBtowardsAandmeasuredrelativetotherod.Atthesameinstant,rodABrotateswiththeangularvelocityωB = 4rad/s and angularaccelerationαB = 1.5rad/s2.Determinethecollar’svelocityandaccelerationatthisinstant.

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EXAM 03 PAGE !/!6 11

vC/B = 2m/s aC/B = 0.25m/s 2

ωB = 4rad/s αB = 1.5rad/s2

X

Y

Z

ENGR 3311: DYNAMICS SPRING 2018

Problem 06

Ifthecartisgivenaconstantaccelerationa = 6ft/s2uptheinclinedplane,determinetheforcedevelopedinrodACandthehorizontalandverticalcomponentsofforceatpinB.ThecratehasaweightW = 150lbwithcenterofgravityatG,anditissecuredontheplatform,sothatitdoesnotslide.Neglecttheplatform’sweight.

(Hint:Youdon’tneedtheappliedforceP,becauseit’snotbeingappliedtothecrate.Treatthecrateandplatformasasinglerigidbody.)

EXAM 03 PAGE !/!7 11

FCBy

Bx

ma

=W

60°

30°

ENGR 3311: DYNAMICS SPRING 2018

Problem 07

Thelifttruckhasamassm1 = 80kgandmasscenteratG.Determinethelargestupwardaccelerationofthespool(m2 = 120kg)sothatnoreactionofthewheelsonthegroundexceeds600N.

EXAM 03 PAGE !/!8 11

=

m2g2NA 2NB

m2a

ENGR 3311: DYNAMICS SPRING 2018

Problem 08

Thediskhasamassm = 25kgandisoriginallyspinningattheendofthestrutwithanangularvelocityofω = 50rad/s.Ifitisthenplacedagainstthewall,forwhichthecoefLicientofkineticfrictionisµk = 0.20,determinethetimerequiredforthemotiontostop.WhatistheforceinstrutBCduringthistime?

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EXAM 03 PAGE !/!9 11

=. .mgFB

N

µkN

IBα

ENGR 3311: DYNAMICS SPRING 2018

Problem 09

Determinetheangularaccelerationofthedivingboard(m = 25kg)andthehorizontalandverticalcomponentsofreactionatthepinAtheinstantthemanjumpsoff.Assumethattheboardisuniformandrigid,andthatattheinstanthejumpsoffthespringiscompressedbyamaximumamount ∆l = 250mm,v = 0,andtheboardishorizontal.Assumek = 7.5kN/m.

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EXAM 03 PAGE ! /!10 11

• •=mg

k∆lAy

Axmatman

Iα

ENGR 3311: DYNAMICS SPRING 2018

Problem 10

TheslenderrodAB(m = 25kg)restsinthepositionshownwhenthehorizontalforceP = 50Nisapplied.Determinetheinitialangularaccelerationoftherod.Neglectthemassoftherollers.

EXAM 03 PAGE ! /!11 11

••mg

NB

NA

P

maxmay

IGα

G

aA

• •ax ay

aA/G]t

aA/G]n

=

=

aB

aB/G]t

aB/G]n