NOTHEN ULINGTON COUNTY EGIONL HIGH SCHOOL Honors and dvanced Placement Program 013 Supplemental ssignment P Physics equired Materials dditional esources None Physics & Math Tutorials on the Web www.hippocampus.org Math review videos Physics Videos at various levels www.physicsclassroom.com/class Due Date(s) Teacher Contact Information Monday, ugust 6 th 013 H.S. Main Office ttn: Physics Department Expected time for completion: 4 Hours Note: The time required to complete this assignment will vary this is only a rough estimate to help with planning. Students should keep in mind their own study habits and pace of work in budgeting time to complete this assignment. Departmental Supervisor s Contact Information: Ms. my Stella Director of Instruction - Math and Science (609) 98-3900, extension 0 astella@nburlington.com Purpose of assignment: This assignment serves as the beginning of our rigorous course of study in P Physics. The primary goal of this assignment is to serve as a math review that will help you brush up on the mathematical concepts utilized throughout the course Skills/Knowledge required for completion: lgebra and Geometry math skills bility to follow a given procedure Grading: Graded for completion and assessed with a Major ssessment within the first week of school NC P Physics, Summer ssignment 013 1
P- Physics Summer ssignment 013 Name Dear Student, Welcome to P Physics at Northern urlington! P Physics is a first year physics course that covers the equivalent of two semesters of college level physics. Due to the large amount of material in the P curriculum and the short amount of time we have to cover that material, this course moves at a very fast pace. This level of academic rigor is likely more than you have experienced in your past studies, but in the end you will not only be prepared to take the P exam, but you will also be ready for the style of academic study found with most college programs. Physics, and P Physics in particular, requires an exceptional proficiency in algebra, trigonometry, and geometry. In addition to the science concepts, Physics often seems like a course in applied mathematics. The following assignment includes mathematical problems that are considered routine in P Physics. This includes knowing several key metric system conversion factors and how to employ them, graphical analysis of data, and understanding vectors. The attached pages contain carefully crafted review, hints, and example problems. It is hoped that combined with your previous math knowledge this assignment is a review and a starting point in your study of physics. Please read the text and instructions throughout. There will be a test covering this packet the first week of class. II. What if I don t get all the problems or don t understand the instructions?. Seek help! 1. Physics & Math Tutorials on the Web www.hippocampus.org Math review videos Physics Videos at various levels www.physicsclassroom.com/class. Show work in order to receive credit. C. Come to class the first day with your questions, in order to resolve these issues prior to the test. NC P Physics, Summer ssignment 013
SECTION ONE: Working with Equations / Scientific Notation 1. The following are ordinary physics problems. Place the answer in scientific notation when appropriate and simplify the units (Scientific notation is used when it takes less time to write than the ordinary number does. s an example 00 is easier to write than.00x10, but.00x10 8 is easier to write than 00,000,000). Do your best to cancel units, and attempt to show the simplified units in the final answer. a. T s 4. 510 kg. 0 10 kg s 3 1 K 4 b. 6.6 10 kg.1110 m / s c. F Nm C 9 9 3.10 C9.610 C 9 9.010 0.3m d. 1 1 1 4. 510 9. 4 10 p P 1.7 10 J 3.310 e. e 3 3 1.7 10 J J f. 1.33sin 5.0 1.50sin P Physics, Summer ssignment 3
Often problems on the P exam are done with variables only. Solve for the variable indicated. Don t let the different letters confuse you. Manipulate them algebraically as though they were numbers. o o, g. v v as s a l. x m ml d, d h. 1 K kx, x m. pv nt, T i. T p, g g n1 n. sin c, c n j. F G m m 1 g, r r o. 1 qv mv, v k. 1 mgh mv, v p. 1 1 1, s i f s s o i SECTION TWO: Measurements When using a measuring device, you MUST estimate between the smallest marks on the instrument. For example, if a ruler is marked off in increments of whole millimeters, you estimate the length of an object to the closest tenth of a millimeter. Use the ruler below to measure the length of the arrow. emember to estimate between the smallest marks. The length of the arrow is mm. P Physics, Summer ssignment 4
