PHYSICS

1. PHYSICS 2017-2018

2. WHAT IS PHYSICS?  “the study of matter, energy, and the interaction between them” -somebody

3. UNIT 0: Math in Physics • Significant Figures • Scientific Notation • Metric System and Unit Conversion • Algebra and Trigonometry • Vectors and Scalars • Component Vectors VECTORS

4. Significant Figures • A measure of uncertainty. Uncertainty exists because measuring tools cannot show an infinite number of decimal places

5. Rules for Counting Significant Figures • Nonzero Integers always count as significant. EXAMPLE: 4756 4 Significant Figures (s.f.)

6. Rules for Counting Significant Figures- ZEROS Leading Zeros Captive Zeros Trailing Zeros Leading zeros(left most zeros) DO NOT count as significant figures. Example: 0.0718 3s.f. Captive zeros always count as significant figures. Example: 15.04 4s.f. Example: 103 3s.f. Trailing zeros(right most zeros) aresignificant only if the number contains a decimal point. Example: 4.700 4s.f. Example: 50 1s.f. Example: 3760.0 5s.f.

7. Operations with Significant Figures- Adding and Subtracting • The number of DECIMAL PLACES in the result equals the number of decimal places in the least precise measurement. However 23.45 has only one decimal place therefore we must rewrite this answer to have only one decimal place. 27.8

8. Operations with Significant Figures- Multiplying and Dividing • The number of significant figures in the result must be equal to the least precise measurement used in the calculation. 11.25 has four s.f., 3.75 has three s.f., and 3.0 has two s.f. The answer must therefore have two significant figures. 11

9. Scientific Notation • Scientific notation is a way to handle very large or very small numbers. • Scientific Notation can be used to express values with proper significant figures. Example: 23.4 * 47 = 1099.8 The answer must be written with two s.f. so: 11000 or

10. Manipulating Scientific Notation • At times you will be required to move the decimal place of a number that has been expressed in scientific notation. • When the decimal place moves to the right, decrease the power by one. • When the decimal place moves to the left increase the exponent by one.

11. Manipulating Scientific Notation EXAMPLE: the speed of light. The speed of light will be expressed in scientific notation as:

12. Unit Conversions and Standard Units • More often than not measurements in physics are expressed in the metric system. • Meters, Kilograms, Seconds • Being able to convert units from the Imperial to the metric system or even from metric to metric of different magnitudes is very important.

13. EXAMPLES • CONVERT: 30ft into meters. 1 inch = 2.54cm, 12 inches = 1 foot

14. EXAMPLES • CONVERT: into meters/second (m/s). 1 inch = 2.54cm, 12 inches = 1 foot, 5,280ft = 1 mile 13.4112 m/s

15. Algebra Be familiar with: • Slope • Equations of lines • Manipulating equations to solve for variables • As we discuss question, I will go over other techniques.

16. Example: • Express time as a function of distance(d), and acceleration (a)

17. Trigonometry • Pythagorean Theorem The square of the hypotenuse is equivalent to the sum of the squares of the legs of a right triangle. • SOHCAHTOA c a b

18. SOHCAHTOA • Be aware opposite and adjacent change relative to the angle we are given. • When given two sides of a triangle and we are asked to find the angle remember the inverse trig function will cancel out with the trig function.

19. VECTORS AND SCALARS • A scalar quantity is a quantity which is fully defined by magnitude alone. MAGNITUDE AND NO DIRECTION • Important scalars include: distance, mass, speed, time • A vector quantity is defined by having a magnitude and a direction. • Important vectors include: displacement, velocity, acceleration.

20. What is happening in this picture? Imagine v and u are two ropes pulling this red ball. Which general direction will this ball move? How can we determine the direction and the overall force the ball will experience?(No math required here.)

21. TIP TO TAIL! • Vector Addition using the tip to tail method: • Start by placing any vector with its tail at the origin.(Starting point) • Place the tail of an unused vector to the tip of the previous vector. • After placing all the vectors in this fashion, the resultant vector is found by drawing a straight line from the tail of the first vector to the tip of the last vector. Resultant

22. How would you get from point A to point B while walking only in straight lines. A B

23. EXAMPLE:

24. The Resultant and the Equilibrant vector • When the vectors are all added together into a single vector, that single vector quantity is known as the resultant. • The vector that directly cancels the resultant is known as the equilibrant. It will have the exact magnitude as the resultant but in the exact opposite direction.

25. THE COMPONENT VECTORS Breaking down VECTORS into different parts.

26. Vectors can be broken down and added together.A vector can be broken down into an infinite number of pieces however we will normally break it down into two pieces. One piece that is parallel to the x-axis.The other piece will be parallel to the y-axis.WE USE TRIANGLES! 60

27. Given all the vectors:Break down each vector into its component pieces.We are only interested in the x and y values of each. WE DO PHYSICS IN TWO SEPARATE AXIS. 10m/s 60 45 8 m/s 15 m/s 30

28. SOLVE FOR THE RESULTANT ALGEBRAICALLY + Since vectors have directions we must be careful that we specify which direction the vector lies. We do this by labeling certain directions as either positive of negative. Another common practice is using compass directions 10m/s 60 + + - 45 8 m/s 15 m/s 30 - HOW CAN WE DESCRIBE THESE VECTORS?

29. SOLVE FOR THE RESULTANT ALGEBRAICALLY + 10m/s Recall that we can only deal with vectors that are on the x or y axis therefore we must break down these vectors. Once we have broken down these vectors we group all the vectors based on what axis they inhabit.(X or Y) DIRECTION MATTERS 60 + - 45 15 m/s -

30. SOLVE FOR THE RESULTANT ALGEBRAICALLY • Sum all the vectors on the y-axis • Sum all the Vectors on the x-axis • Combine the two new vectors using Pythagorean theorem.

31. The angle between the vectors • The angle between vectors has a direct effect on the magnitude of the resultant. • We find that when the angle between two or more vectors is 0 degrees, the magnitude of the resultant vector is at a maximum. • When the angle between two or more vectors is 180 degrees, the magnitude of the resultant vector is a minimum. • Rule of thumb: The smaller the angle between vectors the morethey will “help” each other.

32. PROBLEM SOLVING STEPS • 1. Draw a picture and state a reference direction. • 2. State all given information make sure you use proper signs when necessary. • Solve WHEN SOLVING VECTOR ADDITION PROBLEMS USING AN ALGEBRAIC APPROACH THEY WILL ALL BE SOLVED IN A SIMILAR FASHION • Make sure all vectors given are decomposed into their x and y component vectors. • Sum x and y vectors separately then put them back together using Pythagorean theorem. The angle of the resultant vector can be determined by using the inverse trig. functions and your picture!

33. Distance and Displacement • Recall that distance is a scalar quantity and displacement is a vector quantity. • If you begin at point A and travel due north to point B then due east from B to C. The distance covered is 7m.(4m+ 3m). • The displacement is 5m.

34. Example • An ant crawls 61.0 ft north; then, 6.0 ft, 45 degrees south of east; and finally, 3.0 ft, 45 degrees south of west. What is the magnitude of the displacement (in feet) that would have been needed to go straight to the final destination from where the ant started?

35. CONCURRENT FORCES • When two or more forces act on an object at the same time. These forces are known as CONCURRENT FORCES