Part 1. Getting Out in the World

(1.1) Drawing artifacts (5 pts) Find an interesting artifact in your kitchen, garage, or dorm room that is operated by a force or moment.

Create a storyboard (cartoon-like description) of how the artifact works, including how the force or

moment operates it. Examples of artifacts include a hand mixer, a hole punch, a nail clipper, the machines

in the weight room, or a car jack.

1. Hand Mixer 2. Exert force at the

handle for gripping.

3. Impose moment along

the handle to mix batter

F

F

M

(1.2) Calibrating Your Capacity (5 pts) It is important for engineers to have a sense of how large forces are. One way of developing this sense is

to create reference frames for force comparison; one such reference is your physical capacity. To this

end, find a weight room on campus and record the following information, in the table format shown

below in Table 1. Rather than turning in the table, please input your results at the following link (this is

how you will be given credit for your work):

https://docs.google.com/forms/d/1pgcwHnMM3GGVzkNK_HM3YyFpQ_hWANM6nJ6VBpmOEnA/vie

wform

BENCH PRESS

Maximum weight without hurting yourself.

Weight you can do repetitively 20 times without hurting yourself.

LEG PRESS

Maximum weight without hurting yourself.

Weight you can do repetitively 20 times without hurting yourself.

ARM CURL

Maximum weight without hurting yourself.

Weight you can do repetitively 20 times without hurting yourself.

𝟏𝑵 = 𝟎. 𝟐𝟐𝟒𝟖𝒍𝒃

𝟏𝒍𝒃 = 𝟒. 𝟒𝟒𝟖𝟐𝑵

Students do not need to hand in a table. The following is just an example to show the data.

Part 2. A Foray into Analysis (5 pts)

(2.1) Read: ‘The Bicycle: “Static” doesn’t mean that you aren’t moving’

Goal: To provide a free-body diagram of the bicycle and cyclist traveling at constant speed, estimate the

maximum velocity on a bicycle if the coefficient of drag is reduced by 15% and provide two suggestions

on how to reduce aerodynamic drag.

Given: The values of the variables, which include 𝐴𝑓𝑟𝑜𝑛𝑡𝑎𝑙 = 0.5𝑚2, 𝐶𝑑 = 0.85 × 𝐶𝑑−𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 = 0.765

Assume: Since the question asks for maximum velocity, ‖𝑭𝑑𝑟𝑎𝑔‖ = 167𝑁. This is selected based on the

assumption that the cyclist sustains peak force throughout the stroke. Also, it is assumed that the cyclist is

cycling at sea level, which makes the air density 𝜌 = 1.2𝑘𝑔/𝑚3 for the problem.

Draw: Free-body diagram of the bicycle and the cyclist

Formulate Equations:

‖𝑭𝑑𝑟𝑎𝑔‖ = (𝐶𝑑𝜌𝐴

2) 𝑉2

𝑉𝑚𝑎𝑥 = √2 × ‖𝑭𝑑𝑟𝑎𝑔‖

𝐶𝑑𝜌𝐴

Solve:

𝑉𝑚𝑎𝑥 = √2 × 167𝑁

0.765 × 1.20𝑘𝑔/𝑚3 × 0.5𝑚2= 26.98𝑚/𝑠

Ways to Reduce Drag: The cyclist can wear a tighter clothes, an aerodynamic helmet, or use more

aerodynamic bike wheels.

𝑉𝑚𝑎𝑥 = 27.0𝑚/𝑠

(2.2) Read: ‘The Golden Gate Bridge’

Goal: To provide a free-body diagram of the bridge, estimate the minimum required anchorage weight if

the coefficient of friction is increased by 15% and two suggestions of how to increase the coefficient of

friction.

Given: Friction force that prevents sliding, ‖𝑭𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ = 236.5𝑀𝑁, vertical force from table,

‖𝑭𝐻𝑂,𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙‖ = 84.7𝑀𝑁, coefficient of friction, 𝜇𝑠𝑡𝑎𝑡𝑖𝑐 = 1.15 × 𝜇𝑠𝑡𝑎𝑡𝑖𝑐,𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 = 0.69

Assume: The system is planar.

Draw: Free-body diagram of the bridge and the anchorage

Formulate Equations:

‖𝑭𝑛𝑜𝑟𝑚𝑎𝑙,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ =‖𝑭𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛,𝑚𝑎𝑥‖

𝜇𝑠𝑡𝑎𝑡𝑖𝑐

‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ = ‖𝑭𝑛𝑜𝑟𝑚𝑎𝑙,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ + ‖𝑭𝐻𝑂 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙‖

Solve:

‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ =236.5𝑀𝑁

0.69+ 84.7𝑀𝑁 = 427.45𝑀𝑁

Ways to Increase Friction: Rougher surface between the ground and the anchorage, using adhesives,

tighter bolts to achieve better surface mating between ground and anchorage.

‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ = 427𝑀𝑁

Part 3. Representing and Labeling Forces & Vectors

Make sure that your answers to the problems in this section include all calculations you performed and a

supporting drawing(s).

Furthermore, show only the number of significant figures appropriate for precision of given data: A

practical rule in engineering calculations is to use four figures to record numbers with a leading “1” and

three figures in all other cases in presenting your final answer. Intermediate calculation steps should retain

more significant figures. With this rule, a force of 40 is 40.0 N, and a force of 15 is 15.00 N. Numbers are

generally rounded (as opposed to truncated) in reporting values to the correct number of significant

figures. For example, 29.694 N would be written with three significant figures as 29.7 N with rounding

(and not as 29.6 N, which is what we would get if we truncated the answer).

(3.1) External, Internal and Not-in-System Forces (5 pts) A person grips a pair of locking jaw pliers (more commonly known as vise-grips), as shown in Figure 1,

in order to tighten a nut onto a bolt. Three cases (systems) are described in the top row of Table 2. For

each system identify the external (E), internal (I) and Not-in-System (NIS) forces, and indicate them in

Table 2, including a sketch of each system in the space provided. (It is ok to turn in the next page with

your homework.)

Figure 1

(3.1) continued. (Turn in this page with your homework)

Table 2

Forces

Case 1:

Nut is defined as

the system

Case 2:

Nut and vise-

grips defined as

the system

Case 3:

Vise-grips

defined as the

system

Case 4:

Member C

defined as the

system

Tension in spring NIS I I E

Normal contact

between pin A

and member B NIS I I E

Normal contact

between pin A

and member C NIS I I I

Normal contact

between nut and

member B E I E NIS

Normal contact

between nut and

member C E I E E

Normal contact

and friction

forces between

thumb and vise-

grips at D

NIS E E NIS

Normal and

friction forces

between fingers

and vise-grips at

E

NIS E E E

Weight of vise-

grips NIS E E E, Partially

Weight of nut E E NIS NIS

Normal contact

and friction

forces between

nut and bolt

E E NIS NIS

Sketches of the four systems:

Vice-grips and nut Vice-grips Nut Member C

Pru L.z

Go of ', -To QL{e-rnirtq thr utnit V^(cto r

bc-t*e.., poi,ttt l! a^d h ,

Girn = C-oo. J'nufL a*)-t, du'yr"-

9L'nnnsio-/rc ; c,lu-J.iut.+ O(

fi(o, 0,soo"-,,)

B ( o, tddmr,l, !oo^- 1

ASe ,n fltL ) Notl-, rlLcltr" a

D au",, )

- --_a

Forn^lol" E1u.{."0" t :

? = (x'-{,)

fl"^t h* alox3 , lr'''c

tl a"nl C o^d L ^n-"t D

,/ rCI,,r ,,olul L ^, s wtth

qo.ch I

ota-+ 'C (0, {oor,na, oJ

0 (-4fDp* ,loor'r-, o)

(+.-u,)(2"-*2, )

,{ 7u

) +(y,-V,)' + (2,-2,\'

a ldc',0 n*t

(o - foorv,^"1

4 A

-tUt, =

r-+

,lvl! z

IY'-Y,,(r-y'I

lt-3 {t

r+k

knl

j*jt

So luo

c) .tilVIt ' Jl, -o)'+ ( o-,rr^-*F*ffi-

(x, * x,1

(ildr,- i + (2"0a*n-!oo,,.*^) k

L {Ada p .!

ttl ll?tr =

*lUv

t-,lUu

G ) ltilt =

-1V'/ =

(o-o)3oJ mn

**;-_**-_)(0-0)"f (toora.^- {0or*)';__|7-affilL = L(N-nut

L+ itI00r"* 4( o - I tiila,,.' ]

lA0y*t

k

( -4fa-- - 0tC4o.83nn

(*4{tt^. -o) a ( {0a.--(ooru*,)-* (

+ (lou_tnr- ldoa,aa) -, *9+0 I s-* *

0 - zdo,"t,-)- =540 I

(D- loor^-. .l t-9o.83nr- i

C" ( c,.tt" tt_"/

ur\i+ Vq-t\)"r

v

t^l = - 0, &|lun L* ; 0, 555 r,t,v y"

Chn tk- ,

R"&-,% +, +h{

fv\r.+tl.. h^?t^ +{"r

Sl..I",t/ \avr, ^

(u ) trri 1

tLr llul tl

(c) tl ilrrt

d,nou,.- . +1,,e-J

Ve ttuvl drurt"

,Yry

(,l-t t Ve<-tur r

. ft-tso , tl.*-

t4

I

= ,t GO.rss)'+ 0' + l0,8tt1- z l" 00 0

0+lt+ 0 e l,0Oo

0t0+ tL = ldoo

Probk-- \ \

Gor.[ ' -fo

ex1fY.r

r I

aNol Vudu.

a^/ tg -fi"J

Gi,r* : S d^a3ua*/)P*

(t-T tt = llT, rt

O^, = 7So

fl sl or.

