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Victoria University

Pre-semester Biomechanics Workshop1 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/r3-UuoQ6fbY

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 maths 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

Maths Background Refresh your knowledge by answering

10 questions in 10 min The correct answers:

Question # The right answer

1. c (-5)

2. d (-8)

3. a (18)

4. b (7

8)

5. c (0.7)

6. c (75)

7. b (11)

8. d (2)

9. a (300)

10. a (10m/s)

Integers and Number line

1. What is the value of −9 + 4 ?

• Starting from 0. • Move toward the – sign 9 steps. • We are at −9. Start from here and follow the next instruction to

move toward the + sign 5 steps.

• The answer to the sum is the place where we end up, which is −5 1. Find the value of the following:

3 − 6 =? , 7 − 4 =? , 6 − 9 =? , 1 − 8 =? , −5 + 5 =?

https://www.khanacademy.org/math/arithmetic/absolute-value/adding_subtracting_negatives/v/adding-integers-with-different-signs

Multiplying integers

2. What is the product of 4 and−2 ?

• Rule 1: the product of positive integer and negative integer is a

negative integer. • Rule 2: the product of two positive integers or two negative integers is

a positive integer. • Rule1 and 2 are the same for division(÷)

So now we can use rule 1 to find the value of (+4) × (−2) = −8

2. Find the value of the following: −3 −5 =? (−6) ÷ (2) =? , (7)(5) =? , (8)(−1) =? , (9)(0) =?

https://www.khanacademy.org/math/arithmetic/absolute-value/mult_div_negatives/v/multiplying-positive-and-negative-numbers

(×)

Practice this concept

Order of operations

3. Find the value of 16 + 4 ÷ 2

https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/v/introduction-to-order-of-operations

16 + 2 = 18

5 + 10 ÷ 3 × 6 =

22 − 15 ÷ 3 =

3. Evaluate:

Practice this concept

Fractions

4. Find 3

4+

1

8=

https://www.khanacademy.org/math/arithmetic/fractions

4. Find the value of:

5

6−

2

6=?,

4

5+

2

10=?

• To add fractions with different denominators, you must first change both denominators to be the same.

•3×2

4×2=

6

8 then

6

8+

1

8=

7

8

• Common fractions can be added or subtracted only if they have common denominators (bottom numbers).

• When adding or subtracting fractions with common denominators, add or subtract the numerators (top numbers).

Examples: 2

4+

1

4 =

3

4 ,

7

9−

5

9=

2

9

Practice this concept

Decimals 5. What is

7

10 written as a decimal?

https://www.khanacademy.org/math/arithmetic/decimals

5. Write the following fractions into decimal numbers: 12

100 = ?

23

1000 = ?,

1

2 = ?,

3

4 =?

Practice this concept

Percentage

6. 25% of 300 people is Percentages compare one fraction to another fraction with a denominator of 100.

?

300=

25

100

300×25

100= 𝟕𝟓

6. Find the value of the following: • What number is 2% of 50 ? • What percent(%) of 45 is 9? • 50% of what is 9?

https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/finding-percentages-example

Practice this concept

Algebra

7. Evaluate the expression 3𝑥 + 5 for 𝑥 = 2

7. Evaluate the following expressions: 2𝑦 − 3 𝑓𝑜𝑟 𝑦 = 5

1

2𝑎2𝑡 𝑓𝑜𝑟 𝑎 = 2, 𝑡 = 3

https://www.khanacademy.org/math/in-seventh-grade-math/algebraic-expressions/finding-value-expression/v/evaluate-a-formula-using-substitution

Replacement(Substitution) of 𝑥 by its equal value 2

3 × 2 + 5 = 11

Practice this concept

Cont. Algebra

8. Solve the equation 5𝑣 + 2 = 12

8. Solve the following equations: 4𝑎 = 16 𝑑 + 6 = 13 20 = 15 − 5𝑎

https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/v/solving-one-step-equations

You need 2 steps to solve equation with 2 operations ( ×, +).

To solve the equation means to have the variable by itself on one side.

5𝑣 + 2 − 2 = 12 − 2 subtract 2 from both sides 5𝑣 = 10

5𝑣

5=

10

5 divide both sides by 5

𝑣 = 2

Practice this concept

Metric Conversion

9. 3𝑚 =? 𝑐𝑚

g, m, L

3𝑚 = 300𝑐𝑚 9. Convert the following metric measurements: 120 𝑚𝑔 = ? 𝑔 , 40𝑚 =? 𝑘𝑚 , 25𝐿 =? 𝑚𝐿, 7𝑘𝑚 =? 𝑚

https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/metric-system-tutorial/v/conversion-between-metric-units

Practice this concept

How to solve physics problem ( steps)

1. It is just a problem so calm down 2. Read through the problem, read and understand it in parts.

You can outline these parts as what is given and what do you have to find.

3. It will be easier if you draw a free body diagram to represent the problem.

4. List down anything is given to you in variable form 5. List all the unknown variables in the problem 6. From the list of formulae (equations) choose the one you

think might be applicable to this problem 7. Substitute known values into the equation then solve the

equation 8. Check your answer to insure that it is reasonable and

mathematically correct.

Solving physics problems of motion in 1 D

10. John is jogging with a velocity of 4 m/s when he accelerates at 2 m/s2 for 3

seconds. How fast is john running now? Use this kinematic equation 𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕

https://www.khanacademy.org/science/physics/one-dimensional-motion

𝑣𝑖 = 4𝑚/𝑠 𝑣𝑓 =?

𝑎 = 2𝑚/𝑠2

𝑡 = 3𝑠

There are 5 equations for motion 𝒂 =𝒗𝒇−𝒗𝒊

𝒕 , 𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕

𝑣𝑓 = 4𝑚

𝑠+ 2

𝑚

𝑠2× 3𝑠 = 10

𝑚

𝑠

Practice this concept

Check your understanding

10. A race car accelerates uniformly from rest to

30m/s in 5 seconds. Determine the acceleration of

the car and the distance travelled.

There are 5 equations for motion 𝒂 =𝒗𝒇−𝒗𝒊

𝒕 , 𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕

From rest means 𝑣𝑖 = 0𝑚/𝑠

𝑣𝑓 = 30𝑚/𝑠

𝑡 = 5𝑠

𝑎 =

30𝑚𝑠 −

0𝑚𝑠

5𝑠= 6𝑚/𝑠2

𝑠 =1

2

0𝑚

𝑠+

30𝑚

𝑠× 5 = 75𝑚

The calculator you better bring for tomorrow’s workshop

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