PHYSICS 2010 Final Exam Review Session

Transcription

1 1/9/011 PHYSICS 010 Final Ea Review Session Note that this review is not covering everthing. Rather it is highlighting ke points and concepts. Inforation on Course Web Page The final ea will cover aterial including Chapters 1-14; CAPA hoework assignents 1-15; All Lecture Material, and all Section labs and assignents. Note that the ea is cuulative and there will not be a disproportionate ephasis on the aterial since the 3rd idter. The ea will be ultiple choice questions. The ea is closed book and closed notes. Calculators are allowed, but no sharing of calculators. A forula sheet will be included with our ea, and a preview of that identical sheet is linked here as a PDF file. There is no need to print and bring this sheet as a cop will be included with the ea. A practice ea and solutions are available on the course CULearn page; ou a ignore proble 37 on this ea. The ea will be held on the west side of the Coors Event Center; our seat assignents will be posted on CULearn. Reinder of Materials Available Tetbook and eaple probles in the tet Professor Dubson s Chapter Notes (see link on web page) Clicker questions as posted in lecture notes CAPA probles, solutions on CULearn Practice ea and solutions on CULearn CH. Kineatics in 1D.1 Reference fraes and displaceent. Average velocit.3 Instantaneous velocit.4 Acceleration.5 Motion at constant acceleration.6 Solving probles.7 Falling objects.8 Graphical analsis of linear otion Three idter eas and solutions on CULearn Lab anuals and probles Motion under constant acceleration Motion under constant acceleration What are soe eaple probles? Finall: algebra, trigonoetr, unit conversion. 1

2 1/9/011 A sailboat is being blown across the sea at a constant velocit. What is the direction of the net force on the boat? CH. 3 Kineatics in D: Vectors 3.1 Vectors and scalars 3. Addition of vectors graphicall 3.3 Vector subtraction and ultiplication b a scalar 3.4 Adding vectors b coponents 3.5 Projectile otion 3.6 Solving probles The vector A has agnitude A = 6 c and akes an angle of q = 30 degrees with the positive -ais as shown. A q What is the -coponent of the vector A? A) +4.0 c B) -3.0 c C) +5. c D) - 5. c E) None of the above Football Punter Phsics For a specific pla, the punter wants to kick the ball as far down the field as possible (i.e. aiu range). What is the optial angle to kick the ball at assuing the sae initial speed when kicked regardless of the angle? Football obes the laws of phsics. Constant acceleration case (ignoring air resistance).

3 1/9/011 q 1 t 1 t 0 v0t a 0 v0t a 0 0 v v 0 a 0 0 cos q ( v0 cos q) t 0 0 v v sinq 0 a g ( v sinq) t 1 gt 0 0 Approach 1. At what tie (t) does the ball hit the ground (i.e. when is =0). Then evaluate the position at that tie (thus giving the Range) ( v0 cos q) t ( v sinq) t 1 gt 0 q Clearl at t =0, =0 and =0 (our initial conditions). At what later tie does the football hit the ground? A) t = 10 seconds 0 ( v0 sinq) t 1 gt B) t = v 0 tanq 0 t( v 1 0 sinq) gt C) t = Sqrt( v 0 sinq/g) D) t = v 0 sinq/g ( v 1 0 sinq) gt 0 E) None of the above t ( v0 sinq) / g ( v0 cos q) t ( v sinq) t 1 gt 0 q Tie of football flight (i.e. hang tie) t ( v0 sinq) / g Now plug into -equation to find out position when it hits the ground. ( v0 cos q) v0 sinq / g v0 cosq sinq v sin q 0 g g * Uses trigonoetr identit cosqsinq=sinq Reeber: A large part of what ou ll be epected to do is to appl Newton s Laws. You can t just eorize and appl forulas. Steps for Linear Motion: 1. Draw a free-bod diagra identifing and labeling all forces.. Choose a coordinate sste tpicall with the forces pointing in the coordinate directions (,) as uch as possible. 3. Write down Newton s nd law in each coordinate direction (tpicall), suing the forces. The equation perpendicular to the direction of otion often allows ou to find the Noral Force, which is needed to deterine the force of friction. Σ F = a Σ F = a (for rectilinear otion) If a force is not in a coordinate direction, ou ust find its coponents in the coordinate directions. 4. If there is ore than one ass, then Newton s nd law a be needed for each ass. A oving van collides with a sports car in a high-speed head-on collision. Crash! During the ipact, the truck eerts a force with agnitude F truck on the car and the car eerts a force with agnitude F car on the truck. Which of the following stateents about these forces is true: A) The agnitude of the force eerted b the truck on the car is the sae size as the agnitude of the force eerted b the car on the truck: F truck = F car B) F truck > F car C) F truck < F car M F truck F car Guaranteed b Newton s Third Law 3

