Lecture 1 - Mechanics PDF

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Mechanics...

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PH151/183 – Mechanics & Waves Dr. A. M. Yao [email protected] Room JA7.08

Lectures/Tutorials • Lectures: - Monday 10:00 – 11:00 - Tuesday 10:00 – 11:00

JA317 JA314

• Tutorials: - PH183 (Physics/Maths & Physics): Mondays 11:00 – 12:00 starting 7th October - PH151 (Maths/Chemists): Tuesdays 14:00 – 15:00 starting 8th October •

CHECK MYPLACE FOR TUTORIAL GROUPS & ROOMS

University closed on Monday 30th September • NB: No PH150/PH180 experimental labs this week. - The training labs start in teaching week 3: 07/10/2018.

Course Textbooks Walker, Halliday, Resnick Principles of Physics 10th Edition RRP£55.99JSPrice£47.99

Jordan and Smith Mathematical Techniques 4th Edition RRP£47.99JSPrice£37.99

Available from (among others) John Smith’s Bookshop, University of Strathclyde Level 3 of the Student Union Building in John Street.

Course Support • Myplace PH151/PH183: https://classes.myplace.strath.ac.uk/ • PH181/PH182: Mathematics for Physics 1A & 1B.

• Maths Skills Support Centre http://www.strath.ac.uk/mathsskills/ Livingstone Tower Rm 308 • Drop-in sessions & one-to-one appointments • Supported study • Online resources

• Physics Society Drop-In Sessions 4th & 5th year students offer tutorial support throughout the year. Graham Hills 5.65 • e-mail: [email protected]

Assessment • Continuous assessment (40%) • • • •

In-lecture MCQ tests (5 per semester, per class): Class test in December (1 hour, MCQ): Class test in 2nd semester (1 hour, MCQ): Participation in tutorials:

10% 10% 10% 10%

• May examination (60%) - 2 hours written exam, all questions compulsory • Re-sit exam in August (100%) – 2 hours written exam, all questions compulsory Weekly test marking (out of 4) 0-1 correct: 40%, 2 correct: 60%, 3 correct: 80%, 4 correct: 100%

Assessment: Tutorials (10% final mark) • Tutorial problems will be posted on Myplace, usually one week

before the tutorial session, and you should attempt to solve these problems before the tutorial. • Discuss with your groups and use the lecture material and course textbook to help you to complete the problems. • Make sure you bring a copy of your solutions to the tutorial class. • Model answers will be posted on Myplace after the tutorial.

• Full instructions will be on Myplace.

Assessment: Multiple Choice Tests (10% final mark) •

5 MCQ tests/semester; 4 questions per test

Multiple Choice Answer Sheet Registration Number:

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Name: ………………………………………………………………………

1. Please check you have the correct exam answer sheet

4. Complete using BLUE or BLACK ink 5. DO NOT use correction fluid 6. If you make a mistake, indicate clearly the incorrect answer(s) with a cross: 

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Signature: ………………………………………………………….

Scoring 0-1/4 correct: 40%, 2/4 correct: 60%, 3/4 correct: 80%, 4/4 correct: 100%

Wrong reg. number → marked absent

Progress & Feedback • The MCQ tests and tutorial problems will give you feedback on your progress throughout each semester. • The class tests will give you feedback on how well you are consolidating your learning. • If you are struggling to keep up or are concerned about your progress, please talk to your PDA. • Maths Skills Support Centre http://www.strath.ac.uk/mathsskills/ Livingstone Tower 3.08 • Drop-in sessions & one-to-one appointments • Physics Society Drop-In Sessions 4th & 5th year students offer tutorial support throughout the year. Graham Hills 5.65 • e-mail: [email protected]

Pre-requisites • SQA Higher Physics & Higher Mathematics or equivalent. • Refresher: Chapter 2 of Walker, Halliday & Resnick (WHR) • You should already be familiar with relationships to solve problems involving distance, displacement, speed, velocity, and acceleration for objects moving with constant acceleration in a straight line in 1D:

Pre-requisites • You should also be familiar with the use of vector addition and appropriate relationships to solve problems involving balanced and unbalanced forces, mass, acceleration, and gravitational field strength:

• Use of the principle of conservation of energy and momentum and appropriate relationships to solve problems involving work done, potential energy, kinetic energy, and power:

Work done  Fd

E P  mgh 1 Ek  mv 2 2 p  mv

Course Outline • Motion in 2D – Chpt. 4 • Force & motion – Chpt. 5 & 6 • Work & Energy – Chpt. 7 & 8 • Linear momentum – Chpt. 9 • Gravitation – Chpt. 13

Mechanics • Motion in 2 dimensions • Force & motion • Work & Energy • Linear momentum • Gravitation

So, why do we need to know mechanics?

Mechanics – Why do we care? • Computer games like this rely on “physics engines” – software that simulates different physics systems. • What physics do we need to know to design games like this? • Why else do we care? • Travel – design of cars, roads, airplanes • Sports – projectile motion, velodromes • Fun – roller coasters, movie animations, computer games • Solving crimes – missile trajectories

Position & Displacement Learning objectives: 

Determine the direction and magnitude of a particle's position.



Understand the difference between distance and displacement.



Find a particle's displacement vector from its initial and final position vectors.

• Material covered in section 4.1 of WHR.

Position & Displacement • A position vector locates a particle in space. • Extends from a reference point (origin) to the particle

• Example o Position vector

Position & Displacement • At time t0 the particle is at position A with position vector

8

A 6

B 4

• At time t the particle is at position B with position vector

2

0 0

1

2

3

4

• The distance the particle has travelled is the length of the path from A to B. • Its displacement vector is the change in its position vector:

5

Position & Displacement • Example • Point A has position vector

8

2 ˆi

A

2 ˆj

6

• Point B has position vector

B 4

• What is the displacement vector in moving from A to B?

2

0

0

1

2

3

The displacement of the particle is the vector .

4

5

Displacement : Magnitude & Direction • The magnitude of a vector is given by 8

A

• The direction is given by

6

B 4

• What is the displacement in moving from A to B?

2

0

0

1

•

2

3

4

Angles are measured anticlockwise from the +ve x-axis.

5

Average and instantaneous velocity Learning objectives: 



Determine the average velocity vector given a particle's initial and final position vectors and the time interval between them. Determine the instantaneous velocity vector given a particle's position vector as a function of time.

• Material covered in section 4.2 of WHR.

Average velocity • A particle moves from position A at time t0 to position B at time t. • Its average speed is the distance it has travelled divided by the time interval t. • Its average velocity is its displacement divided by the time interval t. • Its position vector changes from to in time t  t  t0, so

8

A 6

B 4

2

0 0

• Note that the direction of the velocity vector as that of the displacement vector .

1

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must be the same

5

Average velocity • We can write the displacement vector in terms of its displacement components:

8

A 6

• So we can write the velocity vector in terms of its components:

B 4

2

0 0

•

1

2

3

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Note: The components vary independently with time so, for example, any influence in the x direction does not affect the motion in the y direction and vice versa.

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Average velocity • Example • A particle moves from position to position in a time of 2s. What is its average velocity? • Its displacement vector is

• Its average velocity is

•

So its average velocity (a vector quantity) will have a component of 4ms-1 along the x axis, 1ms-1 along the y axis and 2ms-1 along the z axis.

• Example 1-1 • A bird flies east at 10 ms-1 for 400m, then south at 10 ms-1 for 20 s. a) What distance does it fly? b) Calculate its displacement vector c) What are the magnitude and direction of the displacement?...