Victoria University Pre-semester Biomechanics Workshop2 SCC1001 (semester 1- 2016) 1. Basic maths skills preparation 2. Basic physics preparation Haifa Abdelqader Academic Support and Development haifa.abdelqader@vu.edu.au Room M318 (FP) https://youtu.be/HOiH1eVCggw
Outline for the first Day 16 th Feb 2016 10:00-10:30- Introduction and your maths background 10:30-12:00- review in basic numeracy and algebra 12:00-1:00- Break 1:00- 3:00- continue with math skills and some basic examples on how to solve physics problems using Algebra Outline for the second Day 17 th Feb 2016 10:00-10:30- Introduction and your geometry background 10:30-11:00- Practice in Pythagorean theorem 11:00-12:00- Practice in Trigonometry 12:00-1:00- Break 1:00-3:00- Combined examples in Pythagorean theorem and Trigonometry
Geometry Background Refresh your knowledge by answering 10 questions in 10 min The correct answers : Question # The right answer 1. b (-4,2) 2. a (10,9) 3. b (14) 4. c (7) b ( 14 2 + 7 2 ) 5. a ( 50° ) 6. c ( 60° ) 7. d ( 10𝑡 − 15𝑡 ) 8. 9. c (acceleration) 10. b (10m/s)
Coordinate Geometry (the number plane or Cartesian Plane) 1. The coordinates of position A Position of any point in the Cartesian plane can be presented by an ordered pair of numbers ( x, y). They are called the coordinates of the point. The coordinates of point A are ( -4, 2). 2. The coordinates of point B are ( 10, 9). Practice this concept https://youtu.be/N4nrdf0yYfM https://youtu.be/T2-TO8XBNbU https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/v/the-coordinate-plane
The horizontal and vertical displacements in Cartesian plane 3. The horizontal displacement from A to B 𝑦 2 − 𝑦 1 = 10 − −4 = 14 4. The Vertical displacement from A to B 𝑧 2 − 𝑧 1 = 9 − 2 = 7 Practice this concept https://www.mathsisfun.com/data/c artesian-coordinates-interactive.html
Pythagorean Theorem 5. The right equation to find the length of the line AB Use Pythagorean Theorem to derive a formula for finding the distance between two points in 2-D. 𝑧 2 − 𝑧 1 𝑦 2 − 𝑦 1 (𝑦 2 − 𝑦 1 ) 2 + (𝑧 2 − 𝑧 1 ) 2 𝐵𝐶 = (10 − −4 ) 2 + (9 − 2) 2 𝐵𝐶 = 14 2 + 7 2 𝐵𝐶 = Practice this concept https://www.khanacademy.org/math/geometry/right-triangles-topic/pyth_theor/v/pythagorean-theorem
Sum of angles in right angle triangle 6. From Figure-2 the estimated value of angle 𝜄 is In a triangle, the three interior angles always added to 180 ° 𝐵 + 𝐶 + 𝐷 = 180° which means 𝐵 + 𝐶 + 90° = 180° So 𝐵 + 𝐶 = 90° which can tell that 𝐶 = 𝜄 could be 𝟔𝟏° 7. From Figure-3 angle 𝜄 is 𝜄 90° 90° + 30° + 𝜄 = 180° 30° 𝜄 = 180 − 90 − 30 Figure -2 𝜾 = 𝟕𝟏° Figure-3 𝑦 =? 𝑦 = 85° Practice this concept https://www.mathsisfun.com/proof180deg.html
