Introductory Physics I
Introductory Physics I PHYS 201
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This 8 page Study Guide was uploaded by Madyson Sporer on Monday October 5, 2015. The Study Guide belongs to PHYS 201 at Christian Brothers University taught by Staff in Fall. Since its upload, it has received 57 views. For similar materials see /class/219460/phys-201-christian-brothers-university in Physics 2 at Christian Brothers University.
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Date Created: 10/05/15
PHYS 201 STUDY GUIDE FOR PART TWO FORCES AND MOTION INTRODUCTION In this second part ofthe course we consider a two dimensional motion combining 1D motion with vectors b the relation between force and motion which introduces the concept of mass and Newton39s three laws of motion and c one ofthe four fundamental forces gravity We begin this section by looking at two dimensional motion This combines the ideas of position velocity and acceleration with the idea of a vector having components We look at three special cases trajectory motion uniform circular motion and relative velocity We next introduce the concept of INERTIAL MASS as a basic quality of matter It is the quality that determines how a force will affect the motion of an object This extremely important relation between force and motion is contained in a very simple equation 2F m a called NEVVTON39S SECOND LAW We also consider Newton39s first which is a special case of Newton39s Second Law and Newton39s third law which is important in determining who is pushing on whom As an important example of force we consider Newton39s Law of Gravity and how it relates to the concept of GRAVITATIONAL MASS Next we consider the concept of torque or angular force and its relation to rotations and force TWO DIMENSIONAL MOTION OUTLINE 1 Projectile motion work in components M a xt and yt 2 Uniform circular motion turning but not speeding up N a frequency 1 fis frequency in cyclessec 2 n 2nf n is angular velocity in radianssec 3 T 1f T is period in seccycle b tangential velocity vtang or 2nrT circular means rconstant so vradial 0 c radial acceleration aradial mvtang mzr vtangzr d tangential acceleration causes speed to change so uniform circular motion means atang O 3 Relative velocity addition of vectors 0 LETTER PROBLEMS M A ball is thrown from the top of a 14 m high building with a speed of 25 ms directed at an angle of 33 above the horizontal a How far away will the ball hit the ground b How long will it take the ball before it hits the ground N The earth spins with approximately uniform circular motion about its axis The radius of the earth 6378 kilmeters a What is the period ofthe earth39s rotation about its axis b What is the tangential speed of the earth at the equator as it spins c What is the angular velocity ofthe earth as it spins d Is the earth undergoing acceleration as it spins e What is the radial acceleration of the earth at the equator as it spins f What is the tangential acceleration ofthe earth at the equator as it spins O A boat can travel at a speed of5 msec on a calm lake a What direction sould a pilot point his boat to go directly across a river that ows at a rate of 2 msec b How long will it take if the river is 200 meters wide 0 What direction should he head his boat if he wants to just get across the river in the least time d How long will be the least time PHYS 201 Study Guide for Part 2 page 2 ANSWERS TO LETTER PROBLEMS M a 7501 m b 358 sec N a T 1 day 86400 sec b 463 ms 1039 mph 0 727 X 10395 rads d YES e 0034 ms2 f 0 ms2 O a 236 upstream b 436 sec 0 straight across d 40 sec THE LAWS OF MOTION OUTLINE 1 The relation of force and motion Newton39s Laws of Motion P a inertial mass quality of matter b Newton39s second law 2F ma ie 2FX max EFy may 2Fz maz 1 units of mass kg 2 units of force Nt 3 this is a vector equation COMPONENTS c Newton39s first and third laws 1 rst law special case ZF0 ofthe second law 2 third law actionreaction who pushes on whom can39t push yourself 2 Applications QRS a force of gravity on surface of earth Fgr Weight m g down b force of contact or normal force FC is balancing J to surface c friction Ffr S ch ie balancing upto a point to surface d spring force Fspring k X e X