4 1/9/011 A oving van collides with a sports car in a high-speed head-on collision. Crash! M F truck F car During the collision, the iposed forces cause the truck and the car to undergo accelerations with agnitudes a truck and a car. What is the relationship between a truck and a car? A) a truck > a car Step 1: Draw a free-bod diagra Note that Noral Force is alwas Perpendicular (i.e. noral) to the surface. B) a car > a truck Newton s Second Law: F = a C) a truck = a car D) Indeterinate fro inforation given. F g = g In this case, it is not in the opposite direction to the gravitational force. Step : Choose a coordinate sste Step 3: Write down the equations Σ F = a, Σ F = a F g = g We could choose our usual aes. However, we know that we will have otion in both the and directions. If we pick these rotated aes, we know that the acceleration along ust be zero. F g = g Proble: F g doesn t point in a coordinate direction. Must break it into its - and -coponents. Step 3: Write down the equations Σ F = a, Σ F = a N F = g sin(q) F(gravit) a 90 q 90 F = N g cos(q) F(gravit) F(gravit) = g What is the angle a labeled above? A) a = 90 degrees B) a = q C) a = 90 q D) Cannot be deterined F g = g We also know that a = 0, there is no otion in that direction. F =a =0= N g cos(q) 4

5 1/9/011 F a Step 4: Solve the Equations g sin(q) a g sin(q) A ass accelerates down a frictionless inclined plane. + F a a N g cos(q) N g cos( q) 0 N g cos(q) As epected, aiu acceleration if straight down (q=90 degrees), a = g. Recall - definition Which stateent is true? A) N < g B) N > g C) N = g θ + -g cos θ 0 = F = N g cos θ N = g cos θ < g - θ M 1 +T + F g = M g Mass 1: M 1 a = T M -T Mass : M a = M g - T + Frictionless table & pulle. 1)Choose coordinates )Identif forces. 3) Write down F = a for each object What is F = a for ass M? (A) M a T (B) M a T M g (C) M a M g T (D)M a M g You are pushing horizontall with a force of 5000 Newtons on a car that has a weight of 10,000 Newtons. The car is not oving. What can ou sa for certain about the coefficient of friction? A) s = 0 B) s = 0.1 C) s = 0.5 D) k = 0.5 E) None of the above But actuall, s could be even larger since we do not know if we have reached the aiu. F net = 0 = F push F friction 0=F push s Noral s Mg = F push s = F push /Mg = 5000/10k s = 0.5 Incoplete Galler of Probles Involving Newton s Laws: F Chapter 5: Unifor Circular Motion with Gravit w & w/0 friction w & w/0 friction F Bo 1 Bo M f c + M 1 w & w/0 friction T M M w & w/0 gravit Practice setting up the free-bod diagra and F net = a 5

6 1/9/011 Reeber: A large part of what ou ll be epected to do is to appl Newton s Laws. You can t just eorize and appl forulas. Steps for Unifor Circular Motion: 1. Draw a free-bod diagra identifing and labeling all forces.. Choose a coordinate sste one of the directions will point in the radial direction. Others directions: tangent direction (T) or vertical (). 3. Write down Newton s nd law in each coordinate direction (tpicall), suing the forces. Σ F R = a R = v /r Σ F T = a T (for unifor circular otion) 4. If there is ore than one ass, then Newton s nd law a be needed for each ass. Wall-of-Death Proble Spinning around with back against the wall. 1 3 What are the three forces #1,, 3? A) 1 - gravit - centrifugal force 3 friction B) 1 friction noral force of the wall 3 gravit C) 1 - centripetal force noral force of the wall 3 friction D) 1 friction centrifugal force 3 - gravit For ever case of unifor circular otion, there ust be a force directed towards the center. We sa there is a centripetal force. However, there is alwas a specific force that is acting. There is no circle force. Circular otion does not cause a force. Ball circling around tied to a string. Centripetal force Tension Force Wall of Death ride Centripetal force Noral Force Race Car driving in circle Centripetal force Friction Force Consider the force of gravit eerted b the Earth with ass M E on a person of ass on its surface? R E Big G, Little g M F gravit G R F gravit E E 4 11 ) kg ) N / kg ) 9.81 / ) F gravit s F gravit g Gravitational force on an object on the surface of the earth! You are standing on the surface of the earth. The earth eerts a gravitational force on ou F earth, and ou eert a gravitational force on the earth F person. Which of the following is correct: A) F earth > F person B) F earth < F person C) F earth = F person Newton s Third Law D) It s not so siple, we need ore inforation. 6

