# Physics 101 Math Review. Solutions

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Physics 0 Math eview Slutins

2 . The fllwing are rdinary physics prblems. Place the answer in scientific ntatin when apprpriate and simplify the units (Scientific ntatin is used when it takes less time t write than the rdinary number des. s an example 00 is easier t write than.00x0, but.00x0 8 is easier t write than 00,000,000). D yur best t cancel units, and attempt t shw the simplified units in the final answer. a. T s kg. 0 0 kg s 3.98x0 - s b. K kg 0 4. (. m s).47x0 kg m /s c. F N m m 8.64x0-7 N d p P 3.04x0 e. e J J J 8.06x0 - f. 33. sin sin g Kmax J s s.7 0 J h m s m s. Often prblems n the exam are dne with variables nly. Slve fr the variable indicated. Dn t let the different letters cnfuse yu. Manipulate them algebraically as thugh they were numbers. a. v v a s s, a v ( ) - v 0 I g., r μ 0 I / (s-s 0 ) r b. K kx, x (K/k) (/) m L mλl/x h. xm, d m d c. T p l g, g 4π l d. F G m m g, r Gm m r e. f. mgh mv, v T p x x vt at, t F g gh -v v 0 - (x-x 0 )a a i. pv nt T n j. sin c, n k. l..5x0-9 J, pv/n c sin - (n /n ) qv mv, v f s s i, si qv/m f s 0

3 3. Science uses the KMS system (SI: System Internatinale). KMS stands fr kilgram, meter, secnd. These are the units f chice f physics. The equatins in physics depend n unit agreement. S yu must cnvert t KMS in mst prblems t arrive at the crrect answer. kilmeters (km) t meters (m) and meters t kilmeters gram (g) t kilgram (kg) centimeters (cm) t meters (m) and meters t centimeters millimeters (mm) t meters (m) and meters t millimeters elsius ( ) t Kelvin (K) atmspheres (atm) t Pascals (Pa) nanmeters (nm) t meters (m) and meters t nanmeters liters (L) t cubic meters (m 3 ) micrmeters ( m) t meters (m) Other cnversins will be taught as they becme necessary. What if yu dn t knw the cnversin factrs? lleges want students wh can d their wn infrmatin (s d emplyers). a g = kg h. 5.0 m.5x0 = m b.. km = 00 m i..65 mm =.65x0-3 m c. 83 nm = 8.3x0-7 m j. 8.3 m = 8.3x0-3 km d. 98 K = 5 k. 5.4 L = 5.4x0-3 m 3 e m = cm 77 l cm = 0.4 m f. 8.8x0-8 m = 8.8x0-5 mm m. 6.3x0-7 m = 63 nm g.. atm =.x0 5 Pa n..5x0 m =.5x0 8 km 6. Slve the fllwing gemetric prblems. a. Line tuches the circle at a single pint. Line extends thrugh the center f the circle. i. What is line in reference t the circle? Tangent ii. Hw large is the angle between lines and? 90 b. What is angle? c. What is angle? d. Hw large is?

4 e. The radius f a circle is 5.5 cm, i. What is the circumference in meters?.055**pi = 0.346m ii. What is its area in square meters?.055 *PI = 9.5x0-3 f. What is the area under the curve at the right? 4*+.5*4*8 = Using the generic triangle t the right, ight Triangle Trignmetry and Pythagrean Therem slve the fllwing. Yur calculatr must be in degree mde. 0 a. = 55 and c = 3 m, slve fr a and b. a= 8.4m, b= 6.m b. = 45 and a = 5 m/s, slve fr b and c. a= 0.6m/s, b= 0.6m/s c. b = 7.8 m and = 65, slve fr a and c. a= 8.30m, c= 9.6m Vectrs d. a = 50 m and b = 80 m, slve fr and c. 0 = 35.8, c = 308m e. a =5 cm and c = 3 cm, slve fr b and. b= 0cm, 0= 38.7 f. b =04 cm and c = 65 cm, slve fr a and. N slutin valid Mst f the quantities in physics are vectrs. This makes prficiency in vectrs extremely imprtant. Magnitude: Size r extent. The numerical value. Directin: lignment r rientatin f any psitin with respect t any ther psitin. Scalars: physical quantity described by a single number and units. quantity described by magnitude nly. Examples: time, mass, and temperature Vectr: physical quantity with bth a magnitude and a directin. directinal quantity. Examples: velcity, acceleratin, frce Ntatin: r Length f the arrw is prprtinal t the vectrs magnitude. Negative Vectrs Directin the arrw pints is the directin f the vectr. Negative vectrs have the same magnitude as their psitive cunterpart. They are just pinting in the ppsite directin. Vectr dditin and subtractin Think f it as vectr additin nly. The result f adding vectrs is called the resultant. + = S if has a magnitude f 3 and has a magnitude f, then has a magnitude f 3+=5. When yu need t subtract ne vectr frm anther think f the ne being subtracted as being a negative vectr. Then add them. 4

