Pre-semester Biomechanics Workshop2 SCC1001 (semester 1- 2016) 1. - - PowerPoint PPT Presentation

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 16th 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 17th 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) 5. b ( 142 + 72) 6. a (50°) 7. c (60°) 8. d (10𝑡 − 15𝑡) 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).

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane/copy-of-cc-6th-coordinate-plane/v/the-coordinate-plane

https://youtu.be/N4nrdf0yYfM https://youtu.be/T2-TO8XBNbU

Practice this concept

The horizontal and vertical displacements in Cartesian plane

• 3. The horizontal displacement from A to B

𝑦2 − 𝑦1 = 10 − −4 = 14

• 4. The Vertical displacement from A to B

𝑧2 − 𝑧1 = 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.

𝑦2 − 𝑦1

𝑧2 − 𝑧1

𝐵𝐶 = (𝑦2 − 𝑦1)2 + (𝑧2 − 𝑧1)2 𝐵𝐶 = (10 − −4 )2 + (9 − 2)2 𝐵𝐶 = 142 + 72

https://www.khanacademy.org/math/geometry/right-triangles-topic/pyth_theor/v/pythagorean-theorem

Practice this concept

Sum of angles in right angle triangle

• 6. From Figure-2 the estimated value of angle 𝜄 is

90° 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° 𝑦 =?

https://www.mathsisfun.com/proof180deg.html

• 7. From Figure-3 angle 𝜄 is

30° 𝜄 90° + 30° + 𝜄 = 180° 𝜄 = 180 − 90 − 30 𝜾 = 𝟕𝟏°

Figure -2 Figure-3

𝑦 = 85° Practice this concept

Velocity in 2-D motion and Trigonometry

• 10. If 𝜄 = 60° 𝑏𝑜𝑒 𝐰 = 20m/s 𝑢ℎ𝑓𝑜 𝒘𝒚 =

𝑤𝑦is the adjacent line of 𝜄 Use cos 𝜄 =

𝑤𝑦 𝑤 𝑤𝑦 = 𝑤 × cos 𝜄

𝑤𝑦 = 20 × cos 60 𝑤𝑦 = 10𝑛/𝑡 Find the value of vertical velocity 𝑤𝑧 =? 𝑤𝑧 = 𝑤 × sin 𝜄 = 20 × sin 60 𝑤𝑧 = 20 × 0.87 = 17.3 𝑛/𝑡

http://phet.colorado.edu/sims/projectile- motion/projectile-motion_en.html

Practice this concept

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 𝑤𝑦 = 30m/s

𝑤𝑦 = 30𝑛/𝑡 𝑏𝑒𝑘 𝑝𝑞𝑡 To find the angle, use one of the following formulae: 𝜄 = sin−1 𝑝𝑞𝑡 ℎ𝑧𝑞 𝜄 = cos−1 𝑏𝑒𝑘 ℎ𝑧𝑞 𝜄 = tan−1 𝑝𝑞𝑡 𝑏𝑒𝑘 To find angle 𝑦, 𝑦 = cos−1 30

60 =60°

𝐽𝑔 𝑤𝑦=15m/s and 𝑤𝑧=20m/s find Angle x=? 𝑦 = tan−1 20

15 = 53.1°

𝑤𝑗= ? 𝑤𝑗 152 + 202 = 25𝑛/𝑡

https://www.khanacademy.org/science/physics/two- dimensional-motion/two-dimensional-projectile- mot/v/projectile-at-an-angle

Practice this concept

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

What is the velocity of the object during period 0s-5s? 𝑤 = 4

5m/s

What is the velocity of the object during period 5s-10s?𝑤 =

−8 5 =

− 1.6𝑛/𝑡

https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/position-vs-time-graphs

Velocity at a certain point is the slope of the line at this point. 𝑡𝑚𝑝𝑞𝑓 =

𝑧2−𝑧1 𝑦2−𝑦1

Or we can say 𝑠𝑗𝑡𝑓

𝑠𝑣𝑜

Practice this concept

Acceleration in 1-D motion

• 9. The slopes (gradients) of the lines represent

The change of velocity over time is the acceleration of the object. This means the slope (gradient) of each line represents the acceleration.

http://phet.colorado.edu/en/simulation/l egacy/moving-man What is the acceleration of the object in the first 10s? 𝑏 = 60

10 = 6𝑛/𝑡2

What is the acceleration of the object between 10s and 15s?𝑏 = 0 What is the acceleration in the period of 15s-40s? 𝑏 =

−100 25 =−4𝑛/𝑡2

What is the acceleration in the period of 40s-55s?𝑏 = 40

15 = 2.7𝑛/𝑡2

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

Practice this concept

Drop in sessions for math and physics in Semester1 2016 (12:00 pm-2:00pm) at room P202

Drop-in Sem 1 Mon Tues Wed Thu Fri Foot Park Shane Haifa Haifa Nand Nand City Flinders Tom St Albans Haifa

Haifa Schedule

Monday Tuesday Wednesday 11:00-12:00

• ST. ALBANS

1:1 Consultation Room 7.201L 11:00-12:00 FP 1:1 Consultation Room M318 11:00-12:00 FP Biomechanics (Math and physics) tutorial L005B 12:00-2:00

• ST. ALBANS

Drop in Room 7.201L 12:00-2:00 FP Drop-in Room P202 12:00-2:00 FP Drop-in Room P202 2:00-3:00

• ST. ALBANS

1:1 Consultation Room 7.201L 3:00-4:00 FP Biomechanics (Math and physics) tutorial L005A 3:00-4:00 FP 1:1 Consultation Room M318