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1 P Physics Summer ssignment I. The dvanced placement eams are in early May which necessitates a very fast pace. This summer homework will allow us to start on the Physics subject matter immediately when school begins. This packet is a math 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 in particular, requires an eceptional 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. nother key area in Physics is understanding vectors. III. The attached pages contain a brief review, hints, and eample problems. It is hoped that combined with your previous math knowledge this part of the assignment is merely a review and a means to brush up before school begins in the fall. Please read the tet and instructions throughout. IV. Your summer assignment has working parts:. Math review found on the following pages. Equation Flash Cards C. Tetbook ssignment V. It is all DUE the first day of school. Signed Class Epectations Sheet (syllabus to come in Sept.). ead this whole sheet.. Complete the section at the bottom of this form and obtain appropriate signatures.. ll ssignments, separately stapled/organized.. Math review answers on the paper below with work and answers shown on attached loose leaf.. Equation Flash Cards LL of the P physics equations (from the P tables, see link on my website). You must write the equation on the front of the 3 5 inde card. On the back write the main topic that the equation falls under(listed on the P tables), the equation again, leave a space for the name of the equation that we will fill in during the year, and lastly write all of the variables with their names and units for all. 3. The Physics Tetbook ssignment ead Chapter. Complete Problems # s, 5, 0, 4, 9, 4, 30, 33, 40, 48. VI. There will be a test covering the math review during the second week of class (meaning after the first day/week). VII. Complete the questions on the net page. We have read the policies and epectations for P Physics. We understand and accept these policies. Student Signature: Date Parent/Guardian Name (print) Parent / Guardian Signature: Date P Physics, Summer ssignment

2 Complete the following questions with showing your complete work/solution on a separate attached sheet of paper.. 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 eample 00 is easier to write than.000, but 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. kg a. T = s π 0. 0 kg s 3 = K 4 b. = ( kg)(. 0 m / s) = ( )( ) N m C C c. F = = C 0.3m d. = Ω Ω p J J e. e = = J ( ) P = f..33sin 5.0 =.50sinθ θ = K J s s.7 0 J = = g. ma ( )( ) h. γ = ms ms =. Often problems on the P eam 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, a. v = v + a( s s ) a = b. K k, = = μ I = r = π r o g., h. mλl m = d = d, c. T = π p, g g = d. F G mm g = r = r e. f., = = mgh mv, v = + + = o vot at, t i. pv = nt, T = n j. sin θc =, θc = n k. l. qv mv, v = = = +, si = f s s o i P Physics, Summer ssignment

3 3. 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. kilometers (km) to meters (m) and meters to kilometers gram (g) to kilogram (kg) centimeters (cm) to meters (m) and meters to centimeters Celsius ( o C) to Kelvin (K) millimeters (mm) to meters (m) and meters to millimeters atmospheres (atm) to Pascals (Pa) nanometers (nm) to meters (m) and metes to nanometers liters (L) to cubic meters (m 3 ) micrometers (μm) to meters (m) Other conversions will be taught as they become necessary. 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 g = kg b.. km = m c. 83 nm = m d. 98 K = o C e m = cm f m = mm g.. atm = Pa h. 5.0 μm = m i..65 mm = m j. 8.3 m = km k. 5.4 L = m 3 l cm = m m m = nm n..50 m = km 6. Solve the following geometric problems. a. Line touches the circle at a single point. Line etends through the center of the circle. i. What is line in reference to the circle? ii. How large is the angle between lines and? b. What is angle C? C 30 o 45 o c. What is angle θ? 30 o θ d. How large is θ? θ 30 o P Physics, Summer ssignment 3

4 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 under the curve at the right? 4 7. Using the generic triangle to the right, ight Triangle Trigonometry and Pythagorean Theorem solve the following. Your calculator must be in degree mode. 0 a. θ = 55 o and c = 3 m, solve for a and b. b. θ = 45 o and a = 5 m/s, solve for b and c. c. b = 7.8 m and θ = 65 o, solve for a and c. d. a = 50 m and b = 80 m, solve for θ and c. 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. Vectors Most of the quantities in physics are vectors. This makes proficiency in vectors etremely important. Magnitude: Size or etent. 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. Eamples: time, mass, and temperature Vector: physical quantity with both a magnitude and a direction. directional quantity. Eamples: velocity, acceleration, force Notation: or Length of the arrow is proportional to the vectors magnitude. Direction the arrow points is the direction of the vector. Negative Vectors Negative vectors have the same magnitude as their positive counterpart. They are just pointing in the opposite direction. P Physics, Summer ssignment 4

5 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+(-)=. 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 (80 o apart). There are two methods of adding vectors Parallelogram + Tip to Tail It is readily apparent that both methods arrive at the eact same solution since either method is essentially a parallelogram. It is useful to understand both systems. In some problems one method is advantageous, while in other problems the alternative method is superior. 8. Draw the resultant vector using the parallelogram method of vector addition. Eample b. d. a. c. e. P Physics, Summer ssignment 5

6 9. Draw the resultant vector using the tip to tail method of vector addition. Label the resultant as vector Eample : + c. P + V P V - Eample : d. C D C D a. X + Y e. + + C X Y C b. T S T S f. C C Direction: What does positive or negative direction mean? How is it referenced? The answer is the coordinate ais system. In physics a coordinate ais system is used to give a problem a frame of reference. Positive direction is a vector moving in the positive or positive y direction, while a negative vector moves in the negative or negative y direction (This also applies to the z direction, which will be used sparingly in this course). +y - θ + -y What about vectors that don t fall on the ais? You must specify their direction using degrees measured from East. P Physics, Summer ssignment 6