5 is really e j + e j = negative vectr has the same length as its psitive cunterpart, but its directin is reversed. S if has a magnitude f 3 and has a magnitude f, then has a magnitude f 3+(-)=. This is very imprtant. In physics a negative number des nt always mean a smaller number. Mathematically is smaller than +, but in physics these numbers have the same magnitude (size), they just pint in different directins (80 apart). There are tw methds f adding vectrs Parallelgram + Tip t Tail It is readily apparent that bth methds arrive at the exact same slutin since either methd is essentially a parallelgram. It is useful t understand bth systems. In sme prblems ne methd is advantageus, while in ther prblems the alternative methd is superir. 8. Draw the resultant vectr using the parallelgram methd f vectr additin. Example b. d. a. c. e. 9. Draw the resultant vectr using the tip t tail methd f vectr additin. Label the resultant as vectr Example : + a. X + Y Y X - Example : b. T S T S 5

6 c. P + V e. + + P V d. D f. D Directin: What des psitive r negative directin mean? Hw is it referenced? The answer is the crdinate axis system. In physics a crdinate axis system is used t give a prblem a frame f reference. Psitive directin is a vectr mving in the psitive x r psitive y directin, while a negative vectr mves in the negative x r negative y directin (This als applies t the z directin, which will be used sparingly in this curse). +y -x +x -y What abut vectrs that dn t fall n the axis? Yu must specify their directin using degrees measured frm East. mpnent Vectrs resultant vectr is a vectr resulting frm the sum f tw r mre ther vectrs. Mathematically the resultant has the same magnitude and directin as the ttal f the vectrs that cmpse the resultant. uld a vectr be described by tw r mre ther vectrs? Wuld they have the same ttal result? This is the reverse f finding the resultant. Yu are given the resultant and must find the cmpnent vectrs n the crdinate axis that describe the resultant. + y + y + x r + x ny vectr can be described by an x axis vectr and a y axis vectr which summed tgether mean the exact same thing. The advantage is yu can then use plus and minus signs fr directin instead f the angle. 0. Fr the fllwing vectrs draw the cmpnent vectrs alng the x and y axis. a. b. 6

7 c. d. Obviusly the quadrant that a vectr is in determines the sign f the x and y cmpnent vectrs. Trignmetry and Vectrs Given a vectr, yu can nw draw the x and y cmpnent vectrs. The sum f vectrs x and y describe the vectr exactly. gain, any math dne with the cmpnent vectrs will be as valid as with the riginal vectr. The advantage is that math n the x and/r y axis is greatly simplified since directin can be specified with plus and minus signs instead f degrees. ut, hw d yu mathematically find the length f the cmpnent vectrs? Use trignmetry x y cs adj hyp sin pp hyp adj hypcs pp hyp sin x hyp cs y hyp sin x 0cs40 y 0sin 40 x 766. y Slve the fllwing prblems. Yu will be cnverting frm a plar vectr, where directin is specified in degrees measured cunterclckwise frm east, t cmpnent vectrs alng the x and y axis. emember the plus and minus signs n yu answers. They crrespnd with the quadrant the riginal vectr is in. Hint: Draw the vectr first t help yu see the quadrant. nticipate the sign n the x and y vectrs. D nt bther t change the angle t less than 90. Using the number given will result in the crrect + and signs. The first number will be the magnitude (length f the vectr) and the secnd the degrees frm east. Yur calculatr must be in degree mde. Example: 50 at 35 b at 345 x hypcs 35 x 50cs35 x 43 x= 6.8 y= a. 89 at 50 y hyp sin y 50sin 35 y 05 c at 60 x= y=

