I look forward to seeing you in August. Have a wonderful rest of your summer!

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1 PHYSICS Summer Homework 016 Sister Dominic, OP M First & Lst Nme: Due Dte: Der Physics Students, Welcome to Physics where we get to study how our universe works!! In order to do this, we need to effectively use mthemtics in order to descrie the phenomen we encounter. Plese complete the following review ctivities to prepre for our study. The following pges re intended to e rief review of severl topics you hve covered in Chemistry, Alger, nd Geometry. Following ech review there re short section of questions to prctice these skills. There will e n ssessment of the ojectives listed elow during the first week of clsses. Tutoring will e ssigned s needed to chieve mstery of these ojectives. I look forwrd to seeing you in August. Hve wonderful rest of your summer! Sister Dominic, OP Ojectives of Summer Work I cn: 1. Mnipulte nd solve lgeric epressions;. Determine the significnt figures of mesurement nd pply the rules for significnt figures in determining finl nswer to prolem; 3. Apply Scientific Nottion, metric prefies, nd unit conversions; 4. Determine the Best Fit Curve from set of dt points; 5. Apply the properties of Vector Addition, geometry, nd right tringle trigonometry to grphiclly nd numericlly solve for components nd resultnts of vectors, s well s the ngle of the vector. Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 1

2 Properties of Rel Numers Directions: Memorize the following properties nd informtion, e le to pply them, nd nswer questions elow showing ech lgeric step. Use seprte pper nd insert it immeditely fter this pge. Mke sure you re comfortle will ll sic lger skills. Properties of Rel Numers Let,, nd c e rel numers, vriles, or lgeric epressions. Property of Addition Emple Property of Multipliction Emple 1. Commuttive Property + 3 = 3 +. Commuttive Property ( 3 ) = 3 ( ) + = + 3. Associtive Property + ( + c ) = ( + ) + c 5. Distriutive Property ( + c ) = + c 6. Additive Identity + 0 = 8. Additive Inverse + ( - ) = 0 = 4. Associtive Property ( c ) = ( ) c + ( ) = ( + 3 ) + 4 ( ) = Multiplictive Identity = 3 1 = 9. Multiplictive Inverse 3 + (-3) = 0 ( 3 4 ) = ( 3 ) = 3 Note: cnnot = Zero Property 0 = = 0 Order of Opertions () To simply n lgeric epression, order of opertions PEMDAS must e followed: 1 st Prentheses nd other grouping symols, nd eponents, 3 rd multipliction nd division, 4 th ddition nd sutrction. () To solve n eqution for given vrile, the order opposite of PEMDAS is followed to isolte the vrile. It is criticl tht the vrile is in the numertor when it is isolted, otherwise you solved for the inverse or reciprocl of the vrile, not the vrile itself. You will need to e le to lgericlly mnipulte vrious equtions in physics. Solve for the vrile indicted. Mnipulte them lgericlly s though they were numers. Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge

3 Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 3 Comining Frctions Directions: Red the following, e le to mnipulte nd simplify regulr nd comple frctions, nd work out the emples. To dd or sutrct frctions, you must first find the lowest common denomintor nd epress ech frction with it. Emple 1 Emple From Alm Roinson s Summer Pcket y y y y y y y y y ) ( ) ( ) ( ) ( ) ( ) ( To multiply frctions, multiply the numertors nd multiply the denomintors. To divide frctions, multiply y the inverse. See the section on comple frctions for more detils. Multiplying Frctions: y y Dividing Frctions: y y y Questions: Simplify the following. Show ll work. From Alm Roinson s Summer Pcket