7 1/9/011 Incoplete Galler of Probles Involving Newton s Law of Universal Gravitation: A rock of ass is twirled on a string in a horizontal plane. The work done b the tension in the string on the rock is T A) Positive B) Negative C) Zero The work done b the tension force is zero, because the force of the tension in the string is perpendicular to the direction of the displaceent: W = F cos 90 = 0 Conservation of Mechanical Energ E echanical = KE + PE = constant (isolated sste, no dissipation) Consider ass swinging attached to a string of length L. The swing is released fro rest at a height h. What is the speed v of the swing when it reaches height h/? KE = ½ v PE grav = g MEi ME f KEi PEi KE f PE f h vi gh v f g 1 v 1 f gh v f gh A block of ass is released fro rest at height H A block of ass slides down a rough rap of height h. Its initial speed is zero. Its final speed at the botto of the rap is v. on a frictionless rap. It strikes a spring with spring constant k at the end of the rap. h Which is the aount of theral energ, E theral, released fro the block s otion down the rap? A) gh 1 v B) gh 1 theral theral KE i PE i E i KE f PE f E f v C) 1 v gh D) 1 v E) gh 0 gh 0 1 v 0 E theral E theral gh 1 v How far will the spring copress (i.e. )? 0 0 KE i + PE i + W frict + W eternal = KE f + PE f 0 + gh = 0 + (0 + ½ k ) gh k gravitational elastic 7

8 1/9/011 In which situation is the agnitude of the total oentu the largest? A) Situation I. B) Situation II. C) Sae in both. Magnitudes are the sae p total =v p total = v + 0 = v p total = v-v=-v A big ball of ass M = 10 and speed v strikes a sall ball of ass at rest. After the collision, could the big ball coe to a coplete stop and the sall ball take off with speed 10 v? A) Yes this can occur B) No, because it violates conservation of oentu C) No, because it violates conservation of energ p initial ( 10) v 10v p final ( 10v) 10v KE initial KE final 1 (10) v 5v 1 (10v) 50v Rotational Kineatics KE PE constant a tan r Describing rotational otion v r f (Conservation of Mechanical IC Energ) p tot i v i constant L tot Tod I i i constant i i angle of rotation (rads) angular velocit (rad/s) angular acceleration (rad/s ) torque (N ) oent of inertia (kg ) Newton s nd Law Kinetic energ (joules J) KE trans KE rot PE constant angular oentu (kg /s) A sall wheel and a large wheel are connected b a belt. The sall wheel turns at a constant angular velocit ω S. There is a bug S on the ri of the sall wheel and a bug L on the ri of the big wheel? How do their speeds copare? A) v S = v L B) v S > v L C) v S < v L 8

9 1/9/011 Torque rf M KE tot 1 Mv 1 I Three forces labeled A, B, and C are applied to a rod which pivots on an ais through its center. Which force causes the largest size torque? sin45 cos45 1/ A LF sin LF B L F 0.5LF C L 4 F ) 0.5LF I sphere 5 MR I hoop MR I disk 1 Which object has the largest total MR kinetic energ at the botto of the rap? A) Sphere B) Disk C) Hoop D) All the sae. KEi PEi KE f PE 0 MgH KE 0 f f KE f MgH All have the sae total KE. H Consider a solid disk of ass M and radius R with an ais through its center. An ant of ass is placed on the ri of the disk. I 1 MR R I hoop MR, I disk 1 MR Which object will go furthest up the incline? A) Puck B) Disk C) Hoop D) Sae height. KE PE KE 1 i Mv i 1 v I r f PE f MgH The hoop has the largest oent of inertia, and therefore the highest total kinetic energ. The ass-disk sste is rotating. The ant walks toward the center of the disk. The agnitude of the angular oentu L of the sste: A) increases B) decreases C) reains constant As ant oves inward, the kinetic energ of the sste: A) increases B) decreases C) reains constant Unless an outside torque is applied, L = Iω = constant. Because I reduces, ω increases fro the ant s otion. Ch. 9 Statics and Static Equilibriu Static Equilibriu: An object is (1) not translating (not oving up, down, left, right) () not rotating (not spinning CW or CCW). A ass is hanging (staticall) fro two strings. The ass, and the angles α and β are known. What are the tensions T 1 and T? Note: No lever ar. Thus no torques. Not translating: F net 0 i F i F F 0 (net force is zero) (each coponent of the net force is zero) Not rotating: net 0 i i (net torque is zero) Two equations with two unknowns, can solve for T 1 and T after soe algebra. 9

