Ef157-m4-examsolution-2015-p6 - University of Tennessee

EF 157 - Fall 2015 *Exam 4 - Page I of 7 * Section

1) (15 pts) When the 31-kg wheel is subjected to the

clockwise applied torqus of M = 120 N-m, it slips as it rolls. The coefficient of kinetic friction ispr = 0.35.

The wheel hasarudiw of gration about its center

of mass O of Iw: 330 mm.

l20N'm

e) Determine the angular acceleration ofthe wheel.

b) Determine the linear acceleration of the wheel's

center of mass O.

tYt&

;---------=-1

115 t* { ,,0

o o{.rq,ul

?

IZ o

*TL:4

rn,h o

=

3l

rt,r'6,23

n)

' ?4a 37sQ 6&' 2

ry , +rz i:d, t=|nAp ,

: 6

6A

,U

301 "t( Al

N-nJ

$'ltPs'=)

= l,luil

A/= ry ; prv)(?'sr Ylr")

: o"?ffto('// tt) 7 /a 6. 14 'u

I oG ,'/t 'U-

5t r* z hdy =) +{ r*ma, =/ a'7

3l K7

av .7t3,433s 5u-

f+l 'r,

=/

= Ta.x =") #

,t

'(or-v+o)(o"a+

^\

t-r '(r 'M =

"{ a !J- -

4 izt>

= - (3'3)s_7

^on''

4>

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EF 157 -Failz0$ * Exam 4 -Page 3 of 7 * Section

3) (20 pts) At the instant shorarno the 50.0-1b uniform rod is

horizontal and is rotaling clockwise at2.00 rad/s. The

spring attached to its end always remqins vertlcal due to

the roller guide at C, The spdng lenglh of 4.00 ft (i.e., the spring figure at right) and a stiffiress of

has an unstretched

is ft

:un1s2tr.0etcthbe/df.tl.l^the

f

,1,

/f,

.''"

.

t,^

ld;;i. l'{ -7- a) Detennine the angular velocityof the bar the instant it has rotated 35.0o clockwise from th-

b) Determine the angle 0, measwed clockwisefrom the

horipntal, to which the bar rotates before it

: momentarily stops. Hints: You should get o quadratic

equation in terms of sinQ, simply set x stnQ, and

2.00 rad/s 6.00 fr

solve the quadratic equationfor the positive root. Also, the answerfor Part b) must be greater than

t) 35.0" (obviously).

L( se ( anseructro''t u F r' "&1

(.,, Lo& ^) I

ro= j n/'=!(#,r")(rrn

K,vdt =KrrU' fi

/

/t\

fr///lt -.r"

T ,+ = lg" QJJs- sluS'(rL

4 &=3o s

z

JrYu6, t

thftlItt

") | (,r,6 3tit,

=

zg

++

^O-

*

4

o

"S.. /{@/.?'/et-t

c)

{u-, = Z z-e

> , f { ,(on l- ,()tt(/

nr')

-

,+/z (

72'

n)

= n

t[*,"o 24 4.f*r' 2ct,6 +- 7,O

- Z4'{(

, b* (ae kpqr: 4^t J . A y

=

,

6 a*:5. (tF /26r, t'P t'/L{y < LL) = (-/ ,/ P,, d,'2,

L

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