D*-

.,lll" tl = I t)o u-rp

)goFLrt

t\ lt tllru\t+\t /

Y' ,.J/,*'{-.

-alrTr

$t..r in Jt..,r, r o{ t'Le;" n f,n o^1u,

+t'{ ot;rt*ttv, c,o rin<-r r{ 7{d+t tfu nnag.*$,cfr or..{ ollrr-,,*,r - q F-4*

. toov;p {\f,t, *1glHp

Or,= t55o Oxr, 65"

Pln*. (Do,\rt ru-LJ t, nf""q ft z-dar..*t,n (E),lff;.{--n^kc,

p.^l,(r3 , o. E .+rn , ^'ff d Lok * s\

rrt u * toovip

Yl

Trr*

Eq,""{-'')"sItox= -+

ll F,ttl

hi, t F9

far 0x

Tlq

cos €g

= ilF il

Cr s O,A

.7rfrtt

(u,L +ugl,)

ELAa

[r^,^[-{r

@I c'trs

o1 F ?

L4x -

e ,l',0

(c' I h'

LW"tr =

*>T, fb. T'

o?., , 155 o

o$2. 65o

F' T,

e^r- b5o

gt, " tFSu

I

il, I1,

ii'il

i

i

f ,, \. .:i , .i

i :,,\

f t -.

Ckt c2 '

tb t T^fo pr,, c.M cU-

{". T-)ll z loo

?Ir

[Lotk t-,rn fo,r<,ttr

fr.. f)osll; ve xI

kt (o,t L,

U r Dirro.fi^*" c-o si,rt"t

fr,7

I o siltvc lz' e-a v ! e

I dln-tfru,,

JD cLuh fi

rckfit- Lett l* Wx-A {- d*^U frn 'ra sJansq

L;6, ( cr, 15o i* + sin ?io j )1t'e;pL + 1b,t uf +

6rA

^^Jvrv-J

l{1

-7

ru-ld

J0.zs-1'+ o ?d6' =l

ry Pdi'\t ot

7" o^"f

f (ano. Arz. n-le*e b;tt"

f".b:u.*, \- g,

Go"f , Js {^,a tf. urrrf v-q_t,-, o,toY +i, lw_ ,f -o,c-/,wA

+ o f-u-, 1n #* ttu sgtr-u ryL, ,/ 1fi*t)

fi "" o*,1 rt ole-ternn _ tfq lt-- f ., r,,^,_ Lol

, C.a^y fr1" ^ ov4 ttu to l+

Czit * ' D,'o|^* ,f b Prt ,./lL c^r.rn#n {r ^*Lt {(=F

F = ->4- ol.Ls L ={- f-oo .LL,. L + [ . ot) tLr fAstrr,,.. : 6lo*Z

:t, \i$Drr*,n^"-e ,r. -<' -nF

ftrn*++c

(ot\^ +,'*r .

-ttttl =

Utrt -

{tF,r z

ll?tr (u"i; +ut g+

fi=tro rlFy i{

F(t4E tt

uu h,)

€U*?

=)!-+

}'-tiretbt Cos 0r = r.r1

C,os 9.d a U5

(,or' AZ * \e

e.t* ,

(, I ltFl( 'LJt2o.e)zr- (5.oo)'*(8-uo;]ur= )r-rt .(Ls

f,iv= ttoi. + r{5 t r vz Lz _ Lo.othr L * |-oolLs j + &.ooQLr. ktr-11 4Ls 'J LL.lt t bt ^/ >>.lt t Lt E

l. i,

I

l; 1 1

Fr,1i l :,\'/1 '.

',:""

i

I

G o ^ t , T, akft, * ,v tl^^ ryr+,^rt, r( t6^ a,,tu-f o..^.\"/t ,t

t'#- 7p ru 3^A f*u uri 7 d*l {7^l'^"r o,"*l

t'A" htuy,16ay vat,,u 4 t, tuL-- four-inc6n, / s

A4 ] o/, F,t4w tt-*^ Ff*f r,qL*

Gi.,.* , Dra,n*, I tr* aldrrl , +l-, c^*-L;^-J *r;74' o{ 7r-al ( il ' -},flN j ) , bik- rwavr,n i"n or^slz-vf wLoc\

A.ru*a t Pt'on^r, A-n fi'.fr"orrt f"* , 3/*oofL r*cl,'n; uh'u-'lt

Ar-L rvU;U rt^t rkygia,0n Er.+u,g^n ach ,ta

rtt bb, L g

Drzu- ,

.rr*L"{t

F"^ +t

E1* t,o " .

d;o3rar^.