8 d. 7.5x0 4 at 80 x= -7.5x0 4 y= 0 f. 990 at 30 x= 758 y= -636 e. at 65 x= -.05 y= -.95 g at 5 x= -69 y= -69. Given tw cmpnent vectrs slve fr the resultant vectr. This is the ppsite f number abve. Use Pythagrean Therem t find the hyptenuse, then use inverse (arc) tangent t slve fr the angle. Example: x = 0, y = -5 x y tan pp adj x y tan pp adj tan y x a. x = 600, y = 400 r= 7 0= 33.7 c. x = -3, y = 6 r= =-6.6 b. x = -0.75, y = -.5 r=.46 0= 59 d. x = , y = r= 0.0 0= 54. 8

9 e. x = 0,000, y = 4,000 f. x = 35, y = 998 Hw are vectrs used in Physics? They are used everywhere! Speed Speed is a scalar. It nly has magnitude (numerical value). v s = 0 m/s means that an bject is ging 0 meters every secnd. ut, we d nt knw where it is ging. Velcity ate Velcity is a vectr. It is cmpsed f bth magnitude and directin. Speed is a part (numerical value) f velcity. v = 0 m/s nrth, r v = 0 m/s in the +x directin, etc. There are three types f speed and three types f velcity Instantaneus speed / velcity: The speed r velcity at an instant in time. Yu lk dwn at yur speedmeter and it says 0 m/s. Yu are traveling at 0 m/s at that instant. Yur speed r velcity culd be changing, but at that mment it is 0 m/s. verage speed / velcity: If yu take a trip yu might g slw part f the way and fast at ther times. If yu take the ttal distance traveled divided by the time traveled yu get the average speed ver the whle trip. If yu lked at yur speedmeter frm time t time yu wuld have recrded a variety f instantaneus speeds. Yu culd g 0 m/s in a gas statin, r at a light. Yu culd g 30 m/s n the highway, and nly g 0 m/s n surface streets. ut, while there are many instantaneus speeds there is nly ne average speed fr the whle trip. nstant speed / velcity: If yu have cruise cntrl yu might travel the whle time at ne cnstant speed. If this is the case then yu average speed will equal this cnstant speed. trick questin Will an bject traveling at a cnstant speed f 0 m/s als always have cnstant velcity? Nt always. If the bject is turning arund a curve r mving in a circle it can have a cnstant speed f 0 m/s, but since it is turning, its directin is changing. nd if directin is changing then velcity must change, since velcity is made up f speed and directin. nstant velcity must have bth cnstant magnitude and cnstant directin. Speed and velcity are rates. rate is a way t quantify anything that takes place during a time interval. ates are easily recgnized. They always have time in the denminatr. 0 m/s 0 meters / secnd The very first Physics Equatin Velcity and Speed bth share the same equatin. emember speed is the numerical (magnitude) part f velcity. Velcity nly differs frm speed in that it specifies a directin. x v v stands fr velcity x stands fr displacement t stands fr time t Displacement is a vectr fr distance traveled in a straight line. It ges with velcity. Distance is a scalar and ges with speed. Displacement is measured frm the rigin. It is a value f hw far away frm the rigin yu are at the end f the prblem. The directin f a displacement is the shrtest straight line frm the lcatin at the beginning f the prblem t the lcatin at the end f the prblem. 9

10 Hw d distance and displacement differ? Suppses yu walk 0 meters dwn the + x axis and turn arund and walk 0 meters dwn the x axis. The distance traveled des nt depend n directin since it is a scalar, s yu walked = 30 meter. Displacement nly cares abut yur distance frm the rigin at the end f the prblem = 0 meter. 3. ttempt t slve the fllwing prblems. Take heed f the fllwing. lways use the MKS system: Units must be in meters, kilgrams, secnds. On the all tests, including the P exam yu must:. List the riginal equatin used.. Shw crrect substitutin. 3. rrive at the crrect answer with crrect units. Distance and displacement are measured in meters Speed and velcity are measured in meters per secnd Time is measured in secnds (m) (m/s) Example: car travels 000 meters in 0 secnds. What is its velcity? x 000m v v v 00m s t 0s a. car travels 35 km west and 75 km east. What distance did it travel? 0km (s) b. car travels 35 km west and 75 km east. What is its displacement? 8.8 km c. car travels 35 km west, 90 km nrth. What distance did it travel? 5km d. car travels 35 km west, 90 km nrth. What is its displacement? 96.6km e. bicyclist pedals at 0 m/s in 0 s. What distance was traveled? 00m f. n airplane flies 50.0 km at 300 m/s. Hw lng des this take? 833s g. skydiver falls 3 km in 5 s. Hw fast are they ging? 00m/s h. car travels 35 km west, 90 km nrth in tw hurs. What is its average speed? 6.5km/hr i. car travels 35 km west, 90 km nrth in tw hurs. What is its average velcity? 48.3km/hr 0

### AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) =

P Physics Name Summer ssignment 0 Date I. The P curriculum is extensive!! This means we have t wrk at a fast pace. This summer hmewrk will allw us t start n new Physics subject matter immediately when

### Name. Welcome to AP Physics. I am very excited that you have signed up to take the AP Physics class.

Name P Physics Summer ssignment Fall 013-014 Welcome to P Physics. I am very excited that you have signed up to take the P Physics class. You may ask I sure would why a summer packet? There is so much

### Be prepared to take a test covering the whole assignment in September. MATH REVIEW

P- Physics Name: Summer 013 ssignment Date Period I. The attached pages contain a brief review, hints, and example problems. It is hoped that combined with your previous math knowledge this assignment

### VECTORS REVIEW. ii. How large is the angle between lines A and B? b. What is angle C? 45 o. 30 o. c. What is angle θ? d. How large is θ?

VECTOS EVIEW Solve the following geometric problems. a. Line touches the circle at a single point. Line etends through the center of the circle. i. What is line in reference to the circle? ii. How large

P Physics Summer ssignment I. The dvanced placement eams are in early May which necessitates a very fast pace. This summer homework will allow us to start on the Physics subject matter immediately when

### AP Physics C - Summer Assignment Mr. Bartolotta - Half Hollow Hills HS West Fall 2017 Spring Hmmm..I think we need a bigger mule.

P Physics C - Summer ssignment Name Mr. artolotta - Half Hollow Hills HS West Fall 017 Spring 018 Hmmm..I think we need a bigger mule. This upcoming year in physics will be reexamining many concepts you

### AP PHYSICS B SUMMER ASSIGNMENT: Calculators allowed! 1

P PHYSICS SUMME SSIGNMENT: Calculators allowed! 1 The Metric System Everything in physics is measured in the metric system. The only time that you will see English units is when you convert them to metric

### AP Physics 1 SUMMER ASSIGNMENT

Name: P Physics 1 SUMME SSIGNMENT Welcome Welcome to P Physics 1 at Hardin Valley academy. For many of you, this will be your first full physics course. Fortunately, we will cover many of the concepts

### AP-1 Physics. Summer 2016 Assignment Date Period. Name: What is due the first day of school? When is this assignment due? MATH REVIEW =

P- Physics Name: Summer 06 ssignment Date Period I. The attached pages contain a brief review, hints, and example problems. It is hoped that combined with your previous math knowledge this assignment is

### AP Physics 1 Summer Assignment 2016

AP Physics 1 Summer Assignment 2016 You need to do this assignment on your own paper AND YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT. You can put the answers on this assignment sheet or you can put

### NUMBERS, MATHEMATICS AND EQUATIONS

AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

### Putting Scientific Notation to Work

10 Putting Scientific Ntatin t Wrk Physics deals with sme very large and very small numbers. T wrk with such numbers, yu use scientific ntatin. Scientific ntatin is expressed as a number multiplied by

### MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

### Differentiation Applications 1: Related Rates

Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

### SPH3U1 Lesson 06 Kinematics

PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

### AP Physics 1 Summer Assignment

P Physics Summer ssignment. Scientific Notation: The following are ordinary physics problems. Write the answer in scientific notation and simplify the units (π=3). a. T s 4. 50 kg. 0 0 kg s 3 = b. F Nm

### AP Physics 1 Summer Assignment

P Physics 1 Summer ssignment 1. Scientific Notation: "#\$%&''&()*+\$,-#\$&-.)*,-/\$0"/1)1\$0-&3'#415\$\$6-)7#\$7"#\$,*1(#-\$)*\$1)#*7)%)\$*&7,7)&*\$,*.\$1)40')%/\$7"#\$8*)71\$9:;

