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Unformatted text preview: Lt" E'Ij Elia? £111.. In ﬁg $ _ has. V! U; {'33 a S 1 .ﬂtit: Double—chew your wart: to he sure it 11168135 the standards described in class and in the
hand—outs}. Remember: Clal‘ity and neatneSs Gaunt. Engineers must communicate and
convince Stmessfully! Box your ﬁnal answers. 1. What is a. scalar? Give an example of a. physical quantity that is a. scalar.
What is a. vector? Give two examples of a pl‘iysical quantities that are vectors.
: , .. . t . I
2. A car travels at V = 55 Express the. car‘s: speed 111 81 umts by lIll.llt1[Jl.}"11]g
the given expressiun for V by factors of one expressed the fancy way. Here an:
smne equalities fmm which you can form the ueceasary fancy factm‘s (if one. 1 mile z 5280 ft
ft : 12 if: 1 in 2 12.54 cm. 100 (rm. 2 I m 1 hour = 3600 .s' I realize yGu could 100k up a. Single conversion fuctor and (in this pmhkun in one
step, but please (lEEInil'IlfrllTI'ﬂtc that you thllow thc! idea (if multiplying by mm by using all the factors that I’vex suggested here. Ywur ﬁnal answer Hllﬂllltl have! units
of You can chuck your answer by using the single mnvumion factor. :5. Hitdiam and degrees can be coul‘using. A degree is; uu arbitrary Hutu{nadir thing.
There are 360 (icg‘r'rrtih' in at Circle; I think this mu docitlml by thv Eviluric)putzmliunri a.
long time ugn. J3: nuliau l5 :1 pure number. It is (llIIIOEJHjEHIlQSH. It is not mun—made
or arbitrary. it “gamut: from gccmmti'y. In gi—Hmmtry, the length, .‘i<.3f‘d.(:ll“ii1llkl.l' are
is given by .24 = r6, wherv r is the radius of the arc: and f? '15: the angle that the an!
Suhtuuds. lu this: I‘c'lutimmhip= {'3 must he expressed in radians. 6' is dinmusianleus
(it must be (m grounds of diuuzmsimutl (.toiiuistexitty) auul is a. pure: number. Slurpose
an arc subtmuls a. full circle. You know what the are lungth .s is in this gauge in
terms of 3' and it. We can, tluarcfm'c? 5'03 that the angle tnurespoudiug ta a. full
circle iu radians is; 9 = 2% radians. Putting together this gemnctric truth with
the arbitrary whim of the Mesopotamians 3210ch5 the familim‘ 1'UlEttiumship, 360” z ‘21? radians Au angle (.2 equals 175.4“. Fl'mu the preceding relationship, write 1 the fancy way.
Use this 1, the multiplicative identity, to perform the conversion that will express
the uugle, 0c. in mdiuua. 4. My ﬁsh tank is; 2—1 in. wide, 1.5 in tall, am] 18 in. deep. The sphéiﬁcﬁ weight at the
water in the tank E55 7‘ 2 9.?89 Detemiiue W, the weight of the water in the
tank in SI units. Recall that: ll)" : 7V end; use 'l:he Eel ipe t; write some fears; ones it) perform your leaving relations
calculations: 1 in u 2.54 cm lOQcmxlm 5. Study the ﬁgures shown belew: \% #2,; ‘mhuﬁ F13 lg (a) From figure 1, using trigonometry, write an expreeeien for the length a in
terms of the length L and the angle a. (b) From ﬁgure 1, new write an expression. for the length a in terms of the length
L and the angle 6. (e) Pram ﬁgure 1, write an expression fer the length L in terms of the lengths at
end E}. (d) From ﬁgure 1, if a: = 35°E what is the value of ,8?
(e) From ﬁgure 1, if a: = 35° and a. = 3.25 m, whet is the value ef L? (E) Assuming all the previously given dimensions, determine the herizontal (par—
allel to it} and. vertical components (parallel to y} of the vector L, as shown
in ﬁgure 2, 6. Find the resultant of the two farce vectors applied t0 the belt in the ﬁgure below
via the follewing steps. Sample prehlem 2.1 item the text might be helpful.
(8:) Sketch the appropriate parallelogram;
(’9) Use the lew of eeeinee to calculate the magnitude *ef the eeeiiltent. (C) Use the law: (if einee to celeulete the angle the resultant mekee {mm the
herizontel, ‘ ((1) Express the resultant in terme 0f its Cartesian Campanentsl 15.19w in the form
R = i + Be Sure to inelude the appropriate unite. a; hle e 3e lb 7. Repeat the previous problem. This time use the following method. (a) Resolve each vector into horizontal and vertical components. 00) Add the horizontal compenents algebraically. Add the vertical components
algebraically. (0) Again write the result as 1% : (13+ b}. Did you get the same result as you
did by the previous method? You should have. 8. Here is a slightlyr more challenging problem. Two forces are applied to the eye—bolt
as Shown. (3.) Determine the angle 0; such that the resultant is vertical. There are probably
many ways to proceed. I think using the parallelogram law and the law of Sines might be the easiest. (b) Determine the magnitude of the resultant. ﬂail?
(“h 43 ll:
m $7 7"
2% 60“ .5 ff 1'7? ...
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This note was uploaded on 07/31/2011 for the course ME 2301 taught by Professor Hanson during the Spring '10 term at Texas Tech.
 Spring '10
 Hanson
 Statics

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