SECTION THEE: Units Science uses the KMS system (SI: System Internationale). KMS stands for kilogram, meter, second. These are the units of choice of physics. The equations in physics depend on unit agreement. So you must convert to KMS in most problems to arrive at the correct answer. There are two categories of unit conversions: [1] Converting with SI prefixes & [] converting to different unit scales [1] kilometers (km) to meters (m) and meters to kilometers centimeters (cm) to meters (m) and meters to centimeters millimeters (mm) to meters (m) and meters to millimeters nanometers (nm) to meters (m) and metes to nanometers gram (g) to kilogram (kg) [] Celsius ( o C) to Kelvin (K) atmospheres (atm) to Pascals (Pa) liters (L) to cubic meters (m 3 ) [1] One Simple Method for Converting SI Prefixes: Where you see the prefix, simply replace with the exponential notation of the number. Example: 600 nm from above chart n nano 10-9 600 x 10-9 m [] Factor Label Method for Converting Units: Similar to stoichiometry! Example: 150 yards to inches What if you don t know the conversion factors? Colleges want students who can find their own information (so do employers). Hint: Try a good dictionary and look under measure or measurement. Or the Internet? Enjoy. a. 4008 g = kg c. 83 nm = m b. 1. km = m d. 98 K = o C P Physics, Summer ssignment 5
e. 0.77 m = cm i. 8.3 m = km f. 8.8x10-8 m = mm j. 40.0 cm = m g. 5.0 m = m k. 6.3x10-7 m = nm h..65 mm = m l. 1.5x10 11 m = km SECTION FOU: Geometry eview Solve the following geometric problems. a. Line touches the circle at a single point. Line extends through the center of the circle. i. VOC: What is line in reference to the circle? ii. VOC: What is line in reference to the circle? iii. How large is the angle between lines and? b. What is angle C? 30 o C 45 o c. What is angle? 30 o P Physics, Summer ssignment 6
d. How large is? 30 o e. The radius of a circle is 5.5 cm, i. What is the circumference in meters? ii. What is its area in square meters? f. What is the area of the space enclosed between the plotted line on the graph and the x and y axis at the right? 4 1 0 Using the generic triangle to the right, ight Triangle Trigonometry and Pythagorean Theorem solve the following. Your calculator must be in degree mode. a. = 55 o and c = 3 m, solve for a and b. b. = 45 o and a = 15 m/s, solve for b and c. P Physics, Summer ssignment 7
Use the image to the left to solve for the unknown values (this is a problem we will do again a few weeks into the semester when we discuss forces on inclined planes) X = Y = SECTION FIVE: Graphical nalysis You should be familiar with graph construction (by hand and on Excel). This is a topic that often appears on P exams and is an easy way to score points on any assignment. Note: When you are told to graph pples vs. Oranges, the 1st thing goes on the y-axis. The nd thing is on the x-axis. Fill in the following table and plot the points on the grid below as distance versus time. e sure to correctly label the graph (axes labels, including units, and title) Time, t (s) Distance, d (m) 0.0 0 1.0 5.1.0 9.9 3.0 15. 4.0 5. Y X 0 units 60 o Draw the best fit line through your data points. Now use Excel to plot the graph. ecord the equation of the best-fit line and value. basics @ http://www.associatedcontent.com/video/14714/graphing_on_excel.html (ttach Excel graph to this packet or cut and tape in below) What is the slope of the line that you plotted (with correct units)? P Physics, Summer ssignment 8