### making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

### BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT

AP Physics C - Mechanics Due: September 2, 2014 Name Time Allotted: 8-10 hours BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT 2014-2015 Teacher: Mrs. Kent Textbook: Physics for Scientists

### UCONN ECE/AP Physics Summer Assignment

UCONN ECE/AP Physics Summer Assignment Name Fall 06 Spring 07 We have read the policies and expectations for UCONN ECE Physics in the attached syllabus. We understand and accept these policies. Student

### 1 Course Notes in Introductory Physics Jeffrey Seguritan

Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is

### AP Physics 1 Summer Assignment 2017

P Physics 1 Summer ssignment 2017 The attached pages contain a brief review, hints, and example problems. It is hoped that based on your previous math knowledge and some review, this assignment will be

### LOS FRESNOS HIGH SCHOOL

LOS FESNOS HIGH SCHOOL 017 Summer ssignment P Physics 1 and P Physics 1 Dual Course Description lgebra level physics course, with laboratories, that includes study of mechanics, fluids, heat, thermodynamics,

### Mr. Grunbeck - Half Hollow Hills HS East Fall 2018 Spring 2019

P Physics C - Summer ssignment Name Mr. Grunbeck - Half Hollow Hills HS East Fall 018 Spring 019 Hmmm..I think we need a bigger mule. This upcoming year in physics will be reexamining many concepts you

### 1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?

1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is

### Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1

Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs

### NORTHERN BURLINGTON COUNTY REGIONAL HIGH SCHOOL. Honors and Advanced Placement Program Supplemental Assignment. AP Physics B

NOTHEN ULINGTON COUNTY EGIONL HIGH SCHOOL Honors and dvanced Placement Program 013 Supplemental ssignment P Physics equired Materials dditional esources None Physics & Math Tutorials on the Web www.hippocampus.org

### CHAPTER 8b Static Equilibrium Units

CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but

### Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

### AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

### Figure 1a. A planar mechanism.

ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,

### This chapter gets the ball rolling by discussing some fundamental physics measurements.

Chapter Getting Started with Physics In This Chapter Laying dwn measurements Simplifying with scientific ntatin Practicing cnversins Drawing n algebra and trignmetry This chapter gets the ball rlling by

### Chapter 2. Kinematics in One Dimension. Kinematics deals with the concepts that are needed to describe motion.

Chapter Kinematics in One Dimensin Kinematics deals with the cncepts that are needed t describe mtin. Dynamics deals with the effect that frces have n mtin. Tgether, kinematics and dynamics frm the branch

### Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

### CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,

### Introduction to Spacetime Geometry

Intrductin t Spacetime Gemetry Let s start with a review f a basic feature f Euclidean gemetry, the Pythagrean therem. In a twdimensinal crdinate system we can relate the length f a line segment t the

### Cop yri ht 2006, Barr Mabillard.

Trignmetry II Cpyright Trignmetry II Standards 006, Test Barry ANSWERS Mabillard. 0 www.math0s.cm . If csα, where sinα > 0, and 5 cs α + β value f sin β, where tan β > 0, determine the exact 9 First determine

### Trigonometric Ratios Unit 5 Tentative TEST date

1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

### Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec

U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.

### Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

### Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

### Review for the final exam (Math 127)

. Evaluate 3 tan tan 4 3 (b) (c) cs cs 4 7 3 sec cs 4 4 (d) cs tan 3 Review fr the final eam (Math 7). If sec, and 7 36, find cs, sin, tan, ct, csc tan (b) If, evaluate cs, sin 7 36 (c) Write the csc in

### Physics 2010 Motion with Constant Acceleration Experiment 1

. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

### Being able to connect displacement, speed, and acceleration is fundamental to working

Chapter The Big Three: Acceleratin, Distance, and Time In This Chapter Thinking abut displacement Checking ut speed Remembering acceleratin Being able t cnnect displacement, speed, and acceleratin is undamental

### Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

### Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

### PHYS 314 HOMEWORK #3

PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des

### ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

### Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations

STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.

### EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017

OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a

### 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes

### CHAPTER 1 -- MATH REVIEW

Slutins--Ch. 1 (Math Review) CHAPTER 1 -- MATH REVIEW 1.1) Bth Parts a and b are straight vectr additin, graphical stle. Yu need a centimeter stick and prtractr t d them. a.) In this case, the velcit cmpnent

### 14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which

### Mrs. Quire - AP Physics 1 Summer Review

Mrs. Quire - P Physics Summer eview 08-09 Welcome to my P Physics class! It is an algebra based, college level course that will be interesting but challenging! P Physics is NOT an honors level course;

### Concept Category 2. Trigonometry & The Unit Circle

Cncept Categry 2 Trignmetry & The Unit Circle Skill Checklist Use special right triangles t express values f fr the six trig functins Evaluate sine csine and tangent using the unit circle Slve tw-step

### This summer assignment will be worth 55 points in the first quarter.

P PHYSICS SUMME SSIGNMENT Hello: I am very glad that you signed up for P Physics and I look forward to teaching this class! While Calculus is not required as a prerequisite to this course, mastery of lgebra,

### Stage 6 PROMPT sheet. 2 > -2 We say 2 is bigger than -2-2 < 2 We say -2 is less than 2. 6/2 Negative numbers. l l l l l l l

Stage 6 PROMPT sheet 6/ Place value in numbers t 0millin The psitin f the digit gives its size Ten millins Millins Hundred thusands Ten thusands thusands hundreds tens units 4 5 6 7 8 Example The value

### Study Guide Physics Pre-Comp 2013

I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)

### Phys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1

Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively.

### Kinematics. Describing Motion. Reference Frames. Measurements of position, distance or speed must be with respect to a frame of reference.

Kinematics Describing Mtin Reference Frames Measurements f psitin, distance r speed must be with respect t a frame f reference. What is the speed f a persn with respect t the grund if she walks tward the

### Chapter 5: Force and Motion I-a

Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse

### EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016

OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a

### / / Chemistry. Chapter 1 Chemical Foundations

Name Chapter 1 Chemical Fundatins Advanced Chemistry / / Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne

### Physics 1200 Mechanics, Kinematics, Fluids, Waves

Physics 100 Mechanics, Kinematics, Fluids, Waes Lecturer: Tm Humanic Cntact inf: Office: Physics Research Building, Rm. 144 Email: humanic@mps.hi-state.edu Phne: 614 47 8950 Office hurs: Tuesday 3:00 pm,

### M thematics. National 5 Practice Paper C. Paper 1. Duration 1 hour. Total marks 40

N5 M thematics Natinal 5 Practice Paper C Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain

### This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

### M thematics. National 5 Practice Paper E. Paper 1. Duration 1 hour. Total marks 40

N5 M thematics Natinal 5 Practice Paper E Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain

### i-clicker!! x 2 lim Lecture 3 Motion in 2- and 3-Dimensions lim REVIEW OF 1-D MOTION

Lecture 3 Mtin in - and 3-Dimensins REVIEW OF -D MOTION TODY: LSTCHNCETOMKEUPTHEPHYSICS PRETEST(u get pints fr cmpleting the pre and pst tests) Where: SERC 6 (SEC 6) When: Yucanarrieantime3:0pm 6:30 pm

### Chapter 9 Vector Differential Calculus, Grad, Div, Curl

Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields

### 1 PreCalculus AP Unit G Rotational Trig (MCR) Name:

1 PreCalculus AP Unit G Rtatinal Trig (MCR) Name: Big idea In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin will invlve the unit circle which will

### Kinetics of Particles. Chapter 3

Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

### Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).

Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)

### Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law

Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential

### Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

### Algebra2/Trig: Trig Unit 2 Packet

Algebra2/Trig: Trig Unit 2 Packet In this unit, students will be able t: Learn and apply c-functin relatinships between trig functins Learn and apply the sum and difference identities Learn and apply the

### Name AP CHEM / / Chapter 1 Chemical Foundations

Name AP CHEM / / Chapter 1 Chemical Fundatins Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne value and anther.

### LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers

LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the

### EASTERN ARIZONA COLLEGE Precalculus Trigonometry

EASTERN ARIZONA COLLEGE Precalculus Trignmetry Curse Design 2017-2018 Curse Infrmatin Divisin Mathematics Curse Number MAT 181 Title Precalculus Trignmetry Credits 3 Develped by Gary Rth Lecture/Lab Rati

### = m. Suppose the speed of a wave on a string is given by v = Κ τμ

Phys101 First Majr-11 Zer Versin Sunday, Octber 07, 01 Page: 1 Q1. Find the mass f a slid cylinder f cpper with a radius f 5.00 cm and a height f 10.0 inches if the density f cpper is 8.90 g/cm 3 (1 inch