4 Significnt Figures Overll Directions: Wtch the following Video: nd Tke notes. Memorize the following rules nd e le to pply them. PART I Directions: Stte the numer of significnt figures for the following mesurements. Significnt figures of mesurement those digits tht re known with certinty plus the first digit tht is uncertin. Rule 0: All nonzero digits ARE significnt. Rule 1: Zeros etween other nonzero or significnt digits ARE significnt. 1.) 304 m.) 3004 m 3.) m 4.) m Rule : Zeros in front (left) of nonzero digits re NOT significnt. 5.) 003 m 6.) m 7.) m 8.) m Rule 3: Zeros tht re t the (right) end of numer AND lso to the RIGHT of the deciml ARE significnt. 9.) m 10.) m 11.) m Rule 4: Zeros t the (right) END of numer ut to the LEFT of deciml re NOT significnt UNLESS followed y written deciml point (tht is how one shows they hve een mesured). 1.) 3400 m 13.) m 14.) m 15.) 340. m 16.) 3040 m 17.) 30.0 m When mesurement is written in scientific nottion, ll of the digits ARE significnt. 18.) m 19.) 3.0 km 0.) m PART II Directions: Perform the following clcultions nd write the nswer in significnt figures. Addition or sutrction the finl nswer should hve the sme numer of DIGITS to the right of the deciml s the mesurement with the smllest numer of digits to the right of the deciml. 30. m 50.6 s m.876 m m m +.35 s - 1 m m + 0. m Multipliction or division the finl nswer should hve the sme numer of SIGNIFICANT FIGURES s the mesurement hving the smllest numer of significnt figures. 8 m 6 s 11 m.5 m m 4 m 4 s 11 m 3.1 m.0 m Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 4

5 Scientific Nottion Directions: Memorize the following forms nd rules nd e le to pply them. Very lrge nd very smll numers cn e difficult to communicte when written s regulr decimls. Using powers of ten cn mke epressing lrge/smll numers esier. In science nd engineering fields, scientific nottion ( specil form which uses powers of ten) is often used to clerly communicte numer nd its significnt figures. Form of Scientific Nottion & Computtions with Powers of Ten Form of Scientific Nottion: A 10 n A is ny numer with one digit to the left of the deciml All digits in A re significnt n is n integer, equl to numer of plces the deciml ws moved n is positive if the numer is greter thn 1 n is negtive if the numer is less thn 1 Multiplying Numers (A 10 )(B 10 y ) = (A B) 10 +y 1. Multiply the numers efore the 10 s. Add the eponents Emple: ( ) ( 10 ) = (3.0 ) = Adding Numers A 10 + B 10 = (A + B) Rewrite so tht ll hve the sme eponent. Add the numers efore the 10 s 3. Bring down the power of ten Emple: Dividing Numers (A 10 ) / (B 10 y ) = (A / B) 10 y 1. Divide the numers efore the 10 s. Sutrct the eponents Emple: ( ) / ( 10 ) = (6.0 / ) 10 3 = The following re ordinry physics prolems. Plce the nswer in scientific nottion when pproprite nd simplify the units (Scientific nottion is used when it tkes less time to write thn the ordinry numer does. As n emple 00 is esier to write thn.0010, ut is esier to write thn 00,000,000). Do your est to cncel units, nd ttempt to show the simplified units in the finl nswer.. T s kg kg s 3 1 K kg.1110 m / s c. F Nm C C9.610 C m J J d. e J e. m K J s s J Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 5

6 Metric Prefies & Unit Conversions Directions: Be le to pply the following tle. Prefies my e used to symolize powers of ten; in this cse, the prefi is comined with units. For emple: 1,000grms = 1,000g = g = 1kg = 1kilogrm 0.001meters = 0.001m = m = 1mm = 1millimeter Common Metric Prefies nd Powers of Ten Deciml Power Prefi Arevition 1,000,000, gig G 1, 000, meg M 1, kilo k centi c milli m micro μ nno n pico p Directions: () Red nd e le to pply the following informtion on unit conversions. () Answer the following questions showing ll work. After performing numericl clcultions, write the clcultor nswer down. Then write your finl nswer in scientific nottion nd with significnt figures nd o/highlight it. Physics uses the KMS system (SI: System Interntionle). KMS stnds for kilogrm, meter, second. These re the units of choice of physics. The equtions in physics depend on unit greement. So you must convert to KMS in most prolems to rrive t the correct nswer. Mesurements should e in consistent units efore doing clcultions. Mesurement units cn e converted from one to n equivlent using conversion fctor. Multiplying ny numer y the numer 1 does not chnge its vlue (61=6). Since the numertor nd the denomintor of conversion fctors re equl, conversion fctors re equl to the numer 1. For emple, since 1 meter = 3.81feet 1m ft The reson why it is vlid to multiply mesurement y conversion fctor is ecuse we re simply multiplying y the numer 1. If you mesured your height s feet, this could e converted to meters: 6.000ft 1m 1.89m ft Questions 1. How mny seconds re in n hour? A dy? A yer?. A speed of 31.54Gm/hour is how mny meters/second? 3. A o hs volume of 4,70,000 cm 3. Wht is its volume in cuic meters? [Hint: Be creful!] Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 6

