ap physics summer assignment - berkeley county … physics summer assignment ... note: mr. marsili...

AP Physics Summer Assignment For 2014 -15 School Year

Name : _________________________________________________

College Major? : __________________________________________

You MUST PASS a College Physics course if you want a career in any of the following majors:

1. Any Medical Field: a. Nursing b. Pediatrics c. Dentistry d. Surgeon e. Nuclear Medicine f. Veterinarians g. Pharmacists h. Any Pre – med career track

2. Biological Sciences 3. Psychologists 4. Engineering:

a. Civil Engineers b. Mechanical Engineers c. Chemical Engineers d. Electrical Engineers e. Nuclear Engineers f. Aerospace Engineers g. Computer Engineers h. Biomedical Engineering i. Electrical Diagnostics

5. Astronomy and Geosciences 6. Architects 7. Computer Programmers 8. Computer scientists 9. Mathematicians 10. Statisticians

These all require a minimum of 1 – 2 courses in college physics (Excluding 4 - 10)

http://berkeleycountyschools.org/springmillshigh

2

Much of the work we will be doing during the year will require a bit of foreknowledge, while succeeding in physics is not dependent upon being an expert in this foreknowledge. Having a general understanding of this knowledge certainly

Reduces the work load

Increases understanding

Creates a firmer understanding of the material

Reduces the time spent doing homework

Increases the odds of scoring higher on the AP Test In short taking the time during your summer vacation to simply look over the following material will

have a real benefit. Of course at the same time this is your first assignment that is due the first day of school and will be worth a generous amount of points.

Note: Mr. Marsili will be in his Office during the summer months to assist any student with questions

or assist with difficulties. To reach Mr. Marsili simply email me at [email protected]

By signing this, I accept the responsibility to complete the summer packet.

I understand that this packet will be graded and that I will be tested on this material within the first week or two of school.

I realize that knowledge of its content is a course requirement. Signed

By: __________________________________________________ Date: _________________________________________________

3

Table of Contents:

1. Significant Digits Page 4 a. Significant Figures Homework Page 5

2. Scientific Notation Page 6

a. Scientific Notation Homework Page(s) 7 – 8

3. Factor Label Unit Conversion Page 9 a. Metric Conversion Factors Page 10 b. Units and Dimensional Analysis Homework Page 11

4. Unit Analysis Page 12

5. Solving for Variables Page 13 – 14

a. Solving for Variables Homework Page 15 b. Solving for Variables Practice Page(s) 16 – 17

6. Graphing Page(s) 18 – 19

a. The Cartesian Coordinate system Page 20 b. The Cardinal Directions Page 21

7. Trigonometry Page 22

a. Introduction to trigonometry Homework Page 23

8. Vectors Page(s) 24 – 25 a. Triangles and Vectors Page(s) 26 – 27 b. Adding Vectors Mathematically Page(s) 28 – 29 c. Adding Vectors Graphically 0 d. Vectors homework Page 31

4

Significant Digits (also known as significant figures)

Rules for deciding which digits are significant:

1. Nonzero digits are always significant. 2. All final zeros after the decimal point are significant. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant.

Examples:

Using the rules above, 0.0340 mm has 3 , 960 kg has 2 , and 70,080 s has 4 significant figures.

123.479 m + 35.8 m + 5.32 m = 164.599 m = 164.6 m

(In addition or subtraction, work with the numbers as they are written, but the final answer must have the same level of precision as the least precise number – in this case, precision to the tenths place.)

= 3.449134078 = 3.45

(In multiplication or division, work with the numbers as they are written, but the final answer must have the same number of significant digits as the number with the least amount of digits – in this case, 3 significant digits.)

= 2.1 m2

(In multiplication or division, units are multiplied and divided like numbers.)

Exercises 1. State the number of significant digits in each of the following measurements.

a. 32.06 kg ________ b. 0.02 km ________ c. 5400 m ________ d. 2006 s ________

e. 2.9910 m ________ f. 5600 km ________ g. 0.00670 kg ________ h. 809 g ________

2. Solve the following problems and give the answers to the correct number of significant digits. (All numbers must be written with the correct units.)

a. 324.54 cm - 25.6 cm = ________________ b. 28.9 g + 300.25 g + 2.945 g = ________________

c. 82.3 m x 1.254 m = ___________________ d. (1.2 x 106 m)(3.25 x 104 m) = _________________

e.

