Physics 1443 Lecture Summary for Homework #5 by Dr. Jae Jaehoon Yu

PHYS 1443 Section 003 Lecture #7 Monday, Feb. 22, 2021 Dr. Jae Jaehoon Yu CH3: Motion in two dimensions Projectile Motion Maximum range and height CH4: Newton s Laws of Motion Force & Newton s 1st Law of Motion Yu Monday, Feb. 22, 2021 Today s homework is homework #5, due 11pm, Tuesday, March 9!! PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 1

Announcements Quiz #2 beginning of the class next Wednesday, March 3 Covers CH3.4 to what we finish next Monday, March 1 BYOF: You may bring a one 8.5x11.5 sheet (front and back) of handwritten formulae and values of constants for the test No derivations, word definitions, setups or solutions of any problems, figures, pictures, diagrams or arrows, etc! Must email me the photos of front and back of the formula sheet, including the blank at jaehoonyu@uta.edu no later than 12:00pm the day of the test The subject of the email should be the same as your file name File name must be FS-Q2-LastName-FirstName-SP21.pdf Once submitted, you cannot change, unless I ask you to delete part of the sheet! Reminder: Extra credit special COVID seminar at 4pm Saturday, March 20 Extra credit for participation and for asking the relevant questions Dr. Linda Lee, a practicing physician from Wisconsin Term 1 results Class average: 79/102 Equivalent to 77.4/100 Top score: 102/102 Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 2

Evaluation Policy Homework: 25%!!! (clinic: https://www.uta.edu/physics/current/clinics.php) Exams Final Comprehensive Exam (2pm, Mon., 5/10/21): 23% Mid-term Comprehensive Exam (2:30pm, Wed., 3/10/21): 20% One better of the two term Exams (2/10/21 and 4/12/21): 12% Missing an exam is not permissible unless pre-approved No makeup test You will get an F if you miss any of the exams without a prior approval no matter how well you ve been doing in class! Lab score: 10% If passed the lab before, can request a lab exemption (form available on web) Pop-quizzes: 10% Extra credits: 10% of the total Random attendances Strong participation in the class discussions Special projects (BIGGGGG!!!) Special seminars Grading will be done on a sliding scale (poll 9) 100% Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 3

SP #3 Statistical Analysis : COVID19 Make comparisons of COVID-19 statistics between the U.S., South Korea, Italy and Texas from https://coronaboard.com on spreadsheet Total 60 points: 1 point for each of the top 20 cells and 2 points for each of the 12 cells for testing and the 8 cells for vaccination Fill the US Historic event analysis table at the bottom, 1 point each (16 points total) and make a >3 sentence statement on COVID19 with respect to other events (6 points) 22 points total What are the 3 fundamental quantitative requirements for opening up (2 points each, 6 points total)? Must be quantitative! (e.g. number of tests per capita per day, positivity rate, etc) Assess the readiness of the three fundamental requirements U.S. (Do NOT just take politician s words!). Must provide the independent scientific entity s reference you took the information from. (2 point each, total 6 points) Evaluate quantitatively the success/failure of the US responses to COVID-19 in 2020 in 5 sentences and that in 2021 in 5 sentences. Must provide quantitative reasons behind your conclusion! (2 points each sentence, 20 points total) Assess quantitatively the effectiveness of wearing masks (4 points) and at least 4 reasons for it being effective (1 point each, 0.5 point extra after the first 4). Possible maximum: 122 points total Due: 11pm, Friday, March 19 Submit one pdf file SP3-YourLastName-YourFirstName.pdf, including the spreadsheet Spreadsheet will be posted on canvas. Download ASAP. 4

PHYS1443-003, Spring 21, Special Project #3, Statistical Analysis - COVID19 Date? &? time? of? your? COVID-19? Data:? South?Korea Name: Items U.S.A Italy Texas Total? Population Total COVID-19? Confirmed? cases Cases per 1M people Total COVID-19? Deaths Death per 1M people Total COVID-19? Testing Testing per 1M people Poditivity Rate Total COVID-19 Vaccination to date Per 1M people US?Vietnam?War US?World?War?II COVID-19 US H1N1 Time? period? (mm/dd/yy? -? MM/DD/YY) Duration? in? Months US Historic Event Analysis Total? deaths Death? per? month Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 5

Recap: Kinematic Equations in 2-Dim y-component x-component vx= vx0+axt vy= vy0+ayt ( )t ( )t y =1 2vy0+vy x =1 2vx0+vx 2= vy0 2+2ayy 2= vx0 2+2axx vy vx Dy = vy0t+1 2ayt2 Dx = vx0t+1 2axt2 Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 6

Projectile Motion A 2-dim motion of an object under only the gravitational acceleration with the following assumptions Free fall acceleration, g g, is constant over the range of the motion (poll 12) Air resistance and other effects are negligible A motion under constant acceleration!!!! Superposition of two motions Horizontal motion with constant velocity ( no acceleration ) Vertical motion under constant acceleration ( g g ) ( ) 2 m s Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 7

Projectile Motion The only acceleration in this motion. It is a constant!! (poll 12, 13) Monday, Feb. 22, 2021 8