and y component equations f parallel and perpendicular component equations 9 circular motion and centripetal force Fm is due to real forces it is not a different force h pulleys and mechanical advantage count the ropes attached 3 Gravitational force T a gravitational mass quality of matter Fgravityoc m b gravitational mass amp inertial mass different qualities same quantity 0 Newton39s law of gravity F Gm1m2r2 where G667X10 11 Nt m2kg2 d mass and weight Weight Fgravny m g where g G M r2 e gravity weight and g 1 g on earth g G M5 rthRerm2 98 ms2 2 9 above earth 9 G Mearth Rearth h2 gabove lt gsurface 3 g on other planets moons asteroids etc 4 Orbits Circular motion due to gravity U 3 Fgr m acircular or GMearthrT39lsatr2 msatmzr 5 Artificial weight Circular motion seems like gravity V 3 gaffective acircular 1er PHYS 201 Study Guide for Part 2 page 3 6 Torque and rotations WXY a torque causes rotations b c r F sin0 where 0 is the angle between r and F c statics ZF0 and 2 0 d mechanical advantage levers and clubs LETTER PROBLEMS P A body hangs from a spring balance supported from the roof ofan elevator a lfthe elevator has an upward acceleration of 2 ms2 and the balance reads 200 Nt what is the true weight ofthe body b Under what circumstances will the balance read 150 Nt c What will the balance read if the elevator cable breaks Q Given the force as a function oftime Ft 5 Nt cos03 radsect a graph the force versus time b graph the acceleration versus time c graph the velocity versus time d graph the position versus time R What is the acceleration of block A in the figure below given that the mass ofA is 5 kg the mass of B is 3 kg and the coef cient of friction between A and the table is 015 39 mA5kg mB3kg B u015 8 Given that an object of mass 3 kg starts from the origin xo 0 with a speed of 5 ms vo 5ms and given that it is attached to a spring that exerts a force Fsx kx where k 12 Ntm the spring constant nd a the acceleration at t0 when the object starts b assuming that the object experiences this acceleration for 01 seconds nd by numerical methods its approximate new speed and new position at t01 sec 0 do this process nine more times to find the approximate speed and position at the end of the rst full second d graph the acceleration versus time the velocity versus time and the position versus time all between t0 and t1 second e extra credit Try using a computer program or program your calculator to do the above numerical approximation and follow the motion for several seconds See what happens to the motion as your vary the mass T What is the acceleration due to gravity on Mars Mars has a mass of 64 x 1023 kg and a radius of 3400 km U a At what radius should a geosynchronous satellite period 24 hours of mass 50 kg orbit the earth b What speed should this satellite have to remain in orbit c What is the gravitational force on the satellite in orbit d How does this compare to the gravitational force on the satellite when it was on the earth39s surface getting ready for launch PHYS 201 Study Guide for Part 2 page 4 V A space station is built in the shape ofa cylinder of length 1 km and radius 200 m and is spun about the axis of the cylinder a lfan effective gravity of 60 that of earth is desired what should the period ofthe spin be b How fast is the outside edge moving c Which direction is up W Consider a car of known mass m going around a turn ofradius r as fast as it can without sliding off the road don39t worry about ipping over here Consider that the curve is banked at some angle q with respect to the horizontal and that the tireroad coef cient of friction is m a Draw a picture ofthe situation and draw in arrows indicating all the forces that act on the car during the turn You do not have to considerthe force due to the engine orthe force due to air resistance b Draw an arrow indicating the direction ofthe acceleration during the turn c Set up Newton39s Equations of Motion for this situation d Indicate what quantities are knwon and what are unknown in the problem e Indicate any other equations that can be used to solve the problem X a Estimate the distance from your elbow to where your biceps are connected to your forearm b Estimate the distance your hand is from your elbow c Neglecting