Oakland Technical High School. AP PHYSICS SUMMER ASSIGNMENT Due Monday, August 22 nd

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1 Oakland Technical High School P PHYSICS SUMME SSIGNMENT Due Monday, ugust nd I. This packet is a review to brush up on valuable skills, and perhaps a means to assess whether you are correctly placed in dvanced Placement Physics. II. Physics, and P Physics C in particular, requires an exceptional proficiency in algebra, trigonometry, geometry and calculus. 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. nother key area in Physics is understanding the geometry of vectors. ase Units. In the English System of measurement, the fundamental quantities are force, length, and time, which are measured in the standard units: pound, foot, and second. This system is commonly used by merican engineers. On the other hand, the International System (abbreviated SI) uses mass, length and time, which are measured in the standard units: kilogram, meter, and second. We will be using these units in this course. Prefixes. Prefixes will be used with measurements to help us compare quantities. For example, if you had to compare 4. gigabytes of memory space with 700 megabytes, you could probably do it after some thought. ut, it would be even easier to compare 4. gigabytes with.7 gigabytes (which happen to describe the same two quantities as above). Prefixes also let us avoid writing out long numbers. lthough we could compare 4,00,000,000 bytes with,700,000,000 bytes above, it is cumbersome. We can talk about megabytes or megaseconds or megameters. Mega-, wherever it appears, will always mean million of the base unit. megasecond represents the time that goes by in about.5 days. megameter represents the distance from Oakland to Portland, Oregon, or Phoenix, rizona (approximately). You will need to memorize 8 prefixes. From large to small, they are: Prefix Factor Power of 0 Symbol giga-,000,000, G mega-,000, M kilo-, k centi c milli m micro µ nano n pico p Notice that there are two upper-case symbols (G and M), five lower-case symbols (k, c, m, n, p), and one symbol that is a Greek letter (µ, pronounced mu). The symbol for the prefix is used with the symbol for the base unit: m for meter, s for second, and g for gram. Comparisons. The weight of.0 kilogram of mass is about. pounds. (That is, gravity pulls on one kilogram of mass with a force of. pounds.) The mass of a small paper clip is about.0 gram, and the mass of a 5-cent coin is about 5.0 grams. (The kilogram is the only standard SI unit that uses a prefix.)

2 The most common SI units for distance are the meter, kilometer, centimeter, and millimeter. The distance from your nose to the end of your outstretched arm is about a meter. kilometer is about 0.6 mile--a little over one-half. The width of your little finger is about.0 centimeter. The thickness of the most common pencil lead is 0.5 millimeter, so double it to have.0 millimeter. Scientific Notation. Physicists often write very large or very small measurements using scientific notation (or exponential notation in some books). number in scientific notation always is written with two factors: a number between 0 and 0, multiplied by a power of 0. The first factor will have a number of decimal places that show the precision of the measuring instrument that was used. If you used a wall clock to measure a time interval and you counted 5 ticks, you would write your measurement as 5. x 0 seconds (if you wanted to use scientific notation). However, the same time interval might be measured using a precise stopwatch, and the time might be written 5.45 x 0 in scientific notation. You will need to know enough about scientific notation to take a number in standard notation and write it using scientific notation. You will also need to know how to enter a number in scientific notation into your calculator and record a number from your calculator correctly. Conversion of Units and Conversion Factors. Many times, before a calculation can be done with two measurements, one of the measurements must be changed to have the same units as the other. oth the black book and the blue book use the method of conversion factors in this situation. The math is not difficult; it is more a method of record-keeping. Example: Suppose you need to add m plus 50 µm.. Convert 50 µm to the same measurement in m m. Since µm = m, the ratio m is exactly equal to. This means you can multiply any measurement by that ratio without changing the size of the measurement. This ratio is called the conversion factor for this problem. 3. Using the conversion factor method, multiply 50 µm times the ratio shown above. Notice that there is the unit symbol µm in both the numerator and the denominator, so cancel it out of both places. When you multiply the numbers together, you have , and m is the only unit that remains. Now this measurement can be added to m. 4. dd m plus m, to get m, which is the answer to the problem. You will need to use conversion factors to convert several measurements from one unit to another. Derived Units. When a calculation is made with measurements, the units are combined just as if they were variables. The final combination of units is called a derived unit, because it comes from the other units. Example: Find the volume of a box that is. m long, 0.3 m high, and. m deep, using the formula V = lwh.. (. m)(0.3 m)(. m) = The derived unit for the answer is m 3 because (m)(m)(m) = m m 3 is the complete answer, or 3.96 x 0 - m 3 in scientific notation. You will need to write the correct derived units to go with an answer that was calculated using a formula. Vectors are used in the P Physics book to show displacement, velocity, acceleration, and force. We will learn a notation system for doing vector calculations in three dimensions that is slightly different from the black book. However, for the summer assignment, the problems are limited to two dimensions.

