Transcript Lecture 2
“Sex and physics are a lot alike; they both give practical results but that's not why we do them.” Richard Feynman, physicist. Policies on Syllabus, Blackboard, and http://sdbv.missouristate.edu/mreed/CLASS/PHY12 3 Announcements HW1 is on-line now (link on Blackboard) and due Friday Jan. 15 at 5pm. (Problem 16 fixed) I set a practice assignment of odd problems (answers at the back of the book) on WileyPlus. Fundamental Units Units that are basic measurable quantities upon which all other units are derived from. They are: Length- meters is the base Length For reference reading later.... Length is used to measure the location and the dimensions in space of any object. A meter is the standard unit here. Which are the lengths? Mass Mass is the measure of the quantity of matter in an object. A kilogram is the standard unit here. 1kg = 1,000g = 0.068 slugs Mass and Weight are NOT the same thing! Time Time is a duration between two events. The second is the standard unit of time. 1 hour = 60 minutes = 3600 seconds Each day has 86,400 seconds in it. Where are the times? Charge The unit of charge is the coulomb. 1C has the charge of 6.24x1018 electrons (the fundamental unit). When you get shocked touching a doorknob, the charge is about 3x1020C which means that about 2x1039 electrons jumped off your finger. Derived Quantities are any units using a combination of fundamental quantities. Speed = distance/time = m/s Dimensional Analysis Make sure you answer has the right units to know you did it correctly. Watch for unit consistency in doing Conversions and problem - solving. Pay attention to your units. example: The formula for force is F=ma (mass times acceleration) which has a unit we call Newtons. A Newton is not a fundamental unit, but is made up from them. If mass .s2.m has units of kg and acceleration A) N=kg 2, what is the unit 2. has units of m/s B) N=m/(s kg) 2.m) C) N=1/(kg.sof Newtons? D) N=kg.m/s2 E) None of the above. Scientific Notation Written using powers of 10 to show significant figures (watch 0s). Only one number before the decimal point. Watch moving decimal points (left => +; right => -). Watch adding/subtracting and multiplying/dividing exponents. Significant Figures Use common sense! Rounding during calculations will change the final answer. Extremely important for WileyPlus: you have an error amount (usually 9%). If you round outside of this, your answer will be wrong, though you've done it Problem Solving Advice Read the problem through twice and visualize what it is asking for. Draw a diagram with the appropriate labels and directions. Pay attention to it! Reread the problem and make sure your diagram matches what the problem asked for. List what you know and what you need to find. Identify the basic equation(s) you need and symbolically solve for the unknown quantity. Substitute the given values into the equation with the appropriate units. Solve the problem. CHECK to see if the answer is reasonable and that your units are correct. Math: Trigonometry Traditional right (90o angle) triangle. Side b is the adjacent, a is the opposite and c is the hypotenuse. Obviously c is the longest side and by Pythagoras' theorem has the relationship c2=a2+b2. Math: Trigonometry Traditional right (90o angle) triangle. Angles A, B, and C must add to 180o. Math: Trigonometry Relationships between them. Math: Trigonometry Terminology: Lots of times side b is called the X-component and side a is called the Ycomponent of vector c. Math: Trigonometry Relationships between them. Example: a=6 and b=9. What's c and A? A) c=10.8 A=33.7o B) c=9.1 A= 24o C) c=12.4 A=43.2o D) c=14.2 A=33.7o Math: Trigonometry Relationships between them. Example: a=6 and b=9. What's c and A? A) c=10.8 A=33.7o Math: Trigonometry Relationships between them. Example: A=16o What are B and C? A) C=45o so B=1190 B) C=90o so B=29o C) C=90o so B=74o. D) C=45o so B=29o Math: Trigonometry Relationships between them. Example: A=16o What are B and C? C) C=90o so B=74o. Law of sines This can be used with non-right triangles too, which makes it very useful. Law of cosine. Can also be used with non-right triangles. So now you can solve any angle or the length of any side from any triangle. For now just put these in your math locker. We'll review them a bit when we need them. Vectors and Scalars. What's the difference and why do we care? Vectors and Scalars. What's the difference and why do we care? Vectors have direction and scalars are only numbers (like quantities) or the length part of the vector. Vectors and Scalars. What's the difference and why do we care? Examples of scalar quantities: Temperature, mass, volume, density. These don't care about direction. Vectors and Scalars. What's the difference and why do we care? Examples of vector quantities: Location, displacement (how far in which direction), velocity (speed + direction), acceleration (gravity pulls downward), force. Vectors are added by geometric methods (discussed with the triangles!) Vectors and Scalars. What's the difference and why do we care? Vectors have direction and scalars are the length part of the vector. Sometimes we need to know where the vector's going and sometimes we only need to know its magnitude (scalar quantity). The displacement (green arrow), a scalar quantity, from Springfield to Columbia is the same regardless of which route is chosen. But the actual distance traveled is different depending on the route (vector) chosen. In the schematic below, there are 2 forces pulling on the toy car. What now? Vector Addition Vectors are added using vector addition which means that they are added head to tail. The resultant vector is then drawn from where you started to where you finished. Two ways to add vectors: Graphically Components: we will only do this. Adding by components. Determine the X and Y components of each vector and add them together. Adding by components. Determine the X and Y components of each vector and add them together. Adding by components. Determine the X and Y components of each vector and add them together. Then recombine into the resultant vector (if needed). Subtraction: By Components Find the individual x and y components. Subtract them: Rx=Ax-Bx Find the resultant by using R2 = Rx2 + Ry2 Find the angle q=tan-1(Ry/Rx) Watch directions and signs and DO NOT ASSUME that cos always gives x and sin always gives y. Look at your angle and the side you want determines if you use sin or cos. Measure angles from the same axis. Convention is to measure from the positive X axis counterclockwise It is okay to use negative angles. Just remember what direction you're going.