= ____________________________ f.

= _____________________________

g.

= __________________________ h. 5.25 cm x 1.3 cm = _________________________

i. 9.0 cm + 7.66 cm + 5.44 cm = ___________ j. 10.07 g - 3.1 g = ____________________________

5

1. Indicate how many significant figures there are in each of the following measured values.

246.32 m __________ 107.854 m__________ 100.3 m__________ 0.678 m ___________ 1.008 m ___________ 0.003 40 m_________ 14.600 m___________ 0.000 1 m___________ 700 000 m__________ 350.670 m___________ 1.000 0 m___________ 320 001 m__________

2. Calculate the answers to the appropriate number of significant figures, and state the significant figures in each

measurement.

a. 32.567 m + 135.0 m + 1.4567 m = ____________

b. 246.24 kg + 238.278 kg + 98.3 kg = ____________

c. 658.0 mm + 23.5478 mm + 1345.29 mm = ____________

3. Calculate the answers to the appropriate number of significant figures, and state the significant figures in

each measurement.

a. 6.201 cm + 7.4cm + 0.68cm + 12.0 cm =____________

b. 28.662 m + 32.34 m +17.5 m =____________

c. 26.38 kg + 14.531 kg + 30.8 kg =____________


measurement.

a. 23.7 cm x 3.8 cm =____________

b. 45.76 A x 0.25 A =____________

c. 81.04 g x 0.010 g =____________


measurement.

a. 6.47 L ÷ 64.5 L =____________

b. 43.678 L ÷ 64.1 L =____________

c. 1.678 L ÷ 0.42 L =____________

Significant Figures

6

Scientific Notation

Scientific notation is a compact way of writing large or small numbers while using only significant digits and powers of ten. The normal form for scientific notation is:

A x 10b a is a number in the form of 0.00 (i.e. a digit in the ones, tenths, and hundredths place) b is the powers of ten telling us which direction to move the decimal place and how many times.

Examples: 0.00265 written in scientific notation would be 2.65 x 10-3. (The negative three power of ten indicates that the decimal point should be moved three places to the left.)

7.68 x 105 expanded would be 768,000. (The positive power of five indicates that the decimal point should be moved five places to the right. In this case, zeros are needed as placeholders.)

= 3.0 x 103.

(Divide the decimals while keeping the correct number of significant figures. When dividing powers of ten, subtract the bottom power of ten’s exponent from the top power of ten’s exponent. If multiplying, add powers of ten.)

(4.5 x 10-2

) + (8.2 x 10-3

) = 4.5 x 10-2 + 0.82 x 10

-2 = 5.32 x 10-2 = 5.3 x 10

-2.

(Before adding or subtracting numbers in scientific notation, all numbers need to have the same power of ten)

Exercises: Write the following numbers in scientific notation

1) 5800 _______________ 2) 0.0345 _______________ 3) 0.00890 _______________

4) 560 ________________ 5) 43 200 _______________ 6) 4 320 000 _____________

7) 0.00065 _____________ 8) 101.35 _______________ 9) 2.004 _________________

Expand the following numbers:

10) 1.20 x 103_______________ 11) 2.34 x 10 ─ 4___________ 12) 2.00 x 100_____________

13) 1.99 x 104 m_____________ 14) 9.80 x 10─1____________ 15) 6.65 x 10─5 ____________

Solve the below mathematical operations (using the correct number of significant figures)

16) 5 x 107 + 3.54 x 106 =_____________________________________________________

17) 7.0 x 10─4 + 2.11 x 10─3 =____________________________________________________

18) (6.66 x 10─4) (5.0 x 10─8) =___________________________________________________ 19) (6.00 x 10─8) ÷ (2.00 x 10─4) =__________________________________________________ 20) (3.14 x 104) ÷ (2.22 x 106) =____________________________________________________