3 Scalar quantities. Many measurements can be reported without using vectors, because they do not refer to a direction. For example, time, temperature, and mass can be described completely without using direction. They are scalar quantities. Vector quantities. Vector quantities, on the other hand, are measurements that cannot be completely described without using direction. For example, a car may be moving at 90 kilometers per hour, but the result after one hour would be very different if it were moving west compared to the result if it were moving east. Therefore, to completely describe the velocity of the car, you would need to say 90 km/h, East. Displacement (s), velocity (v), and acceleration (a) are the vector quantities we will use to describe the motion of an object. Force vectors also must include direction. The direction may be written as an angle, or it may be shown by writing the two components of the force vector (horizontal and vertical, or x and y). Therefore, the force vector 0 N, 60 (read 0 newtons, at a 60 angle) means the same thing as a force vector where F x = 0 N, and F y = 7.3 N. They are two different ways of showing the direction of the vector. The magnitude of the vector remains the same: 0 N. For the majority of situations in the blue book, the force vectors will be concurrent; that is, all vectors in a problem will act on a single point. This is a change from the black book, in which the majority of problems had vectors that acted on different point along an object. In that sense, the problems in the blue book will be less complex. In the blue book, the complexity will come in the motion of the object that results from the forces. free-body diagram is used to represent the force vectors. n accurate free-body diagram is the first step in a successful solution of a force problem. In the blue book, since the forces are concurrent, the free-body diagram will be drawn so that the endpoints (or tails) of the vectors are touching. This will be the consistent method used throughout P Physics. When the problem involves a large object, the tails of the vectors will all meet at the center of gravity of the object, and the arrows will point out from there. In most of the problems that we solve in P Physics, we can represent the object with a point mass without any loss of accuracy. Example: In the free-body diagram shown, suppose vectors,, and C represent concurrent forces, and the center of gravity of the object is at point D. To find the resultant of the three forces, the blue book will find the x-component of the resultant and the y-component of the resultant, and then combine them using the Pythagorean Theorem. Suppose force is 50 N, force is 50 N, and force C is 0 N. Then x = (50)(cos 30 ) = 43.3 N. x = (50)(cos 0 ) = 50 N. C x = (0)(cos(-00 )) = -3.5 N. lso, y = (50)(sin 30 ) = 5 N. y = (50)(sin 0 ) = 0 N. C y = (0)(sin(-00 )) = -9.7 N. The resultant of the forces,, has the following x- and y-components: x = Fx = 43.3 N + 50 N + (-3.5 N) = 89.8 N. y = Fy = 5 N + 0 N + (-9.7 N) = 5.3 N. Using the Pythagorean Theorem to find the magnitude of the resultant, = x + y. So, = (89.8) + (5.3) = 90.0 N. The angle, θ = tan - ( y / x ) = 3.4. The resultant force of combining forces,, and C, is a force of 90.0 N at an angle of 3.4 above the x-axis. The short form of this statement is = 90.0 N, 3.4. is called the net force, or the sum of the forces. You must be able to calculate the net force exerted on an object by combining the individual forces correctly. C D 3

4 POLEMS. rea For each figure, estimate the area. Your answer will have three parts: (a) the best answer, (b) the greatest reasonable answer, and (c) the least reasonable answer. riefly explain your reasoning for each problem. Use your best judgment, and support your judgment with reasoning

5 4.. lgebra. Often problems on the P exam are done with variables only. Solve each problem for the variable indicated. Don t let the different letters confuse you. Manipulate them algebraically as though they were numbers. Many subscripts are used as labels in physics (for example:,, c, o, i); simply keep the subscript with the variable in your solution. 0 0 a. v v a x x, a = b. U kx, x = c. T p, g = d. F g, r = g mm G r e. mgh mv, v = f. xx 0v0t at, t =, r = h. x ml r m d g. 0, d = i. pv nt, T = n, c = j. sin c n 5

6 k. qv mv, v = l., s f s s i = o i 3. Quadratic Equations. Frequently, equations in physics will require the quadratic formula to find a solution. Solve each of the following quadratic equations. a. x 8x 0 b. x 3x 0 c. 3x4 x d. x 5 3x e. xx 5 f. x x 6x 6x 6 4. Geometry eview. Solve the following geometry problems. Line touches the circle at one point. Line passes through the center of the circle. a. Describe line in relation to the circle: b. What is the angle between and? C c. What is the measure of angle C? 30º 45º 6