7 Plotting Dt Points & Best Fit Curves Directions: Red the following informtion, complete the ctivity nd e le to plot dt points nd determine est fit curves. Grphing Dt Once eperimentl dt hs een collected, grphicl nlysis cn led to insights. The steps for grphing dt re 1. T - Title grph. A - Lel es with quntity nd units (nd if necessry fctor, such s 10 9 ) Independent vrile is on the horizontl, -is (this is often time ) Dependent vrile is on the verticl, y-is 3. S - Choose nd lel scle Lel ll long the es, either every, or every two, or every five grid lines 4. P - Plot points Mke them lrge enough to see 5. B - Choose nd drw the est fit curve The est fit curve my e liner, ut could lso e qudrtic, inverse, etc. The line should etend through the dt rnge nd only slightly eyond If liner, use ruler NEVER connect the dots NEVER drw rrows on the ends of the est fit curve Emple Dt Oject Displcement Time (s) Displcement (m) Oject Displcement Time ( 10 3 s) 6. S Often you will need to find the slope (see review pge on slope) Alwys use two (convenient) points on the est fit curve; lwys include units nd the fctor NEVER use only one point, NEVER use dt points unless they fll on the est fit curve Slope rise run y y m 4m s 510 s m / s y1 1 Grphing Activity Prt I: Eplore curve fitting: Discuss your findings elow. Prt II: Use the informtion in the dt tles to construct grphs ccording to the ove procedure nd nswer the ccompnying questions. Dt Set 1. Wht is the type of est fit curve is used? Dt Set 1 Time (s) Speed (m/s) Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 7

8 Dt Set 1 continued. Determine the slope of the grph with units. Eplin your procedure. Show clcultions. c. The slope of this grph tells us the ccelertion of the oject eing oserved since ccelertion = chnge in speed / chnge in time. Descrie wht the grph would look like if the oject were decelerting. Dt Set Dt Set Time (s) Distnce (m) Wht is the type of est fit curve is used? Dt Set 3 represents dt from n eperiment in which the velocity of n oject in circulr motion ws kept constnt while vrying the rdius of the motion. The ccelertion ws then determined. Dt Set 3 Rdius (m) Accelertion (m/s ) Wht is the type of est fit curve is used? Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 8

9 Geometry Prctice Solve the following geometric prolems.. Line B touches the circle t single point. Line A etends through the center of the circle. i. Wht type of line is line B in reference to the circle? ii. How lrge is the ngle etween lines A nd B? B. Wht is ngle C? A 30 C 45 c. Wht is ngle? d, How lrge is? 30 o 30 e. The rdius of circle is 5.5 cm, i. Wht is the circumference in meters? ii. Wht is its re in squre meters? 4 f. Wht is the re under the curve (function) t the right? Using the generic tringle to the right, Right Tringle Trigonometry nd the Pythgoren Theorem, solve the following. Your clcultor must e in degree mode. 1 0 g. = 55 o nd c = 3 m, solve for nd. h. = 45 o nd = 15 m/s, solve for nd c. i. = 17.8 m nd = 65 o, solve for nd c. j. = 50 m nd = 180 m, solve for nd c. k. =5 cm nd c = 3 cm, solve for nd. l. =104 cm nd c = 65 cm, solve for nd. Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 9

10 Trigonometry Directions: Red nd study the informtion. Answer the following questions. Be le to pply the Pythgoren Theorem, sine, cosine, nd tngent functions, nd their inverses. 1. There re degrees in circle. Supplementry ngles dd to degrees.. Complementry ngles dd to degrees. The sum of the interior ngles in tringle is degrees. 3. A right ngle is degrees. 4. A right tringle hs one ngle which is degrees; the sum of the other two interior ngles is degrees. 5. The hypotenuse is the leg of right tringle which is locted cross from. Compred to the other sides of tringle, the hypotenuse is the. 6. The Pythgoren Theorem sttes. 7. Drw Right Tringle. Lel the legs of the tringle &. Lel the Hypotenuse c. If = 3m nd =4m how long is c? 8. Your fmily is moving to new house nd rents moving truck. To lod the truck rmp ws uilt. If the rmp is 3.3m long nd the horizontl distnce from the ottom of the rmp to the truck is.5m, wht is the verticl height of the rmp? Sketch digrm efore solving. 9. Using the lelled tringle elow, write down the three equtions given for sin θ, cos θ, nd tn θ. Here θ represents n ngle mesured in degrees. You will lern the mening of the trig functions in you mth clsses if you hve not lredy. Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 10