10 1/9/011 Ch. 10 Fluids P gh Hdrostatic Pressure Equation Cube A has edge length L and ass M. Cube B has edge length L and ass 4M. Which has greater densit? Pascal s Principle Archiedes Principle Floating Object Continuit Equation F OUT A OUT A IN F IN F buo fluid g fluid Vg V displaced V object object fluid The buoant force equals the weight of the fluid displaced. A 1 v 1 A v or 1 A 1 v 1 A v A) A has larger densit B) B has larger densit C) A and B have the sae densit. g 1 1 v 1 P 1 g 1 v P Bernoulli s Equation Cube A has larger densit. ρ A = M/L 3, ρ B = (4M)/(L) 3 = (1/)M/L 3 so object A has twice the densit of object B. 56 The air pressure inside the Space Station is P = 1 psi. There are two square windows in the Space Station: a little one and a big one. The big window is 30 c on a side. The little window is 15 c on a side. How does the pressure on the big window copare to the pressure on the little window? As shown, two containers are connected b a hose and are filled with water. Which picture correctl depicts the water levels? Different depths would give different pressures! The net force on the fluid at the connection tube would not be zero and there would be flow! A) sae pressure on both windows B) ties ore pressure on the big window C) 4 ties ore pressure on the big window P gh Pressure onl depends on the depth; at a given depth the pressure is the sae D) 9 ties ore pressure on the big window Two identical bricks are held under water in a bucket. One of the bricks is lower in the bucket than the other. The upward buoant force on the lower brick is.. The weight of displaced fluid does not depend on depth Incopressible blood flows out of the heart via the aorta at a speed v aorta. The radius of the aorta r aorta = 1. c. What is the speed of the blood in a connecting arter whose radius is 0.6 c? A) v aorta B) v aorta C) () 1/ v aorta D) 4 v aorta E) 8 v aorta v arter A aorta A arter r aorta r arter v aorta r aorta r arter v aorta 4v aorta v aorta F buo fluid g fluid Vg

11 1/9/011 CH. 11 &1 Vibrations, Waves, & Sound Siple Haronic Oscillator k f 1 k T 1 f k E tot = ½ v + ½ k = ½ ka (Cons of E) Eaple: Pendulu g L f 1 T 1 f F=-k=a Interpret plots of displaceent, velocit, and acceleration. Aplitude & period. L g g L (Hooke s Law) Waves Transverse & longitudinal. v T f Standing waves on strings: odes of oscillation fundaental ode (n=1) overtones (n=,3,4, ) f n = v/λ n = nv/l = nf 1 The position of a ass on a spring as a function of tie is shown below. When the ass is at point P on the graph A) The velocit v > 0 B) v < 0 C) v = 0 v is the slope at P P t 6 Wave Eaples Soe coon eaples of waves are Sound waves (pressure waves) in air (or in an gas or solid or liquid) Longitudinal in gas/liquid, both transverse and longitudinal in solid Waves on a stretched string Transverse Waves on a slink Transverse and Longitudinal Waves on the surface of water - Transverse and Longitudinal "The Wave" at the ballpark stadiu. The ediu is the people Transverse Electroagnetic waves (light) this is the onl kind of wave which does not require a ediu! Their properties indicate the are transverse, but ou ll learn ore on EM waves net seester. The graph below shows a snapshot of a wave on a string which is traveling to the right. There is a bit of paint on the string at point P. vwave P At the instant shown, the velocit of paint point P has which direction? v 63 E) None of these 64 Three waves are traveling along identical strings (sae ass per length, sae tension, sae everthing). Wave B has twice the aplitude of the other two. Wave C has 1/ the wavelength than A or B. Which wave has the highest frequenc? A B C D) All have sae f A vwave v f Fundaentals and Overtones When ou pluck (or bow) the string it vibrates with an different standing waves. These standing waves have to have nodes at the fied points at the ends. λ = L and f 1 = v string /L This is the pitch of this note B No dependence on aplitude λ = L and f = v string /L = f 1 C Sallest wavelength λ gives highest frequenc f 65 λ = L/3 and f 3 =3 v string /L = 3f 1 In general overtones are weaker, but not alwas! 66 11