7

Express the following measurements in scientific notation. 1)

a. 5800 m _______________________________

b. 450 000 m _______________________________

c. 302 000 000 m _______________________________

d. 86 000 000 000 m _______________________________

2) a. 0.000 508 kg _______________________________

b. 0.000 000 45 kg _______________________________

c. 0.0036 kg _______________________________

d. 0.004 kg _______________________________

3)

a. 300 000 000 s _______________________________

b. 186 000 s _______________________________

c. 93 000 000 s _______________________________

4) a. 0.0073 m _______________________________

b. 0.000 87 m _______________________________

c. 0.0032 m _______________________________

5)

a. 650 000 kg _______________________________

b. 5 000 000 s _______________________________

c. 226 m _______________________________

d. 4500 s _______________________________

Scientific Notion

8

Addition and Subtraction in Scientific Notation:

6) a. 5 x 107 m + 3 x 107 m =______________________________

b. 6 x 108 m + 2 x 108 m =_______________________________

c. 4.2 x 104 m + 3.6 x 104 m =_______________________________

d. 1.8 x 109 m + 2.5 x 109 m =_______________________________

7)

e. 6.0 x 108 m2 + 4 x 107 m2 =_______________________________

f. 7.0 x 104 kg + 2 x 103 kg =_______________________________

g. 4 x 104 kg + 3.0 x 105 kg =_______________________________

h. 6.0 x 1010 m + 5.0 x 1011 m =_______________________________

Multiplication and Division in Scientific Notation:

8) i. (2 x 104 m)(4 x 108 m) =_______________________________

j. (3 x 104 m)(2 x 106 m) =_______________________________

k. (6 x 10─4 m)(5 x 10─8 m) =_______________________________

l. (2.5 x 10─7 m)(2.5 x 1016 m) =_______________________________

9)

m. (6 x 108 kg) / (2 x 104 m3) =_______________________________

n. (6 x 108 kg) / (2 x 10─4 m3) =_______________________________

o. (6 x 10─8 m) / (2 x 104 s) =_______________________________

p. (6 x 10─8 m) / (2 x 10─4 s) =_______________________________

9

Factor-Label Unit Conversion

For the problems below, show all conversion factors, work. And do not use the conversion factor feature on your calculator to do these problems.

1. Carry out the following conversions using the prefix information shown above.

a. 35 nm (

) b. 450 cm (

)

c. 1500 µg (

) d. 250 km (

)

e. 346 ms (

) f. 543 mg (

)

g. 4008 g (

) h. 239 mm (

)

i. 48 mL (

) j. 38 kg (

)

Common Prefixes: nano has the symbol, n, and means 10

–9 (or 0.000000001)

micro has the symbol, µ , and means 10 –6

(or 0.000001)

milli has the symbol, m, and means 10–3

(or 0.001)

centi has the symbol, c, and means 10–2

(or 0.01)

kilo has the symbol, k, and means 103 (or 1000)

10

Order of Magnitude Prefix Abbreviation

1018 exa - E

1015 Peta - P

1012 Tera - T

109 Giga - G

106 Mega - M

103 Kilo - K

102 Hecto - H

101 Deka - da

100 BASE ------

10 -1 deci - d

10-2 centi - c

10-3 milli - m

10-6 micro -

10-9 nano - n

10-12 pico - p

10-15 femto - f

10-18 atto - a

Metric Prefixes

11

1. Compute the number of seconds in an hour, day, and year.

2. The maximum sodium intake for a person on a 2000 calorie diet should be 2400 mg/day. How many grams

of sodium is this per day?

3. The recommended daily allowance (RDA) of the trace element chromium is 120 μg/day. Express this dose

in grams per day

4. An intake of vitamin C up to 500 mg/day is considered safe. Express this intake in grams per day.

5. The electrical resistance of the human body is approximately 1500 ohms when it is dry. Express this

resistance in Kilohms.

6. An electrical circuit of about 0.020 amps can cause muscular spasms so that a person cannot, for example

let go of a wire. Express this current in milliamps.

7. Starting with the definition 1.00 inches = 2.54cm, find the number of kilometers in 1.0 miles.

8. In medicine, volumes are often expressed in milliliters; prove that a milliliter is the same as a cubic

centimeter.