11 10. You cn use your clcultor s uttons leled sin, cos, nd tn for these functions nd sin -1, cos -1, tn -1 uttons for their inverses. Use your clcultor to find the nswers to these common ngles in trigonometry. Keep the nswer s frction.. sin 0 o =, sin 30 o =, sin 90 o =. cos 90 o =, cos 60 o =, cos 0 o = c. tn 0 o =, tn 90 o =, tn 45 o = Sketch the following tringles nd lel. Use the trig equtions to solve the prolems. Show ll work! 11. In right tringle XYZ, hypotenuse XY=0.m nd ngle X=37º. Find the length of leg YZ. 1. In right tringle XYZ, leg YZ=35m nd ngle Y = 53º. Find the length of the hypotenuse YX. 13. In right tringle XYZ, leg YZ=1m nd leg XZ=4m. Find ngle X. 14. A ldder.7m long lens ginst wll nd mkes n ngle of 60º with the ground. Find to the how high up the wll the ldder will rech. Sketch digrm efore solving. Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 11

12 Vectors Directions: Use your pst mth lerning nd the internet to ssist you in nswering the following. Be le to pply the concepts. Itlicized portions re from Stephnie Spencer s Summer Pcket or Northview HS Summer Pcket There re three types of numericl vlues used in science nd shown in the tle. Type Sclrs Vectors Prts Numer Only Mgnitude & Units Mgnitude, Units, & Direction Emple Coefficient of Friction μ = 0.05 Speed = 5m/s Velocity = 5 m/s Est Notes Rtios of vlues with the sme units Mny of the quntities in physics re vectors. This mkes proficiency in vectors etremely importnt. Mgnitude: Size or etent. The numericl vlue. Direction: Alignment or orienttion of ny position with respect to ny other position. Sclrs: A physicl quntity descried y single numer nd units. A quntity descried y mgnitude only. Emples: time, mss, nd temperture Vector: A physicl quntity with oth mgnitude nd direction. A directionl quntity. Emples: velocity, ccelertion, force Nottion: A or A Length of the rrow is proportionl to the vectors mgnitude. Direction the rrow points is the direction of the vector. 1. Identify the following s sclr (s) or vector (v). ) + 3 m/s c) 50 m/s Est ) crs d) 7.01 m e) 51 m/s f) 37 m upwrds Negtive Vectors Negtive vectors hve the sme mgnitude s their positive counterprt. They re just pointing in the opposite direction. Vector Addition nd sutrction A A Think of it s vector ddition only. The result of dding vectors is clled the resultnt. R A B R A + B = R So if A hs mgnitude of 3 nd B hs mgnitude of, then R hs mgnitude of 3+=5. When you need to sutrct one vector from nother, think of the one eing sutrcted s eing negtive vector. Then dd them. A B is relly A B R A + B = A negtive vector hs the sme length s its positive counterprt, ut its direction is reversed. So if A hs mgnitude of 3 nd B hs mgnitude of, then R hs mgnitude of 3+(-)=1. This is very importnt. In physics negtive numer does not lwys men smller numer. Mthemticlly is smller thn +, ut in physics these numers hve the sme mgnitude (size), they just point in different directions (180 o prt). Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 1 R

13 Adding Colliner Vectors Vectors hve oth mgnitude nd direction, thus we must tke the direction into ccount when dding or sutrcting vectors. The simplest cse occurs when vectors re colliner. Vectors re normlly represented y rrows. When dding, we used til-to-hed reltionship. Thus the til of the vector eing dded to the originl vector is plced t the hed of the originl vector. If they re in the sme direction, simply dd the mgnitudes of the vectors. The direction will e the sme s tht of the individul vectors. For emple, if someone wlked 10 m Est nd then 16 meters Est, we would drw the vectors s: The resultnt vector would e 6 m Est. It is drwn from the til of the first vector to the hed of the second one. If vectors re in the opposite direction, dd them, keeping in mind they hve opposite signs. The resultnt vector would e 6 m West. Sutrcting Colliner Vectors To sutrct two vectors, we simply hve to tke the opposite of the second vector nd dd it to the first.. Prctice: Add or sutrct the vectors s indicted. 15 m/s N + 0 m/s S. 40 m E + 60 m N c. 8 m N 15 m S Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 13