Velocity in 2-D motion and Trigonometry 10. If 𝜄 = 60° 𝑏𝑜𝑒 𝐰 = 20m/s 𝑢ℎ𝑓𝑜 𝒘 𝒚 = 𝑤 𝑦 is the adjacent line of 𝜄 Find the value of vertical velocity 𝑤 𝑦 Use cos 𝜄 = 𝑤 𝑤 𝑦 = 𝑤 × cos 𝜄 𝑤 𝑧 =? 𝑤 𝑧 = 𝑤 × sin 𝜄 = 20 × sin 60 𝑤 𝑦 = 20 × cos 60 𝑤 𝑧 = 20 × 0.87 = 17.3 𝑛/𝑡 𝑤 𝑦 = 10𝑛/𝑡 http://phet.colorado.edu/sims/projectile- Practice this concept motion/projectile-motion_en.html
Continue with Velocity in 2-D motion and Trigonometry Find the angle 𝑦 of the ball if the initial velocity is 60𝑛/𝑡 and the horizontal velocity 𝑤 𝑦 = 30m/s To find the angle, use one of the following formulae: 𝜄 = sin −1 𝑝𝑞𝑡 ℎ𝑧𝑞 𝜄 = cos −1 𝑏𝑒𝑘 𝑝𝑞𝑡 ℎ𝑧𝑞 𝜄 = tan −1 𝑝𝑞𝑡 𝑏𝑒𝑘 𝑏𝑒𝑘 To find angle 𝑦, 𝑤 𝑦 = 30𝑛/𝑡 𝑦 = cos −1 30 60 = 60 ° 𝐽𝑔 𝑤 𝑦 =15m/s and 𝑤 𝑧 =20m/s find Practice this concept Angle x=? 𝑦 = tan −1 20 15 = 53.1° https://www.khanacademy.org/science/physics/two- 𝑤 𝑗 = ? 𝑤 𝑗 15 2 + 20 2 = 25𝑛/𝑡 dimensional-motion/two-dimensional-projectile- mot/v/projectile-at-an-angle
Displacement vs Time graph (1-D motion) 8. The object stopped at period http://phet.colorado.edu/en/simulation/l egacy/moving-man At period 10s-15s the object was at rest. The velocity =? 𝑤 = 0 Velocity at a certain point is the slope of the line at this point. 𝑧 2 −𝑧 1 𝑡𝑚𝑝𝑞𝑓 = 𝑦 2 −𝑦 1 Or we can say 𝑠𝑗𝑡𝑓 𝑠𝑣𝑜 What is the velocity of the object during period 0s-5s? 𝑤 = 4 5 m/s What is the velocity of the object −8 during period 5s-10s? 𝑤 = 5 = − 1.6𝑛/𝑡 Practice this concept https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/position-vs-time-graphs
Acceleration in 1-D motion 9. The slopes (gradients) of the lines represent http://phet.colorado.edu/en/simulation/l egacy/moving-man The change of velocity over time is the acceleration of the object. This means the slope (gradient) of each line represents the acceleration. What is the acceleration of the object in the first 10s? 𝑏 = 60 10 = 6𝑛/𝑡 2 What is the acceleration of the object between 10s and 15s? 𝑏 = 0 −100 25 = −4𝑛/𝑡 2 What is the acceleration in the period of 15s-40s? 𝑏 = What is the acceleration in the period of 40s-55s? 𝑏 = 40 15 = 2.7𝑛/𝑡 2 Practice this concept https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/acceleration http://dev.physicslab.org/document.aspx?doctype=3&filename=kinematics_positiontimegraphs.xml
Drop in sessions for math and physics in Semester1 2016 (12:00 pm-2:00pm) at room P202 Drop-in Sem Mon Tues Wed Thu Fri 1 Foot Park Shane Haifa Haifa Nand Nand City Flinders Tom St Albans Haifa Monday Tuesday Wednesday 11:00-12:00 11:00-12:00 11:00-12:00 ST. ALBANS FP FP Haifa Schedule 1:1 1:1 Biomechanics (Math Consultation Consultation and physics) tutorial Room 7.201L Room M318 L005B 12:00-2:00 12:00-2:00 12:00-2:00 ST. ALBANS FP FP Drop in Drop-in Drop-in Room 7.201L Room P202 Room P202 2:00-3:00 3:00-4:00 3:00-4:00 ST. ALBANS FP FP 1:1 Biomechanics (Math 1:1 Consultation and physics) tutorial Consultation Room 7.201L L005A Room M318
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