THE TJNIVERSITY OF BRITISH COLUMBIA2006 / 2W7 WINTER S ES SION

PHYSICS T7O MECTIAMCS IMidterm Examination: 1930 to 2030, Monday, March 5,2007

Write all work to be marked in the Answer Booklets provided.You may consult a single-page 8 %nch by I I inctr, hand-writren information sheet.You must hand in your information sheet with your Answer Booklet in order for your exam to be marked.You may use a graphing calculator.The exam consists of 2 questions. Question I is worth 15 marks and Question 2 is worth 25 marks.The exarn counts for a total of 20 nnds towards your Final Grade for the course.

. OTJESTION I

The diagram below shows points A, B and C on a rigid body. A force F of magnitude 500 N acts at point B.The coordinate direction angle of F to the positive y-axis is 40". The coordinate direction angle of F to thepositive z-aris is 70'. The coordinate direction angle of F to the positive x-axis is greater than 90".

a) Determine the coordinate direction angle of F to the positive x-axis. (3 marks)b) Write the position vector r which points from A to B as a Cartesian vector. (2 marks)c) Determine the moment of F about point A. (4 marks)d) Write the unit vector u which points from A to C as a Cartesian vector. (2 marks).c) Dstermine the magnitude of the moment of F about an axis extending from A to C. (4 marks)

a m

--;'

lO . t t

q,)

5)

c.)

PHYSICS 170 MECHANICS I

Midterm Examination: 1930 tD2030, Monday, March 5,20Q7

OUESTION 1: SOLUTION (Page l)

c ( t , - .1 r)-f___

B (-s,1 b)"n

f f ( " , l o r s ) m

J

F = 5oo

*.("o

( * "

A ' -

:L

- - b o - - r o - + 'T + c*s .+d | + qs-rD 0" ) trl

G s - ' / - t J ' , - . . . t q 8 - G t a ) a o

( - r ? - s i * t ) r n

) = E

V. fir

- 5 - 5? C - (' g R

-{r -+ -+f i - - r ( F

--5&.I

DLot 1O

.-L

- 9(!E e(

R= 5 0 0 J

- 8o

<eS &f O

r0 --n

-l

L +( ' , l . r s

")

- + / 1f t ) = U , . ( rRc")

PHYSICS 170 IIfECHANICS IMidterm Examination: 1930 tn2030, Monday, March 5,2007

QUESTION 1: SOLUTION (Page 2)

-+. \, 1 , F ) :

soD - l - t 4 2- 1 - g Ic.so( (.!qoa (.5los

N. rO

aa . f f i a c - - - 1 . 1 J d , ' v ' r n

-> -+c c - r R

r -l> --.r l'| " " - "o I

". L

-->,- r ' r i + l g l

-.>\ t = = { f f i

re+ rT?

quESTroN 2

The diagram below shows a rigid body ABCD in equilibrium. A force and couple act at point C wherep=(30 i+40 j -50k )Nand114 : (20 i+ l0 j -60k )Nmwhere i , j , ka re theusua lCar tes ianun i t vec to rs .

ABCD is supported at B and D by cables and at A by a smooth journal bearing. The weight of ABCD may beneglected.

Draw a large, clear free-body diagram for ABCD. (4 marks)Determine the three scalar force equations of equilibrium for ABCD. (7 marks)Determine the vector moment equation of equilibrium for ABCD.Take moments about point A and use forces at their point of action on ABCD. (5 marks)Determine the three scalar moment equations of equilibrium for ABCD. (3 marks)Solve the six scalar equations of equilibrium for ABCD to determine the Cartesian components of thereaction at A and the magnitudes of the tension in cables BG and DH. (6 marks)

6

4rn

a)b)c)

d)

e)

t 5

,

PHYSICS 170 MECHANICS IMidterm Examination: 1930 to 2030, Monday, March 5,2007

QUESTION 2: SOLUTION (page l)

r , l / ^ n r \F \ - ts v (p ,n )J J

--,F

Dlt

e

-5

h

-SLG ( t', o,9)n o

-r-RcgE :

C (,:5',o) m-+F-.1rb

-.>F

6-).t-s6

4

t-D H

-->F

-*rno\

rD

6 / ,j,1o)",

--> rtQ r c + A r L

( a i - s i + + i ) X ,

(-ci- si* qt ) v,( lo i+rrof- s0d ) o. ,

X =

'{ a

Fr./v?1;Foru /

-| 6-t

r 0 L + f n 0 t* ?

I -s -.b * ' .{ mT+ roJ- (o L J W, .n

aovlL€ rnOnZrIS ' .

. o ' .

: O ' .

OLJESTION 2: SOLUTION (page 2)

F o R c E 6 q u r r r o u { b t r 6 Q r . t r L r g C l v w ) ' .

0 + a X - ' 6 Y + 3 O = OL

- s > 4 , S Y + t + O = O

H + q X r G Y S o = O

PHYSICS 170 MECHANISS IMidterm Examination: 1930 to 2030, Monday, March 5,2007

u s t T ( 6es

t t )

tz)

(3-r

--+L

I

3o

1 Ya.

( z

-tJ

,540

tko6

X-+Mo.+

+ll

l v .

s +L 1 l .

R

-+-.+ af f ) L + f n L +: L I

--5L

->J

..>. L

* - )

- G

-.}>J

-,s

Y +-.>f$o-so

v N r 7 5 ARE t{ " t1

d) 6,-

z ({)A

J r n * = o :*

f f - O ' .b

<t*E f o8<€

-5J:

F 5

Tlf" Cov P !! 1rro,rrygr{T

Z rn

Q Oorntru? € Qv nr t5613 o t r E Q u r t - t B R t v r r n i

ao + l o - Q o-.:9L

r n + 3 o X + 3 o Y ? 3 O = o:.-

(r,l

{ s t

tc)

* r h X + l r Y

- 3OK + qoY

+ G o : O

= Ocf)a

_ ) 1 0