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 (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