7 30º d. If is parallel to, what is the measure of angle? e. What is the measure of angle? 30º f. The radius of a circle is 5.5 m. i. What is the circle s circumference in meters? ii. What is the circle s area in square meters? 5. ight Triangle Trigonometry. Use the generic right triangle shown in the figure. Solve the following, using the same units in your answer as are given in the problem a. θ = 55º and c = 3 m, solve for a and b. b. θ = 45º and a = 5 m/s, solve for b and c. c. b = 7.8 m and θ = 65º, solve for a and c. d. a = 50 m and b = 80 m, solve for θ and c. 7

8 e. a =5 cm and c = 3 cm, solve for b and θ. f. b =04 cm and c = 65 cm, solve for a and θ. 6. Measurement. Scientists use the mks system (SI system) of units. mks stands for meter-kilogram-second; these are the preferred units for solving physics problems. They are referred to as base units. You must check to be sure all measurements are converted to mks before beginning a solution. This is known as agreement of units. In preparation for P Physics, you must know how to make the following conversions: kilometers (km) to meters (m) centimeters (cm) to meters (m) millimeters (mm) to meters (m) micrometers (m) to meters (m) grams (g) to kilograms (kg) minutes (min) to seconds (s) hours (h) to seconds (s) days (d) to seconds (s) years (y) to seconds (s) Complete each of these conversions g = kg.. km = m m = m K = ºC cm = m mm = m g = kg cm = m Write each measurement using the correct mks base unit grams = milligrams =. 50 milliseconds =. 3.3 centimeters = days = 4. 7 years = micrometers = minutes = Write each measurement using scientific notation and the correct mks base unit mm = mg = kg = µg = µg =.,308 µs = s = ms = µs = kg = 8

9 7. Vectors. Most of the quantities that are used in physics are vectors. Therefore, students must be proficient in using vectors. Definitions. Magnitude size or extent. Magnitude is the numerical portion of a vector s description. Direction alignment or orientation of any position with respect to any other position. Direction is often given as an angle. Scalar a physical quantity that is described by a single number and units. Vector a physical quantity that is described by a magnitude and a direction. directional quantity. Examples: force, velocity Notation: or Length of the arrow is proportional to the vector s magnitude. Direction of the arrow is the vector s direction. The head of the vector has the arrow; the tail of the vector is the other end. and are identical vectors because they both have the same magnitude and direction. Negative Vector It is possible to have a negative vector. The negative vector has the same magnitude as its positive counterpart, but it is pointing in the opposite direction. Vector ddition dd vectors by combining both the magnitude and the direction. The result of adding two vectors is called the resultant. There are four situations to learn: i. oth vectors point in the same direction (parallel). (dd the magnitudes) ii. The vectors point in opposite directions (anti-parallel). (Subtract the magnitudes. esultant direction is same as vector with greater magnitude.) iii. The vectors are perpendicular. (Find the resultant magnitude with the Pythagorean Theorem.) These two vector diagrams show the same vector addition in two different ways. iv. The vectors are in different directions. Either of two different methods will give the same resultant. a. Parallelogram Method. The tails of and are connected to form adjacent sides of a parallelogram. The resultant points from the point where the tails connect to the opposite corner of the parallelogram. b. Head-to-Tail Method. The vectors are drawn with their correct directions, so that the tail of is connected to the head of. The resultant points from the tail of to the head of. Many vectors can be connected using the head-to-tail method, and the resultant will point from the tail of the first vector in the chain to the head of the last vector. 9

10 Vector Subtraction Vector subtraction is exactly the same as adding the negative of the second vector. ( ). Instructions. For each problem, draw the diagram to show the resultant for the vector addition of each of the following. Draw the given vectors using either the parallelogram method or the head-to-tail method. a. b. c. d. e. f. Draw the resultant for C D C D 0

11 System of equations: Often there will be multiple unknowns to solve for in physics problems. You will need the same number of equations as you have unknowns in order to solve for the unknown quantities, these are called systems of equations. ) Using the following 3 equations find the value of x 3x + 4y = 0 and 7x-3y= ) Using the following 3 equations find the value of x 9x y = and y3 4z = 4 and z + 3y = 90

Name. Welcome to AP Physics. I am very excited that you have signed up to take the AP Physics class.

Name. Welcome to AP Physics. I am very excited that you have signed up to take the AP Physics class. Name P Physics Summer ssignment Fall 013-014 Welcome to P Physics. I am very excited that you have signed up to take the P Physics class. You may ask I sure would why a summer packet? There is so much