biomechanics presentation 2 (pdf, 1.018 kb)
TRANSCRIPT
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
[email protected] 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 (10𝑠 − 15𝑠)
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
𝑥2 − 𝑥1 = 10 − −4 = 14
4. The Vertical displacement from A to B
𝑦2 − 𝑦1 = 9 − 2 = 7
Practice this concept https://www.mathsisfun.com/data/cartesian-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.
𝑥2 − 𝑥1
𝑦2 − 𝑦1
𝐴𝐵 = (𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
𝐴𝐵 = (10 − −4 )2 + (9 − 2)2
𝐴𝐵 = 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 𝜃 is
90°
In a triangle, the three interior angles always added to 180° 𝐴 + 𝐵 + 𝐶 = 180° which means 𝐴 + 𝐵 + 90° = 180° So 𝐴 + 𝐵 = 90° which can tell that 𝐵 = 𝜃 could be 𝟓𝟎°
𝑥 =?
https://www.mathsisfun.com/proof180deg.html
7. From Figure-3 angle 𝜃 is
30°
𝜃
90° + 30° + 𝜃 = 180° 𝜃 = 180 − 90 − 30
𝜽 = 𝟔𝟎°
Figure -2
Figure-3
𝑥 = 85°
Practice this concept
Velocity in 2-D motion and Trigonometry
10. If 𝜃 = 60° 𝑎𝑛𝑑 𝐯 = 20m/s 𝑡ℎ𝑒𝑛 𝒗𝒙 =
𝑣𝑥is the adjacent line of 𝜃
Use cos 𝜃 =𝑣𝑥
𝑣 𝑣𝑥 = 𝑣 × cos 𝜃
𝑣𝑥 = 20 × cos 60 𝑣𝑥 = 10𝑚/𝑠
Find the value of vertical velocity 𝑣𝑦 =?
𝑣𝑦 = 𝑣 × sin 𝜃 = 20 × sin 60
𝑣𝑦 = 20 × 0.87 = 17.3 𝑚/𝑠
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 𝑥 of the ball if the initial velocity is 60𝑚/𝑠 and the horizontal velocity 𝑣𝑥 = 30m/s
𝑣𝑥 = 30𝑚/𝑠
𝑎𝑑𝑗
𝑜𝑝
𝑠
To find the angle, use one of the following formulae:
𝜃 = sin−1𝑜𝑝𝑠
ℎ𝑦𝑝
𝜃 = cos−1𝑎𝑑𝑗
ℎ𝑦𝑝
𝜃 = tan−1𝑜𝑝𝑠
𝑎𝑑𝑗
To find angle 𝑥,
𝑥 = cos−1 30
60=60°
𝐼𝑓 𝑣𝑥=15m/s and 𝑣𝑦=20m/s find
Angle x=? 𝑥 = tan−1 20
15= 53.1°
𝑣𝑖= ? 𝑣𝑖 152 + 202 = 25𝑚/𝑠 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/legacy/moving-man
At period 10s-15s the object was at rest. The velocity =? 𝑣 = 0
What is the velocity of the object
during period 0s-5s? 𝑣 =4
5m/s
What is the velocity of the object
during period 5s-10s?𝑣 =−8
5=
− 1.6𝑚/𝑠
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.
𝑠𝑙𝑜𝑝𝑒 =𝑦2−𝑦1
𝑥2−𝑥1
Or we can say 𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
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/legacy/moving-man
What is the acceleration of the object in the first 10s? 𝑎 =60
10= 6𝑚/𝑠2
What is the acceleration of the object between 10s and 15s?𝑎 = 0
What is the acceleration in the period of 15s-40s? 𝑎 =−100
25=−4𝑚/𝑠2
What is the acceleration in the period of 40s-55s?𝑎 =40
15= 2.7𝑚/𝑠2
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