9. How many cubic centimeters are there in a 1.00 liter bottle of drinking water?

(Hint: 1 cm3 = 1 mL)

10. Bacteria vary somewhat in size, but a diameter of 2.0μm is not unusual. What would be the volume (in

cubic centimeters) and the surface area (in square millimeters) of such bacterium assuming that it is

spherical? (Consult Appendix A of your book for assistance)

Units and Dimensional Analysis

12

Unit Analysis

Unit analysis involves the placement of units in an equation to check for unit agreement on both sides of the equals sign. When substituting values into an equation in physics, you must state the units as well as the numerical values. Including units in your calculations helps you keep units consistent throughout and assures you that your answer will be correct in terms of units. The proper units for variables are included in the table below.

Examples

Equation with Unit Agreement

The equation being inspected is

its units

indicate that

The units on the left are equal to the units on the right of the equal sign. This equation is correct in terms of units.

Equation with Unit Disagreement

The equation being inspected is its units indicate that

(

) (

)

(Notice that coefficients, such as the number 2, in the equation are ignored in dimensional analysis)

The units on the left are

but the units on the right turn out to be

The units do not agree. This final velocity equation is incorrect in terms of its units.

Problems Use the method described above to determine if the following equations have unit agreement. Show your work and write “correct” next to the equation if it is correct and “incorrect” if it is incorrect in terms of its units.

1. 2. ⁄ ( ) 3.

4.

5. √

Quantities Units Units

(d) displacement (m) Meters

(vo) original velocity (vf) final velocity

( ) average velocity

(meters per second) m/s

(a) acceleration (meters per second

squared) m/s2

(t) time s (seconds)

13

Solving for Variables PROBLEM SOLVING When solving motion problems, or, indeed, any physics problem, use an orderly procedure like the one listed below. 1. Identify the quantities that are given in the problem. 2. Identify the quantity that is unknown, the one you have to find. 3. Select the equation that contains the given and unknown quantities. 4. Solve the equation for the unknown quantity using algebra. 5. Substitute the values given in the problem, along with their proper units, into the equation and solve it. 6. Check to see if the numerical value of your answer is reasonable and make sure that the answer has the correct units.

Example Solve for each variable in the equation below. The variable should be placed alone on the left side of the equation.

(It is already solved for vf, so it only needs to be solved for vo, a, and t.)

Problems 1. In the equation, ⁄ ( ) , solve for vf and t.

2. In the equation,

, solve for vo and a.

3. In the equation,

, solve for vf, vo, and d.

14

Solving for Variables Examples

Solve the following equation for c.

(Divide both sides by m)

(Take the square root of both sides and there will be a positive and negative solution for c)

√

or finally, √

Solve the following equation for k.

√

(Multiply both sides by g)

√ (Divide both sides by 3)

√

(square both sides of the equation)

Problems Solve the following equations for the variable(s) requested.

1. E = ½mv2 for m and v 2.

for d

3. E = mgh for h 4. E = hf - Wo for Wo and h

5.

= for si 6. ax2 + b = c for x

Solve for x in the following problems.

7.

___________________________ 8.

___________________________

9.

___________________________ 10.

√

___________________________

15

Directions: Solve for the following for the variable a please show all of your work in a step by

step method, and circle your answers.

1.

2. √

3. √

4.

5.

Solving For Variables

16

Solve for… …in this equation.

1. d t

dv

2. t t

dv

3. m F = ma

4. a atvv of

5. t atvv of

6. a 2

2

1attvd o

7. vo 2

2

1attvd o

8. d advv of 222

9. vo advv of 222

10. a advv of 222

11. vo tvv

dof

2

12. t tvv

dof

2

13. vf tvv

dof

2

14. m KE = ½ mv²

15. v KE = ½ mv²

16. v r

mvFc

2

17

17. r r

mvFc

2

18. r 2

21

r

mGmFg

19. m2 2

21

r

mGmFg

20. L g

LTP 2

21. g g

LTP 2

22. k k

mTS 2

23. m k

mTS 2

24. R1 2

1

2

2

2

1

R

R

I

I

25. R2 2

1

2

2

2

1

R

R

I

I

26. x μmgd = mgh + ½ mv2 + ½ kx

2

27. m μmgd = mgh + ½ mv2 + ½ kx

2

18

Graphing

Plotting Graphs These steps will help you plot graphs from data tables. 1. Your graph should be titled Y vs. X (or the vertical information versus the horizontal information). 2. Decide on the scales needed for the x and y axes. Choose scales that will spread out the data.