7 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 ais that describe the resultant. + y + y + or + ny vector can be described by an ais vector and a y ais vector which summed together mean the eact same thing. The advantage is you can then use plus and minus signs for direction instead of the angle. 0. For the following vectors draw the component vectors along the and y ais. a. c. b. d. Obviously the quadrant that a vector is in determines the sign of the and y component vectors. P Physics, Summer ssignment 7

8 Trigonometry and Vectors Given a vector, you can now draw the and y component vectors. The sum of vectors and y describe the vector eactly. gain, any math done with the component vectors will be as valid as with the original vector. The advantage is that math on the and/or y ais 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 0 40 o 0 y cosθ = adj hyp adj sinθ = opp hyp = hypcosθ opp = hypsinθ = hypcosθ y = hypsinθ o o = 0cos 40 y = 0sin 40 = 766. y = 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 and y ais. emember the plus and minus signs on you 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 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. Eample: 50 at 35 o c at 60 o = hypcosθ 35 o = 50cos 35 = 43 o 50 a. 89 at 50 o y = hypsinθ y = 50sin 35 o y = 05 d at 80 o b at 345 o e. at 65 o P Physics, Summer ssignment 8

9 f. 990 at 30 o g at 5 o. Given two component vectors solve for the resultant vector. This is the opposite of number above. Use Pythagorean Theorem to find the hypotenuse, then use inverse (arc) tangent to solve for the angle. Eample: = 0, y = -5 = + y tanθ = opp adj θ 0-5 = + y = = 5 θ = tan θ = tan opp adj y o o o = 33. a. = 600, y = 400 d. = , y = b. = -0.75, y = -.5 e. = 0,000, y = 4,000 c. = -3, y = 6 f. = 35, y = 998 P Physics, Summer ssignment 9

10 How are vectors used in Physics? They are used everywhere! Speed Speed is a scalar. It only has magnitude (numerical value). v s = 0 m/s means that an object is going 0 meters every second. ut, we do not know where it is going. Velocity Velocity is a vector. It is composed of both magnitude and direction. Speed is a part (numerical value) of velocity. v = 0 m/s north, or v = 0 m/s in the + direction, etc. There are three types of speed and three types of velocity Instantaneous speed / velocity: The speed or velocity at an instant in time. You look down at your speedometer and it says 0 m/s. You are traveling at 0 m/s at that instant. Your speed or velocity could be changing, but at that moment it is 0 m/s. verage speed / velocity: If you take a trip you might go slow part of the way and fast at other times. If you take the total distance traveled divided by the time traveled you get the average speed over the whole trip. If you looked at your speedometer from time to time you would have recorded a variety of instantaneous speeds. You could go 0 m/s in a gas station, or at a light. You could go 30 m/s on the highway, and only go 0 m/s on surface streets. ut, while there are many instantaneous speeds there is only one average speed for the whole trip. Constant speed / velocity: If you have cruise control you might travel the whole time at one constant speed. If this is the case then you average speed will equal this constant speed. trick question Will an object traveling at a constant speed of 0 m/s also always have constant velocity? Not always. If the object is turning around a curve or moving in a circle it can have a constant speed of 0 m/s, but since it is turning, its direction is changing. nd if direction is changing then velocity must change, since velocity is made up of speed and direction. Constant velocity must have both constant magnitude and constant direction. ate Speed and velocity are rates. rate is a way to quantify anything that takes place during a time interval. ates are easily recognized. They always have time in the denominator. 0 m/s 0 meters / second The very first Physics Equation Velocity and Speed both share the same equation. emember speed is the numerical (magnitude) part of velocity. Velocity only differs from speed in that it specifies a direction. v = v stands for velocity stands for displacement t stands for time t Displacement is a vector for distance traveled in a straight line. It goes with velocity. Distance is a scalar and goes with speed. Displacement is measured from the origin. It is a value of how far away from the origin you are at the end of the problem. The direction of a displacement is the shortest straight line from the location at the beginning of the problem to the location at the end of the problem. How do distance and displacement differ? Supposes you walk 0 meters down the + ais and turn around and walk 0 meters down the ais. The distance traveled does not depend on direction since it is a scalar, so you walked = 30 meter. Displacement only cares about you distance from the origin at the end of the problem = 0 meter. 3. ttempt to solve the following problems. Take heed of the following. P Physics, Summer ssignment 0

11 lways use the KMS system: Units must be in kilograms, meters, seconds. On the all tests, including the P eam you must:. List the original equation used.. Show correct substitution. 3. rrive at the correct answer with correct units. Distance and displacement are measured in meters (m) Speed and velocity are measured in meters per second (m/s) Time is measured in seconds (s) Eample: car travels 000 meters in 0 seconds. What is its velocity? m v = v = 000 t 0s v = 00 m s a. car travels 35 km west and 75 km east. What distance did it travel? b. car travels 35 km west and 75 km east. What is its displacement? c. car travels 35 km west, 90 km north. What distance did it travel? d. car travels 35 km west, 90 km north. What is its displacement? e. bicyclist pedals at 0 m/s in 0 s. What distance was traveled? f. n airplane flies 50.0 km at 300 m/s. How long does this take? g. skydiver falls 3 km in 5 s. How fast are they going? h. car travels 35 km west, 90 km north in two hours. What is its average speed? i. car travels 35 km west, 90 km north in two hours. What is its average velocity? P Physics, Summer ssignment