### WYSE Academic Challenge Regional Mathematics 2007 Solution Set

WYSE Academic Challenge Reginal Mathematics 007 Slutin Set 1. Crrect answer: C. ( ) ( ) 1 + y y = ( + ) + ( y y + 1 ) = + 1 1 ( ) ( 1 + y ) = s *1/ = 1. Crrect answer: A. The determinant is ( 1 ( 1) )

### Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

### Preparation work for A2 Mathematics [2017]

Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will

### Study Guide: PS. 10 Motion, Forces, Work & Simple Machines DESCRIBING MOTION SPEED

DESCRIBING MOTION Distance: hw far smething has mved; SI unit meters (m) Reference pint: nn-mving bject used as a cmparisn pint t detect an bject s mtin. Displacement: the distance between the starting

### ( ) + θ θ. ω rotation rate. θ g geographic latitude - - θ geocentric latitude - - Reference Earth Model - WGS84 (Copyright 2002, David T.

1 Reference Earth Mdel - WGS84 (Cpyright, David T. Sandwell) ω spherid c θ θ g a parameter descriptin frmula value/unit GM e (WGS84) 3.9864418 x 1 14 m 3 s M e mass f earth - 5.98 x 1 4 kg G gravitatinal

### Trigonometry, 8th ed; Lial, Hornsby, Schneider

Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the

### CHAPTER 6 -- ENERGY. Approach #2: Using the component of mg along the line of d:

Slutins--Ch. 6 (Energy) CHAPTER 6 -- ENERGY 6.) The f.b.d. shwn t the right has been prvided t identify all the frces acting n the bdy as it mves up the incline. a.) T determine the wrk dne by gravity

### Solution to HW14 Fall-2002

Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

### Trigonometric Functions. Concept Category 3

Trignmetric Functins Cncept Categry 3 Gals 6 basic trig functins (gemetry) Special triangles Inverse trig functins (t find the angles) Unit Circle: Trig identities a b c 2 2 2 The Six Basic Trig functins

### PRE-CALCULUS B FINAL REVIEW NAME Work out problems in your notebook or on a separate piece of paper.

PRE-CALCULUS B FINAL REVIEW NAME Wrk ut prblems in yur ntebk r n a separate piece f paper. CHAPTER 5 Simplify each t ne trig wrd r a number: tan (1) sec sec () sin ct + 1 + cs + ( sin cs ) () sin - cs

### Preparation work for A2 Mathematics [2018]

Preparatin wrk fr A Mathematics [018] The wrk studied in Y1 will frm the fundatins n which will build upn in Year 13. It will nly be reviewed during Year 13, it will nt be retaught. This is t allw time

### NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 3 Trigonometry, 9th Edition; Lial, Hornsby, Schneider Fall 2008

NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 Departmental Objectives: Departmental Final Exam Review fr Trignmetry Part : Chapters

### 4. Find a, b, and c. 6. Find x and y.

Grace Brethren Christian Schl Entering Trig/Analysis: Page f Summer Packet fr Students entering Trig/Analysis Review prblems frm Gemetry: Shw yur wrk!. Twice the cmplement f angle A is 35 less than the

### Kansas City Area Teachers of Mathematics 2011 KCATM Math Competition GEOMETRY GRADES 7-8

Kansas City Area Teachers f Mathematics 2011 KCATM Math Cmpetitin GEOMETRY GRADES 7-8 INSTRUCTIONS D nt pen this bklet until instructed t d s. Time limit: 20 minutes Yu may use calculatrs. Mark yur answer

### Biochemistry Summer Packet

Bichemistry Summer Packet Science Basics Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne value and anther.

### INSTRUCTIONAL PLAN Day 2

INSTRUCTIONAL PLAN Day 2 Subject: Trignmetry Tpic: Other Trignmetric Ratis, Relatinships between Trignmetric Ratis, and Inverses Target Learners: Cllege Students Objectives: At the end f the lessn, students

### Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W

Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = 60 9. 81 =

### Higher Mathematics Booklet CONTENTS

Higher Mathematics Bklet CONTENTS Frmula List Item Pages The Straight Line Hmewrk The Straight Line Hmewrk Functins Hmewrk 3 Functins Hmewrk 4 Recurrence Relatins Hmewrk 5 Differentiatin Hmewrk 6 Differentiatin