P Physics 1 Summer ssignment 1. Scientific Notation: "#$%&''&()*+$,-#$&-.)*,-/$0"/1)1$0-&3'#415$$6-)7#$7"#$,*1(#-$)*$1)#*7)%)$*&7,7)&*$,*.$1)40')%/$7"#$8*)71$9:;<=5 a. T s $ # 4. 5" 10 kg 3. 0 " 10 kg s " = b. ' 9 N ) m ( * 9.0 10 + # 9 # 9 % 3." 10 C &% 9.6" 10 C & F ", C - % 0.3m& #= c. 1 1 1. 4. 5" 10 / 9. 4 " 10 / p P $ % = # 34 14 # 19 K 6.63 10 J s 7.09 10 s.17 10 J " ) " # " & '() = d. max % &% & e. 0 1 8. 5" 10 m s 1# 8 300. " 10 m s *= 1 K 6.610 kg.1110 m s &= 4 f. % &% & g. % 1.33& sin 5.0 % 1.50& sin1 += P Physics 1, Summer ssignment 1
. Solving Equations: "#$%&'()*+$,-&)%&#.$&/0&$1,&($&3)%$&45#.&6(5*+$-&)%+78&&9)+6$&")(&#.$&6(5*+$&5%35:#$38&&;)%<#&+$#&#.$& different letters confuse you. Manipulate them algebraically as though they were numbers. 1 a. K kx, x b. Tp ", g g c. F G m m 1 g r r, d. 1 mgh mv, v e. 1 # # x xo vot at, t $ I o f., r " r m% L d g. xm, d h. pv nt, T n1 i. sin & c,& c n j. 1 qv mv, v P Physics 1, Summer ssignment
3. Conversion 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 (m) to meters (m) Other conversions will be taught as they become necessary. "#$%&'%()*%+),-$%.,)/%$"0%conversion factors? Colleges want students who can find their own information (so do 013)(04567%%8&,$9%:4(%#%;))+%+&<$&),#4(%#,+%3)).%*,+04%=10#5*40>%)4%=10#5*4010,$>7%%?4%$"0%@,$04,0$%%,C)(7 a. 4008 g = kg b. 1. km = m c. 83 nm = m d. 98 K = o C e. 0.77 m = cm f. 8.8x10-8 m = mm g. 1. atm = Pa h. 5.0 m = m i..65 mm = m j. 8.3 m = km k. 40.0 cm = m l. 6.3x10-7 m = nm m. 1.5x10 11 m = km P Physics 1, Summer ssignment 3
4. Geometry Solve the following geometric problems. a. Line touches the circle at a single point. Line extends 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? 30 o 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 under the curve at the right? 4 1 0 P Physics 1, Summer ssignment 4
5. T rigonometry Using the generic triangle to the right, ight Triangle Trigonometry and Pythagorean Theorem solve the following. Your calculator must be in degree mode. g. = 55 o and c = 3 m, solve for a and b. h. = 45 o and a = 15 m/s, solve for b and c. i. b = 17.8 m and = 65 o, solve for a and c. j. a = 50 m and b = 180 m, solve for and c. k. a =5 cm and c = 3 cm, solve for b and. l. b =104 cm and c = 65 cm, solve for a and. P Physics 1, Summer ssignment 5
Vectors Most of the quantities in physics are vectors. This makes proficiency in vectors extremely important. Magnitude: Size or extend. 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. 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. 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. 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). There are two methods of adding vectors Parallelogram + Tip to Tail + - - - - P Physics 1, Summer ssignment 6
6. Drawing esultant Vectors Draw the resultant vector using the parallelogram method of vector addition. Example b. d. a. c. e. Draw the resultant vector using the tip to tail method of vector addition. Label the resultant as vector Example 1: + - Example : f. X + Y X Y g. T S T S h. P + V P V i. C D C D P Physics 1, Summer ssignment 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 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. 7. esolving a vector into its components For the following vectors draw the component vectors along the x and y axis. a. c. b. d. Obviously the quadrant that a vector is in determines the sign of the x and y component vectors. P Physics 1, Summer ssignment 8
"#$%&'(")*&+",-.(/& & The equation of a line is given by the formula y = mx + b, m equals the slope of a line and b equals the y-intercept. This equation of the line is called the slope-intercept form because it easily shows both the slope and the intercept of the line. To find the equation of a line given the slope and the intercept, simply plug in the correct values into the equation. Example 1 Write an equation of the line with a slope of that has a y-intercept of 5. y = mx + b write the slope-intercept formula. y = x + 5 substitute m = and b = 5 The answer is y = x + 5 Sometimes the slope of the equation is not given. To find the equation of a line that passes through two points, you must first calculate the slope, then substitute in one point into the equation to solve for the y-intercept. Example Write the equation of the line that passes through the points (3, -) and (-, 8). "#$ "# " " The answer is y = -x -1 Write the slope formula Substitute (x1, y1) = (3, -) and (x, y) = (-, 8). Write the point-slope formula Substitute m = - and (x, y) = (-, 3) Simplify Subtract 4 from each side Substitute m = - and b = -1 into the point-slope formula 01&,/)3#$4&,/5%#5*& Find the equation of the line that has the given slope and y-intercept. a. m = and b = 7 c. m = 10 and b = -3 b. m = -3 and b = 10 d. m = 5 and b = -10 Find the equation of the line that passes through the given points. Find the equation of the line with the given slope that passes through the 17.given (1, )point. and (-1, 5) 18. (-7, -7) and (-1, 4) e. m = and (-1, 5) g. m = 3 and (0, 7) f. m = -1 and (4, 5) h. m = and8) (10, 19.0 (1, and7)(-3, 4) 0. (1, 5) and (, 0) Find the equation of the line that passes through the given points i. (1, ) and (-1, 5) k. j. (-8, 4) and (, -1) l. Find the equation of the line for each graph below. 1. (6, 10) and (, 8) (6, 10) and (, 8) (-7, -7) and (-1, 4). (-8, 4) and (, -1) Find the equation of each line graphed below. 3. 4.