14 Adding non-colliner Vectors There re two methods of dding vectors tht will e discussed further in our -dimensionl kinemtics unit nd elow. Adding Perpendiculr Vectors The net simplest cse occurs when vectors re perpendiculr to ech other. We use the Pythgoren theorem to dd these vectors. For emple, if we hd force of 40 N pushing n oject due West nd force 30 N pushing n oject due North, we know the oject would move long pth etween the two forces s shown y the dshed line. A: Perpendiculr Vectors B: Direction of Resultnt C: Grphiclly dd the vectors hed-to-til nd drw the resultnt vector from the til of the first to the hed of the lst. Arrnging the vectors til-to-hed, the resultnt is now the hypotenuse, so it would equl 50 N s determined from the Pythgoren Theorem. To find the ngle, θ, tht the resultnt force cts long, we cn use the inverse tngent function. θ = Tn -1 (30/40) = 37 o ove the horizontl This tells us tht the two originl forces could e replced y single force of 50N cting t 37 o ove the horizontl. The 50N force t 37 o ove the horizontl is the sum of the originl forces. 3. Clculte the mgnitude nd direction of the resultnt vectors. (Hint: drw picture first then pply the Pythgoren theorem nd tngent function; rememer vectors hve mgnitude nd direction!). 5 m Est nd 4 m North. 3 m North nd 7 m West c. 5m/s N + m/s S + 4 m/s E + 6 m/s N Adding Vectors tht re not colliner nd not perpendiculr To dd vectors such s 70 m due E to 50 m t 30 o S of E we cn still use the grphicl technique of plcing the vectors hed-to-til nd drwing the resultnt vector from the til of the first vector to the hed of the second vector. It does not mtter which order we put the originl vectors in, the resultnt will lwys e the sme (give it try! However, if we wnt more ccurte numericl nswer, we will need to use n lgeric/trigonometric pproch. If we rek ech vector into its nd y components, we cn dd ll of the -components of the vectors s colliner vectors; similrly with ll the y-components. Then we cn use the Pythgoren theorem to dd the perpendiculr vectors tht we hve clculted. See the net pge! Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 14

15 Algeric/Trigonometric Approch to Finding the Resultnt A. Strt y drwing picture. Don t skip this step; it will help you void direction errors. Set up n -y system. Lel the positive nd negtive directions. B. Use trig to determine the nd y components of ech vector. Be sure to tke directions into ccount y using + nd signs.. The 70 meter vector lies long the + is. Its component is its full length, 70m nd it hs no y component.. The 50 meter vector must e roken into components. Drw the components in the nd y direction to mke right tringle. The originl vector is the hypotenuse. c. The component of the 50 m vector cn e found using the cosine function in this cse. The y component cn e found using the sine function Note the negtive sign since we re going in the negtive y direction. Cos 30 = /50, so = 50 cos30 = 43.3 m Sin 30 = -y/50, so y = -50 sin30 = -5 m Note: the component won t lwys e cosine. It depends on the ngle you use. C. Mke tle to orgnize your dt. D. Add the components nd the y components. E. Use the Pythgoren Theorem to determine the resultnt vector. F. Use the tn -1 function to find the ngle θ = tn -1 (5/113.3) = 1.4 o 4. How does one do mthemticl (i.e. not grphicl) vector ddition? 5. Resolve the following vectors into their components. (Hint: drw picture first then pply the sine nd cosine functions.). 35 m upwrds t n ngle of 5 o ove the horizontl. 5m/s t n ngle of 300 north of west Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 15

16 6. A ct climed verticlly up tree trunk m nd then wlked 3m out on horizontl rnch. Wht is its displcement from the ottom of the trunk? Clculte the mgnitude nd direction of the resultnt vector. (Hint: drw picture first then pply the Pythgoren theorem nd tngent function) 7. Tim climed 17m upwrds t n ngle of 6o ove the horizontl. () Wht is his horizontl displcement? () Wht is his verticl displcement? (Hint: drw picture first then pply the sine nd cosine functions to resolve the vector into its components.) 8. Add the following vectors oth grphiclly nd numericlly. m 15 o N of E + 64 m 5 o W of N + 38m due N THE END! Adpted y, Dominicn Sisters of Mry, Mother of the Euchrist pge 16