the weight of the forearm and hand how much force must the biceps exert for you to hold a 2 lb object in your hand assume that the forearm is horizontal and the elbow is bent at an angle of 90 Y You are to pick up and hold horizontal a board that has a weight of 25 lb and a length of8 ft You do so by lifting up 1 ft from the left end with the right hand and pushing down on the left end at the end with the left hand a What is the force that the right hand must exert to hold the board horizontal b What is the force that the right hand must exert ANSWERS TO LETTER PROBLEMS P a m 1695 kg W 1661 Nt b a 95 ms2 c T 0 Nt Q 276 ms2 R You are on your own S You are on your own See if your answer corresponds to what you would expect of a spring T 38 gem 37 ms2 U a 42300 km b 3076 ms c 224 Nt d 118490 or 2 V a 3664 sec b 3429 ms c toward the axis W You are on your own X answer will depend on your physical stature Y a 100 lb b 75 lb PHYS 201 STUDY GUIDE FOR PART ONE VECTORS AND BASIC MOTION INTRODUCTION In this first part ofthe course we consider 1 what physics is 2 the concept of vectors and 3 the basic description of motion We first of all consider what physics is A first attempt at a definition might be this Physics is the science that considers the basic structure of matter the basic properties of matter the basic interactions between pieces of matter and the basic descriptions of motion Physics attempts to describe as many natural phenomena happenings as it can in terms of as few basic principles laws as it can Note Natural phenomena are usually very complex things and to start with we will be making many idealizations and simplifying assumptions Once the basic principles are known you can begin to consider removing some ofthese simplifying assumptions and try to obtain more and more accurate descriptions of real phenomena INTRODUCTION OUTLINE 1 Introduction A a de nition of physics b review of math algebra simultaneous equations 0 measurements dimensions and units d the metric system meters kilograms seconds e dimensional analysis f order of magnitude estimates 2 Positions BCD a lengths b angles 9in radians sr where s is arclength 0 2 D coordinate systems 1 rectangular Xy most basic due to addition properties 2 polar re most common magnitude direction 3 lattitude and longitude on curved surface of earth d transformations from one form to the other 1 polarto rectangular X r cose y r sine 2 rectangularto polar r IX2 y2 e tan391yX 3 Vectors E a idea ofa vector magnitude and direction position is example b components of a vector MOST IMPORTANT 1 rectangular X and y components 2 polar magnitude and direction 3 three or more dimensions 0 addition and subtraction of vectors addsubtract rectangular components 4 Force a the idea of force a push or pull b force is a vector it has magnitude and direction 0 forces can be added as vectors to get resultant force Phys 201 Part 1 page 2 LETTER PROBLEMS A Given the following three equations solve them for X y and z ax by CZ 5 where abc are the last three digits of your phone number eg 3213448 means a4 b4 c8 dX ey f2 8 where def are the last three digits of your oryour parent39s street address or box number gX hy k2 0 where ghk are the last three digits of your or your parent39s zip code HINT in the look back stage step 7 check your answers by substituting in your answers into the equations to show that they indeed work B lfthe arc length is 30 meters and the radius is 12 meters what is the angle a in radians b in degrees c in revolutions C The moon has a diameter of 3500 km and is 384000 km away What angle does the moon make with a person39s eye D What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls fonNard 34 ofa revolution The radius of the wheel is 39R39 and the 39Xaxis39 is the forward direction HINT break the motion into two part the translation of the wheel and the rotation ofthe wheel Only look at initial and final points not the actual trajectory E A car drives five blocks East turns North for two blocks then turns back West for 2 blocks What is the nal position ofthe car relative to the initial position Express in both rectangular and polar form ANSWERS TO LETTER PROBLEMS A you are on your own you should be able to check this yourself B a 025 