Show that a projectile motion is a parabola!!! vxo= v0cosq0 v0sinq0 vy0= x-component y-component In a projectile motion, the only acceleration is gravitational one whose direction is always toward the center of the earth (downward). (poll 6) axi + ayj =-gj a = xf t = = vx0t = v0cosq0t fx ax=0 v0cosq0 = v0sinq0t -1 yf= vy0t +1 ( )t2 xf 2gt2 2-g 2 -1 xf Plug t into the above f y = v0sinq0 2g v0cosq0 v0cosq0 xf g yf= xftanq0- 2 What kind of parabola is this? (poll 13) 2cos2q0 2v0 Monday, Feb. 22, 2021 9

Example for Projectile Motion A ball is thrown with an initial velocity v=(20i+40j)m/s. Determine the time of flight and the distance the ball is from the original position when landed. Which component determines the flight time and the distance? 40t +1 ( )t2=0m f y = ( t 2-g Flight time is determined by the y component, because the ball stops moving when it is on the ground after the flight. ) = 80 0 gt So the possible solutions are 80 g = = 0 or 8 sec t t Distance is determined by the x component in 2-dim, because the ball is at y=0 position when it completed it s flight. Why isn t 0 the answer? 8sec t ( ) 20 8 160 m = fx = v t = xi Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 10

Example for a Projectile Motion A stone was thrown upward from the top of a cliff at an angle of 37o to horizontal with an initial speed of 65.0m/s. If the height of the cliff is 125.0m, how long is it before the stone hits the ground? = = 65.0 cos37 = cos iv xi v 51.9 / m s = = 65.0 sin37 = sin v v 39.1 / m s i i yi 1 2 fy = 2 125.0 = v t gt Becomes yi 9.80t2-78.2t-250=0 gt2-78.2t-250= ( ) 2- 4 9.80 (-250) 2 9.80 t 4 . 10 or = t =78.2 -78.2 = . 2 43 s t t s s Monday, Feb. 22, 2021 4 . 10 = The stone lands after the initial time. PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 11 11

Example contd What is the speed of the stone just before it hits the ground? = = = 65.0 cos37 = cos iv v v 51.9 / m s xf xi = 39.1 9.80 10.4 62.8 / = = = sin v gt m s v v gt i i yf yi ( ) + = v = 2 2 2 v v + = 2 51.9 62.8 81.5 / m s xf yf What are the maximum height and the maximum range of the stone? Do these yourselves at home for fun!!! Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 12 12

Example for a Projectile Motion A rescue plane flies at 198km/h (=55.0m/s) and constant height h=500m toward a point directly over a victim, where a rescue capsule is to land. What should be the angle of the pilot s line of sight to the victim when the capsule release is made? Once the rescue capsule is release, it will undergo a projectile motion, and this becomes a simple trigonometry problem. What is the initial angle of capsule release? The initial angle of capsule release q0= 0 vx0= v0cosq0m/ s ( Dx = vx0t = v0cosq0t Dy = vy0t -1 t = 2h g = 2 500 9.8 = 10.1 s ( ) \Dx = vx0t = v0t =55.0 10.1=555.5 m The angle for the line of sight is tanf =x );vy0= v0sinq0 2gt2= v0sinq0t -1 2gt2= -1 2gt2= -h ( ) h= tan-1555.5 h f = tan-1x = 48 500 What is the velocity of the capsule as it reaches the water? If it stops after pushing the victim 50cm into the water, what would be the acceleration of the capsule? Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 13 13

Horizontal Range and Max Height Based on what we have learned, one can analyze a projectile motion in more detail Maximum height an object can reach Maximum range What happens at the maximum height? At the maximum height the object s vertical motion stops to turn around!! vyi+ ayt sin i v = = v yf =0 gt vi A h sin v = i t Solve for tA A g This is the time to reach the peak! Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 14 14

Horizontal Range and Max Height Since no acceleration is in the x direction, it still flies even if vy=0. v ( ) 2At xi v t = sin g v = R = 2 cos i i v xi i i 2 2 sin v = i i R Range g 2 1 2 sin g sin g v v 1 2g ( ) fy = + h = 2 v t g t = i i i i sin v yi i i 2 2 sin 2 v = = Height i i y h f g Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 15 15

Maximum Range and Height What are the conditions that give the maximum height and range to a projectile motion? This formula tells us that the maximum height can be achieved when i=90o!!! 2 sin2 v = i i h 2 g This formula tells us that the maximum range can be achieved when 2 i=90o, i.e., i=45o!!! 2 2 sin v = i i R g Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 16 16

Force We ve been learning kinematics; describing motion without understanding what the cause of the motion is. Now we are going to learn dynamics!! FORCE is what causes an object to move. Can someone tell me what FORCE is? The above statement is not entirely correct. Why? Because when an object is moving with a constant velocity no force is exerted on the object!!! FORCE is what causes changes to the velocity of an object!! (poll 6) When there is force, there is change of velocity!! What does force cause? (poll 10) What does this statement mean? an acceleration What happens if there are several forces being exerted on an object? Force is a vector quantity, so vector sum of all forces, the NET FORCE, determines the direction of the resulting acceleration of the object. F F1 1 F F2 2 NET FORCE, F= F F= F1 1+F +F2 2 When the net force on an object is 0 0, it has constant velocity and is at its equilibrium!! Monday, Feb. 22, 2021 PHYS 1443-003, Spring 2021 Dr. Jaehoon Yu 17