SECTION SIX: Vectors Most of the quantities in physics are vectors. This makes proficiency in vectors extremely important. Magnitude: Size or extent. The numerical value. Direction: lignment or orientation of any position with respect to any other position. Scalars: physical quantity described by a single number and units. quantity described by magnitude only. Examples: time, mass, and temperature Vector: physical quantity with both a magnitude and a direction. directional quantity. Examples: velocity, acceleration, force Notation: or Length of the arrow is proportional to the vectors magnitude. Negative Vectors Direction the arrow points is the direction of the vector. Negative vectors have the same magnitude as their positive counterpart. They are just pointing in the opposite direction. Vector ddition and subtraction Think of it as vector addition only. The result of adding vectors is called the resultant. + = So if has a magnitude of 3 and has a magnitude of, then has a magnitude of 3+=5. When you need to subtract one vector from another think of the one being subtracted as being a negative vector. Then add them. is really + = negative vector has the same length as its positive counterpart, but its direction is reversed. So if has a magnitude of 3 and has a magnitude of, then has a magnitude of 3+(-)=1. This is very important. In physics a negative number does not always mean a smaller number. Mathematically is smaller than +, but in physics these numbers have the same magnitude (size), they just point in different directions (180 o apart). Vectors in dimensions Tip to Tail (draw the first vector & at the tip of the first vector then draw the nd vector) http://www.youtube.com/watch?v=cdhqylzfegm + - - P Physics, Summer ssignment 9
Draw the resultant vector using the tip to tail method of vector addition. Label the resultant as vector Example 1: + b. T S T S Example : - c. P + V P V a. X + Y d. C D X Y C D Component Vectors resultant vector is a vector resulting from the sum of two or more other vectors. Mathematically the resultant has the same magnitude and direction as the total of the vectors that compose the resultant. Could a vector be described by two or more other vectors? Would they have the same total result? This is the reverse of finding the resultant. You are given the resultant and must find the component vectors on the coordinate axis that describe the resultant. + y + y + x or + x ny vector can be described by an x axis vector and a y axis vector which summed together mean the exact same thing. The advantage is you can then use plus and minus signs for direction instead of the angle. P Physics, Summer ssignment 10
For the following vectors draw the component vectors along the x and y axis. a. Obviously the quadrant that a vector is in determines the sign of the x and y component vectors. Trigonometry and Vectors Given a vector, you can now draw the x and y component vectors. The sum of vectors x and y describe the vector exactly. gain, any math done with the component vectors will be as valid as with the original vector. The advantage is that math on the x and/or y axis is greatly simplified since direction can be specified with plus and minus signs instead of degrees. ut, how do you mathematically find the length of the component vectors? Use trigonometry. 40 o 10 40 o 10 x y cos adj hyp sin opp hyp adj hyp cos opp hyp sin x hyp cos y hyp sin x o o 10cos 40 y 10sin 40 x 7. 66 y 6. 43 Solve the following problems. You will be converting from a polar vector, where direction is specified in degrees measured counterclockwise from east, to component vectors along the x and y axis. emember the plus and minus signs on your answers. They correspond with the quadrant the original vector is in. Hint: Draw the vector first to help you see the quadrant. nticipate the sign on the x and y vectors. Do not bother to change the angle to less than 90 o. Using the number given will result in the correct + and signs. The first number will be the magnitude (length of the vector) and the second the degrees from east. Your calculator must be in degree mode. Example: 50 at 35 o x hyp cos 35 o x 50cos 35 x 143 o a. 89 at 150 o 50 y hyp sin y 50sin 35 o y 05 P Physics, Summer ssignment 11
b. 6.50 at 345 o c. 0.00556 at 60 o Given two component vectors solve for the resultant vector. This is the opposite of the above. Use Pythagorean Theorem to find the hypotenuse, then use inverse (arc) tangent to solve for the angle. Example: x = 0, y = -15 x y tan opp adj 0-15 x y 5 0 15 tan tan 1 1 opp adj y x d. x = 600, y = 400 f. x = -3, y = 16 e. x = -0.75, y = -1.5 g. x = 0.0065, y = -0.0090 How are vectors used in Physics? They are used everywhere! P Physics, Summer ssignment 1