Activity 2 Dimensional Analysis

Transcription

1 Activity 2 Dimensinal Analysis Gals! Develp cnversin factrs frm cmmn equalities.! Use cnversin factrs t cnvert between different units f measure.! Apply the cncept f dimensinal analysis t string tgether cnversin factrs frming mathematical epressins. Cncepts t Review Cnversin factrs Dimensinal analysis Units f measure Mathematical peratins with significant figures Scientific ntatin Calculatr use Intrductin The fllwing prblems invlve cnverting frm ne unit t anther. If the unit f measure changes, the number in frnt f the unit will als change. All f these calculatins require tw things: defined relatinships between different units and sme methd t cnvert ne int anther. Dimensinal analysis invlves setting up the prblem in such a way as t cancel the unwanted units with nly the desired units remaining. A cnsistent methd f prblem slving including unit cancellatin is invaluable in succeeding in this curse. Cncepts t Review: English units, Metric units, Cnversin factr, temperature (scales, cnversins between scales), Eact vs. Measured Numbers, Significant figures in Calculatins invlving Measurements, Density vs. Specific Gravity. Use yur tet t find ther cmmn equalities (Table.) and the relatinships needed t cnvert temperatures. Als lk fr similar prblems t help yu learn hw t successfully set up these prblems. Required Materials Scientific calculatr, selectin f cmmercial prducts - -

2 Activity 2 Dimensinal Analysis Wrksheet Name Sectin Date Eercise Measured and Eact Numbers Lk at the cmmercial prducts in lab r at yur hme and create cnversin factrs (ratis) fr fluid unces t liters r milliliters. T d this, read the amunts present in bth English units (fluid unces, pints, quarts, punds, unces, etc.) and metric units (milliliters, liters, grams, kilgrams, etc.) and then divide ne value by the ther, keeping the units. Prduct English Measurement Metric Measurement Cnversin Factrs Cca Cla 2 fl z 55 ml 55 ml 2 fl z r 2 fl z 55 ml Many AnswersPssible - 4 -

3 Questins and Prblems Dimensinal Analysis Fr all f the fllwing calculatins, shw all yur wrk. If yu need mre space than is prvided, yu may d yur wrk n separate pages but be sure t attach these when yu are dne. Write yur crrect answers in the space prvided. If yu nly prvide the answers withut shwing yur wrk, yu will nt be given full credit. All answers shuld be clearly identified (bed ff), written in scientific ntatin if the values are less than r greater than 000, and all shuld have the crrect number f significant figures.. Hw many secnds are in eactly ne day t five significant figures? Rad map day hr min see def def def day 2 2. Seventeen apples weigh.25 punds. They cst 59 cents fr pund. What is the cst f apples? Rad Map apples apples es. The distance frm Santa Cruz t Santa Barbara is abut 280 miles. If a car gets 2.6 miles per galln, and the price f gas is 2 cents per liter, hw much will it cst fr gas t drive frm Santa Cruz t Santa Barbara? 4. It is fund that 5 pears weigh an average f.9 punds. A b f pears cst $7.94. The price per pund is 55 cents. Hw many pears are in eactly 7 bes? 5. During surgery a patient receives 5.0-pts f. ( quart = 2 pints, liter =.057 qt) a. Hw many milliliters f were given? b. Hw many dl were given? i Sec 86400µV lbs Radmap miles gal L s z 280mi mi RadMap bes lbs pears Efftes 4 b zraddrefap pts f qt 5pts j peas 27Opeas Late Mh zg mL 42400K Raddenfap pts qt lazy d L 5pts dL 24dL y

4 6. Hw many cubic meters f sil are needed t fill a flwer b that is.5 feet lng, 8 inches wide and ft deep? m 7ft.5ft.5ft Radmap ft r 8 in can in m 42in8 m 2in 42cn 0 42in 02n 24,5 0,5 m cm m 0.07in 7. Bdy temperatures abve 4. C can lead t cnvulsins, especially in children. 4, C 80f Ezact C b. What is this temperature in K? OF f RundEven rule µ Ftz ct27.5 K K E E C OF I a. What is this temperature in F? 8. The daily dse f ampicillin fr the treatment f an ear infectin is 5 mg ampicillin per kg f bdy weight. The pill is dispensed in 500. mg tablets. Hw many tablets shuld be given daily fr a 75 pund child? An IV pump delivers medicatin at a cnstant rate f 24 mg/hr. Hw lng des it take t deliver mg? this parttyp RadMap lbsbdy defgbdy kgbdy mgamp pillsrtablets y z pills sbdy lbsbdy 000gbdy bdy 5000mg drp kg ampy.qp.ua 9. The vlume f bld in adults is. L. The density f bld is.0 g/cc. Hw many punds f bld are there in the average adult bdy? (Hint: Yu can use the density as a cnversin factr.) RadMap def 2 IL l L def ml l cc l ml cc g 0. Which is the higher temperature, 8 F r -.0 C? T lbs lbs my 7 Olbs Cmpare cnvert f t c r ther way g 7.8 C r.0 7 Higher

5 . A bttle f Cabernet Sauvignn is labeled as having an alchl cntent f 2.5% by vlume. a. Write the percentage f the alchl in the wine as a cnversin factr. I2ismbalchly 00 ml Wine b. If an individual were t cnsume 20. ml f the wine, hw many fluid unces f pure alchl wuld the individual have ingested? ( pint = 6 unces; 8 pints = gal) z Rad Ulap ugh wine unlatched L galfrets ut wire 2.5mLalchl L 8.785L l gal lpts 58708z.507A 2. Urine is a water-based slutin cntaining a variety f disslved slids. The specific gravity f a urine sample f a yung wrestler is.045, which is utside the nrmal range f (The specific gravity f a substance is its density divided by the density f water at 4 O C, at which the assumptin stated belw is accurate.) a. What is the density (d) f the urine sample? (Assume that d(h 2 O) =.00 g/ml) specifiggravity daenasi.tv densityespecifiggraitydensitylb0l z 045l 000g ml wbf l045g b. Is it mre likely that the wrestler is dehydrated r that he recently drank a large amunt f water? Yu will use wrds fr this answer, n calculatins necessary. (Hint: Review the definitin f density) hydrated dehydrated 00gImh.00glube.045gmL w Bdehyd - 7 -