Do not choose scales that compress the data points into a tiny portion of the graph paper. Your graph should fill up the graph paper.

3. Number and label the x and y axes (including necessary units).

4. Draw the best straight line (using a straight edge) or smooth curve that passes through as

many data points as possible. Do not just connect the data points together with a series of straight line segments.

Graphing Data Values The steps listed above were followed to set up the plotting of the data shown below.

Time (s)

Speed (m/s)

0 4

1 15

2 20

3 37

4 55

5 59

Exercises 1. Plot the data values on the graph provided above and draw one straight line that best fits the data (use a straight edge to make the line). 2. What is the slope of the line of best fit (find the number)? _____________________ m/s2

(Slope = rise/run) 3. What is the speed at 3 s? ________________________________________________ m/s 4. Using the graph, what is the speed at 6 s? __________________________________ m/s 5. At what time is the speed 20 m/s (using your graph) ___________________________ s

19

Graphing There are three relationships that occur frequently in physical processes. They are depicted in the three graphs shown below.

Exercises 1. Plot the data values on the graph provided above and connect the points together with a smooth curve that follows the data. 2. Approximately what is the radius when the speed is 5 m/s? _______________________m. 3. This type of curve is known as a _______________________________________________. 4. This graph follows an equation of the form radius = k(speed)2. Radius and speed squared are ________________________________ related.

The Cartesian Coordinate system

Speed (m/s)

Radius (m)

0 0

1 4 2 16

3 36 4 48

20

The Cartesian coordinate system is the linear system we will be using most often when

creating graphs and plots, or when describing the directions of a vector. This system should be familiar to you.

Angles and reference points: The angles increase in a counter clockwise rotational direction. Negative angles are rotating in the clockwise direction. An important point to be aware of is that whenever measuring an angle we ALWAYS use the x – axis as the reference axis.

When measuring an angle from the positive x – axis your calculator will know exactly where that specific angle is.

When measuring an angle from the negative x – axis your calculator will automatically assume the angle is in the first quadrant (So do not allow your calculator to make a fool out of you.)

Make sure you know your positive directions from your negative directions. There are four Quadrants:

I. From 0o to 90o x = positive values, y = positive values II. From 90o to 180o x = negative values, y = positive values

III. From 180o to 270o x = negative values, y = negative values IV. From 270o to 360o or 0o x = positive values, y = negative values

Draw the following approximate angles.

I. 45o

II. 150o

III. 110o

IV. 335o

V. 240o

Cardinal Directional Handout

0o 180

o

90o

270o

21

The Phrase: 40o North of West Meaning: The first direction “North” tells us the direction the angle will be revolving from our reference axis (This direction tells us that our angle is turning from the Western axis in the Northern direction) The second direction “West” is the axis of reference. (It is from this axis that our angle will start)

The Phrase: 45o West of South Meaning: The first direction “West” tells us the direction the angle will be revolving from our reference axis (This direction tells us that our angle is turning from the Southern axis in the Western direction) The second direction “South” is the axis of reference. (It is from this axis that our angle will start)

40o

45o

22

Trigonometry Trigonometry is an extremely useful branch of mathematics that deals with the relationships between the sides and angles of right triangles.

The Pythagorean Theorem is a

method for finding missing sides of right

triangles.

It states that the hypotenuse (the longest side) is

related to the other two sides of a triangle by

the

following equation.

(where c is the length of the hypotenuse and a and b are

the lengths of the other two sides)

The three commonly used trigonometric functions

are

The sine:

The Cosine:

The Tangent

(Memorizing SOH CAH TOA is one way of memorizing

these trigonometric functions.)