I1r*p'VW,,,* r[tre,,ri_

V-p*p., = C-ts (10-p)

I,?q,yz-'6t?

N

-at^)

Yabl 2 *a(o'X,r L

Iato,,1 ,tt =-Cos

9,at5,vl--cos

I '.Fp.*-t^"u; . $ pT '-)F*rr-ir.c[;a= So,to,,X'

/"wry

+ {orry,V !P

(9 0 -p)

Y^,,n> Y,1..1,,

r-t

F-.tI p&f _' ^c(,(^,

eotre ,

G) Wfn, bs4

FPr1, -'"r,*-=

(?o-pti - r..ls

(^'.(ro*p) y

Ca,, [?O -

S|.o*rl k

L0 Y, z)

1D \o

p{(r,ls l,)'

rrl

(t

o-7r-l

*Tro ru I. t/v

Cts L Iltu - 1fONI

H,ato^a -ht13 L*

6(/l-ato,Ui,.c{^* = ( -cos

-tur F

04( (10 -01 ifi iu -ar(tr-Urr.

-=6-/''

,r'-?-ui - c^r

-ts'u J

Lto -f )l . -?dD Ni--|F. - rr.c{,ru = Tgo nl o,rt ( 1o - p\

tb)--5'tl {-l ,^*^A

- incL. lo

;l

?I-pvp - i*l-tunt

,cus (1 0 -p)(,ts

tt

A,.s r,0re {"*"

@ki^, f

UrP

alc o L-

ol;o3v.n

cor (

stn p

-)lo/ r( Fm-ix<t)^<

t o,Lo

C-lu^L"kJ ut'1

t- P < o !0

r r tb. 611'

F,m -r^eL^r b.J EroT -r^r1,.^.

fuypoa^.-fu c (ulchor. h^,

Fp1-iu.{.,^r z

h,.A - iruJaw z.

Ce,^

+1,*

Jqux

Tf, ru

rut\2,rr 3 - S

Ctrol

Giu."t

rlt sr^r*.

D rot

*r, f ,e -tu^

,t tL, -Fo ,

P-u f*nfi'* t o*J tb-

Itn* ,{toll u a^At

k(r-.r-n

t" ^{l V(_4ln aloS th.c)-r-{v*'* tt,^ }t,

V , +

O,,, +t*- L r.r^rt , ^yV

a-cfr'q

4 ft^-

J

)^

q 10o rv-

t.5,1.0)^t(o t.-u-- -r-)l -/'

tb

Dtjrr-^ "f *rtn [rsa. Ba.t Di3"'*

/)/F.tr B"{y

l

j

I

[Ax t + uyl + uzk.(r,tr,)' ;* - ,#, u:1

rrPrt (u. L + ur t + vu h\Ur, . v1v z -:---=llvi rl llvirl

h.tx^t t E1,^"t,o,,- -:>(r( ) Liv z

Urt ,

lz

tbt €=

t t c^!

(3,-z,tL

fu"u- va+{-,^r- ;{ etff**+ frf.*'u,/s 3""*)i0,1 , ^ ,! fi^JlCt"* -,-{-o fft (0.s, ls, t.o

Firu ut-nn"+-*L

' Non, ,.l- cLrro1 -

-L

r",-I '\-.i\

-...i

- -tro t

+kt^i*h

L-

B(

Cat>.d, "k a/-r-t (L4

t -0, 6. a , _ ll. oJw,

A-ry (rt. (*u^n,

Ulrt =(ra:+ji,".

= o ttee ug" +#= o L41

(.) c,\,s o

fr,

M:

Itfr tt ?

(tn; fi <

F5r

fto' Au

cls e

4 fr" tb) ,

-) ->Aro Are? .-:=--_-:-

Itftott l(*-gtl

(o - o,E) n" L

- 0.5n" I

(r o -o.s)-( s^ L +

lz.forn

u*=(=";T.i;\*= -0 130

wt -< )ot

lL .7\tut

-5[/v= 0 ttttL + 0.14q J - A.lso b

,LL\ P= loarr(o.rrug+ o.r+l j. -0.11u k")-)P Ir.(!r,r i + r+..1 N) -1t.oN k

Jffi?t.tytn'L = lL .10r,

( s s) tr.r),4.s

4.9,,.(r 8?-r"),Ttr--161

gz +1 .3,

+ q - t s)(+. k)n -F (_r. o) [ _rr.o)r,,r

-

'f +tu

.frt. fnr*n"<r [<.cy.<-{-vr_,

+]^.

+." vL-ut\r 'f-^t^x(

ofgosrtc d,.u6-* 4 (6) ,

'1

Fz. -l( (gr.{ L -r+.1N j +1y.0^r(

is

$,oTh,

vr't * Jvc.4u.

/vtLo,ay

L-,

\v