12 1/9/011 CH. 13 & 14 Teperature & Heat 13. Teperature 13.4 Theral epansion EXTRAS 14.1 Heat as energ transfer 14.3 Specific heat Calorietr & latent heat A projectile is fired straight up and then coes back down to the ground. There is a force of air resistance. During the entire flight, the total work done b the force of gravit is: A) Zero B) Positive C) Negative During the entire flight, the total work done b the force of air resistance is: A) Zero B) Positive C) Negative A pendulu is launched in two different was. During both launches, the bob is given an initial speed 3 /s and the sae initial angle fro vertical. Which launch will cause the pendulu to swing the largest angle fro the equilibriu position to the left side? A) Launch 1 B) Launch C) Both are the sae. A block of ass with initial speed v slides up a frictionless rap of height h inclined at angle q as shown. Assue no friction. A block of ass slides down a rough rap of height h. Its initial speed is zero. Its final speed at the botto of the rap is v. h Whether the block akes it to the top depend on the angle q. What do ou think about this stateent? A) True B) False Which is the aount of theral energ, E theral, released fro the block s otion down the rap? A) gh 1 v B) gh 1 theral theral KE i PE i E i KE f PE f E f v C) 1 v gh D) 1 v E) gh 0 gh 0 1 v 0 E theral E theral gh 1 v 1

13 1/9/011 A pendulu consists of a ass at the end of a string of length L. When the string is vertical, the ass has speed v 0. Ball 1 of ass oving right with speed v bounces off ball with ass M (M > ) and then oves left with speed v. What is the aiu height h to which the ass swings? What is the agnitude of the ipulse of Ball #1 A) v B) v C) 3v D) ½ v E) 0 A bullet of ass traveling with initial speed v hits a block of ass M on a frictionless table. The bullet buries itself in the block, and the two together have a final velocit v f. The total kinetic energ of the bullet+block after the collisions is the total KE before the collision. A) Greater than B) Less than C) Equal to What is the torque about the origin? A) r F sinq B) r F cosq C) zero origin Two light (assless) rods, labeled A and B, each are connected to the ceiling b a frictionless pivot as shown. Both rods are released fro a horizontal position. Which one eperiences the larger torque? A) A B) B C) Sae θ I i r i i Two light (assless) rods, labeled A and B, each are connected to the ceiling b a frictionless pivot as shown. Both rods are released fro a horizontal position. Which one has the larger oent of inertia? A) A B) B C) Sae I i r i i F gsinq θ F g = g I A L L I B () 1 L A F L Lgsinq B L gsinq Lgsinq 13

14 1/9/011 A sall wheel and a large wheel are connected b a belt. The sall wheel turns at a constant angular velocit ω S. There is a bug S on the ri of the sall wheel and a bug L on the ri of the big wheel? How do their speeds copare? A) v S = v L B) v S > v L C) v S < v L A rock of ass is twirled on a string in a horizontal plane. The work done b the tension in the string on the rock is T A) Positive B) Negative C) Zero The work done b the tension force is zero, because the force of the tension in the string is perpendicular to the direction of the displaceent: W = F cos 90 = 0 Roller Coaster Proble g N F net, = N-g = a = v /r If the car oving rightward at the top of this hill: A) The net force on the car is upward. B) The net force on the car is downward C) The net force on the car is zero v Approiatel circular arc Two paths lead to the top of a big hill. Path #1 is steep and direct and Path # is twice as long but less steep. Both are rough paths and ou push a bo up each. How uch ore potential energ is gained if ou take the longer path? A) none B) twice as uch C) four ties as uch D) half as uch h d h #1 # θ d d h 4d h PE gh in both cases. φ A big ball of ass M = 10 and speed v strikes a sall ball of ass at rest. After the collision, could the big ball coe to a coplete stop and the sall ball take off with speed 10 v? A) Yes this can occur B) No, because it violates conservation of oentu C) No, because it violates conservation of energ p initial ( 10) v 10v p final ( 10v) 10v KE initial KE final 1 (10) v 5v 1 (10v) 50v 14