23

1. Using the Triangle to the right please do the following:

a. Find the length of side c two ways and justify your answer.

b. Find the angle of each corner of the triangle

2. If the angle theta is 35 degrees find the length of

a. Side y

b. Side x

3. Using the triangle on the right proved the following:

a. The tangent ratio of the sides

b. The cosine ratio of the sides

c. The sine ratio of the sides

4. The diagram to the left illustrates the path a

raft would follow across a 40 meter river that has

a strong upward current. (The current moves

towards the top of the page)

a. What does the hypotenuse represent?

b. How far down the river does the

raft travel?

c. How far is the raft displaced?

c 4

3

10

y

x

θ

z

y

x

θ

45o

Introduction to Trigonometry

25

Vectors Calculations 1. Find the horizontal and vertical components of the velocity vector shown below. (Please show your work.)

26

Show ALL of your work!

1. Find the length of the missing side and then find the

following for the triangle shown at the right:

a. sinθ b. cosθ c. tanθ

d. sinγ e. cosγ f. tanγ

2. Find the angles θ and γ in the triangle above.

3. In the triangle shown to the right, find the following:

a. Angle θ b. Side A

c. Side B

14 m

?

θ 17 m

γ

γ

B

A

165 km

θ

26˚

Triangles and Vectors

27

4. In the triangle shown at the right, find the

following without the Pythagorean Theorem: a. Angle α

b. Angle β

c. Side R

5. Break the Following vectors into their horizontal (X) component and (Y) vertical

Component.

A. 45 m/s at 225o

B. 67 km at 56o

6. Add the Vectors from Number 5 to obtain the magnitude of the resultant vector.


Component.

A. 57 N at 216o

B. 123 N at 337o



Component.

A. 45 m/s at 0o

B. 145 m/s at 45o

C. 23 m/s at 50o


R

64.8 cm

68.2 cm β

α

28

1.

2. a. X components using, | |

| |

| |

b. Y components using, | |

| |

| |

3.

a.

b.

4. Determine the magnitude of the Resultant

Vector

√

√

√

5. Direction / Angle.

Second Quadrant:

(

)

1. Clearly determine the:

a. Magnitude of the Vectors.

b. Direction of the Vectors.

2. Break Each Vector into its:

a. X components using,

| |

b. Y components using,

| |

3. Sum up all of the components in each

direction (remember to apply + and - )

a. Sum all the X components

b. Sum all the Y components

4. Use the Pythagorean theorem to

determine the magnitude of the Resultant

Vector

√

5. To determine the direction of the

Resultant Vector in reference to the

Positive X axis we must use the

Arc Tangent.

(

)

Adding Vectors Mathematically

30

1.

2.

3.

4. This problem only has two vectors.

5.

1. Clearly determine the:

a. Magnitude of the Vectors.

b. Direction of the Vectors.

2. Draw the first Vector to scale on the

coordinate system.

a. Make sure that the Vector is in the

correct direction and quadrant.

3. Draw a mini coordinate system at the head

of the first Vector.

a. Draw the next vector head to tail of

the last vector.

4. Repeat step 3 for each Vector…

5. After drawing all vectors, draw the

Resultant Vector from the origin to the head

of the last vector.

𝜃

𝐴

𝜃

𝜃

𝐴

��

𝐶

𝜃

𝜃

𝐴

��

Adding Vectors Graphically

31

Directions: Answer the following assigned questions on a separate sheet of paper. Be sure to answer each

question using scientific notation and to the best of your ability. Don’t forget to circle your answer!

43. If a vector has the following components, use trigonometry to find its magnitude and the

counterclockwise angle it makes with the + x axis.

a.

b.

c.

d. ,

44. Compute the x and y components of vectors = (12.0 m), = (15.0m), and = (6.0m) shown in the figure

below.

45. Vector has components ; vector has components

. Find

a. The components of the sum

b. The magnitude and direction of

c. The components of the vector difference

d. The magnitude and direction of

46. A plane leaves Seattle, flies 85 mi at 22o north of east, and then changes direction to 48

o south of east, After

flying at 115 mi in this new direction, the pilot must make an emergency landing.

a. In what direction and how far should the emergency crew fly to go directly to the site of the emergency

landing?

b. Check the reasonableness of your answer by graphically adding the vectors.

49. A disoriented physics professor drives 3.25 km north, then 4.75 km west, and then 1.50 km south.

a. Use components to find the magnitude and direction of the resultant displacement vector of this poor

professor.

b. Check the reasonableness of your answer by graphically adding the vectors.

40o 60

o

37

o

Vector Classwork sheetz

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