radians b 1432 0 00398 revolutions o 911 x103 radians o52 D 571R 100R or 580R 99 E 3 blocks East 2 blocks North or 361 blocks 337 North of East MOTION IN ONE DIMENSION OUTLINE 1 Introduction Motion is change in position with time 2 Velocity change in position with time a average velocity vxavg AXAt use with DISCRETE DATA POINTS amp NUMERICAL METHODS computers b velocity is a vector magnitude speed and direction but work in rectangular c instantaneous velocity vxdnst dxtdt calculus derivative use with FUNCTIONS A v Acceleration change in velocity with time F a average acceleration axavg AvXAt use with DISCRETE DATA POINTS amp NUMERICAL METHODS computers b acceleration is a vector magnitude and direction but work in rectangular c instantaneous acceleration axing dvxtdt another derivative use with FUNCTIONS Phys 201 Part 1 page 3 4 Going backward nding vX from ax X from vX G 3 AVX aXavg At or VX nal VXinit aXavgt b AX VXavg At or Xfinal Xinit VXavgt c for functions can use calculus inverse of derivative is integral 5 A useful special case constant acceleration H a formulas from calculus Xt Xo vot 12at2 vt vo at b freely falling bodies ay 98 ms2 means up means down freely means with negligible air resistance 6 Motion graphs JKL a getting velocity from position slope of xt lt3 value ofvt b getting acceleration from velocity slope of vt lt3 value of at c getting position from velocity value of vt lt3 slope ofXt d getting velocity from acceleration value of at lt3 slope ofvt LETTER PROBLEMS F Below are the numerical values of position at specific times a Calculate the average velocity between each two times b Assuming the average velocities calculated in the previous part are equal to the velocities at the midpoint in the time interval calculate the average accelerations between the midpoints in time which are approximately the accelerations at the actual time points X in m t in sec X in m t in sec 500 0 250 4 433 1 433 5 250 2 500 6 000 3 433 7 G Below are the numerical values ofvelocity at specific times as well as the functional eXpression for velocity a Using the numerical method calculate both the average acceleration during the time between t8 and t9 seconds and calculate the position at t9 seconds You should assume that x20 m when t0 ie Xo20m b To check yourself use the functional form for at and Xt given below this was derived using calculus assuming Xo20 Speci cally evaluate the acceleration at t85 sec and compare to the average accleration between t8 and t9 sec and evaluate the position at t9 sec and compare to what you got using the numerical procedure HINT remember for the numerical method you use vg AXAt and a5 g AvAt where AX X1 X At t1 t NUMERICAL DATA vO sec 500 ms v5 sec 325 ms v1 sec 493 ms v6 sec 248 ms v2 sec 472 ms v7 sec 157 ms v3 sec 437 ms v8 sec 52 ms v4 sec 388 ms v9 sec 67 ms v10sec 200 ms FUNCTIONAL FORMS vt 50 ms 0700 ms3t2 at 1400 ms3t Xt 20m 500 mst 0233 ms3t3 Phys 201 Part 1 page 4 H A car accelerates assume uniformly from rest with an acceleration of 18 ms2 a How long a time will it take forthe car to reach a speed of 25 ms b How far will the car have gone in this time c How fast will the car be going after 10 seconds d How far will the car have gone after 10 seconds A ball is thrown upwards from the top ofa building 14 meters high with an initial speed of 25 ms a How long will it take the ball to reach it39s highest point b How high will this highest point be c How long will it take the ball to hit the ground at the bottom of the building d How fast will the ball be going when it hits the ground J For the situation in problem G above graph vt versus t From this graph be able to qualitatively graph Xt versus t and at versus t K Below is a graph of Xt On the graphs beside it sketch vt and at L Below is a graph of axt On the graphs beside it sketch Xt and vxt assuming that Xo gt O and vxo lt O ANSWERS TO LETTER PROBLEVIS F a v in ms tin sec v in ms tin sec b a in ms2 tin sec a in ms2 tin sec 067 05 116 1 183 45 067 4 183 15 067 55 067 2 116 5 250 25 067 65 000 3 134 6 250 35 G anum 119 ms2 acal 119 ms2 Xnum 25885 m Xcal 26014 m H a 1389 sec b 17361 m c 18 ms d 90 m l a 255 sec b 4589 m c 561 sec d 2999 ms
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