Name: AP Physics 1/ Summer Assignment Math Review Scientific Notation a method for writing large or small numbers using powers of 10. 005 =.005 10 3 OR.005E3 0.0001 = 1. 10-4 OR 1.E-4 Note that the letter capital E can be substituted for 10 and is considered to have the same value. Write each of the following using scientific notation. 1) 4316 ) 0.004 3) -700000 4) -0.0000150 SI Prefies a set of symbols used to abbreviate large or small numbers can be used in conjunction with scientific notation. Prefi Symbol Meaning tera T 10 1 giga G 10 9 mega M 10 6 * kilo k 10 3 deci d 10-1 * centi c 10 - * milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-1 * you should MEMORIZE the italicized prefies To remove SI prefi sub power of 10 for symbol 3.0 mm = 3.0 10-3 m = 0.003 m.0 kw =.0 10 3 W = 000 W To add SI prefi sub symbol in for power of 10 40 m = 0.40 10 3 m = 0.40 km 0.0056 s = 5.6 10 10-3 s = 5.6 ms Rounding a method for truncating numbers into a shorter form; often used in conjunction with significant digit rules. Round off each of the following numbers to the number of digits shown AND rewrite it using scientific notation. 5) round 634000 to digits 6) round 0.0345 to digits 7) round 8.655 to 3 digits Note that SI prefies are simply placeholders for powers of 10 it is essential to understand this! Come up with at least TWO ways to rewrite 0.04 meter using SI prefies. 8) 9) Write an equivalent epression for 5000 kj using a different SI prefi. 10)
Significant Digits a set of rules used to determine how many digits in a given measurement are meaningful/desirable for reporting. Rules - If the number contains a decimal point then all digits ecept for leading zeroes are significant..450 contains 4 sig. digits 0.003 contains sig. digits 4.00510 contains 6 sig. digits 50. contains sig. digits - If the number does not contain a decimal point then all digits ecept for leading AND trailing zeroes are significant. Adding/Subtracting with Significant Digits Line up all of the numbers on the decimal point. Perform the operation and then truncate the final answer using the left-most digit as a guide. 1 3. 0 0 5. 4 + 1 4 5. 3 1 8 0. 6 3 5 Final answer - 180.6 Multiplying/Dividing with Significant Digits Determine number of significant digits in operands. The answer should be rounded to the same number of significant digits as the operand with the LEAST number of significant digits. 30,000 contains 1 sig. digit 3050 contains 4 sig. digits 456. 3. 0.0056 = 59.69504 (4) (3) () Indicate the number of significant digits in each number. 11) 3100.0 1) 0.0013 13) 0.0040 14) 7330.0 15) 300 km 16) 15 students 17) 0.0300 We can t have more than TWO significant digits in our answer. So the final answer is 59. Evaluate each epression, showing the correct number of significant digits in your answer. 18) + 45.5 + 0.36 19) 0.003 953 0) 005.4 4.8 1).4 10 3 / 1. 10 4 P a g e
Unit Conversions a method for turning one set of units into a different set of units to arrive at an equivalent epression of the same value. The factor-label method uses a series of ratios that are arranged to cancel out eisting units and introduce desired ones. Eamples: Convert 3.0 minutes into seconds. 3.0 min 1 60s 1min 180 min s 180s 1min *Note that we can cross out units that cancel BEFORE rewriting the numbers at the end. Convert the following ) 4 hours into minutes 3) 3500 mm into km Convert 5.0 km into miles (note that 1 mi = 1.61 km) 5.0km 1mi 5mi 3.1mi 1 1.61km 1.61 4).3 meter/second into kilometers /hour Convert 1km into mm 3 3 1km10 m 1mm 1(10 )(1) mm 6 110 mm 3 3 1 1km 10 m (1)(1)(10 ) Convert 45 mi/hr into km/min 45mi 1.61km 1hr 1hr 1mi 60min 45(1.61)(1) mi 1.mi/ min (1)(1)(60)min 5) 57 m 3 into km 3 3 P a g e
Graphing there are TWO skills that you need in dealing with graphs in physics. 1. Be able to identify a graph that shows the relationship between two values in an equation. Constant value graph y = constant Given the set of epressions below, determine the type of graph that would relate the stated variables. (Note that you must assume that all variables not involved in the graph must remain constant) F net ma Gm1m F g r v a c r R L A Ad b hd ru 6) Sketch the relationship between F net and a. Direct Relationship (positive slope) y = ; y = ; y = 0.7 7) Sketch the relationship between F g and r. Direct Relationship (negative slope) y = - ; y = -5 8) Sketch the relationship between a c and v. Polynomial Relationship y = ; y = 4 3 9) Sketch the relationship between R and A. Inverse Relationship y = 1/ ; y = 1/ 30) Sketch the relationship between b and A. 4 P a g e
. Be able to graph data and determine slope of a graph and its meaning. A tower of increasing height was built upward from a base using a set of blocks. Two blocks were added each time and the height of the tower was measured. The following is a data table representing the height of the tower (from the floor) at each two block interval. 34) Formulate the equation for this line using the epression: y = m+ b. 35) What physical measurement does the slope of this line represent? Base floor Blocks Height (cm). 4 3.3 6 4.0 8 5.5 10 6. 1 7.8 14 8.1 36) What physical measurement does the y- intercept of this line represent? 31) Using the grid below, mark an appropriate scale, label the aes with units, plot the data, and draw a best-fit line (using a straightedge!) 3) Calculate the slope of the line. 33) Estimate the y-intercept of the line: 5 P a g e
Algebra in order to do physics on the advanced placement level your algebra skills must be perfect BEFORE the year begins. Evaluate/simplify each epression. 43) E p mgh Given: E p = 15, g = 9.8, h =305 find m. 37) 3 5 38) 6 4 44) vi v f d t Given: d = 10.0, v i = 5.0, t =.0 find v f 39) 4 5 14 d 45) f d v t t f i i Given: v =.0, d f = 5, d i = 10, t f = 1.5 find t i 40) 5 41) 18 9 46) d vit 1 at Given: d = 1, t =.1, a = -4.3 find v i 4) 16 4 6 P a g e
47) v f = v i + ad Given: v f = 13.7, a = -.5, d = 54 find v i 51) L L 0 v 1 c Given: L = 13.0, v =.1 10 8, c = 3.0 10 8 find L 0 48) E 1 k mv Given: E k = 16, v =.35 find m 5) m m 0 v 1 c Given: m =.5 10 6, m0 =. 10 6, c = 3.0 10 8, find v 49) E 1 k mv Given: E k = 101, m =1 find v 53) n 1 sinθ 1 = n sinθ Given: n 1 = 1.35, n = 1.04, 1 = 4, find Gm1 m 50) Fg r Given: G = 6.67 10-11, m 1 = 3.45 10 16, m = 1.34 10 7, F g = 1.6 10 4 find r 7 P a g e
Trigonometry the use of the relationship between sides and angles of triangles to determine unknown characteristics of those triangles. Relies on the following set of rules: opp sin hyp cos opp tan adj sin a A adj hyp b B sin c sin C θ 35 1 56) = a b c Use the rules above to determine the unknowns in each triangle. 57) θ = 0 16 θ 7 60⁰ A 54) = B 58) A = 55) θ = 59) B = 8 P a g e