Summer Assignment for Physics First Honors As part of the Physics First Honors course and curriculum, there is a required summer assignment that all students must complete prior to the first day of school. During our first week, this assignment will be collected and we will have an initial assessment on these concepts/topics. The material, mostly mathematical, is very important to know in order to be successful in solving physics problems throughout the year. PLEASE KEEP IN MIND: The concepts are ordered in a purposeful manner. They build upon one another. Once you master concept 1, you will be expected to use your knowledge in concept 2 and then that material for concept 3. After you finish, you will be an expert in expressing numerical answers. 1.
Converting Very Large and Very Small Numbers to and from Scientific Notation and Adding/Subtracting/Multiplying/Dividing Numbers in Scientific Notations. • Read Exponents: Scientific Notation explanation, then complete Worksheet 1. After that, review the following videos. Take notes during the videos! • Adding/Subtracting: https://www.youtube.com/watch?v=p0zVNTko7z4 • Multiplying/Dividing: https://www.youtube.com/watch?v=UADVIDjdaVg • Complete Worksheets 2 and 3
2. Expressing Numerical Answers With Proper Significant Digits • View videos – take notes! • Significant Figures: https://www.youtube.com/watch?v=eCJ76hz7jPM • Multiplying and Dividing with Significant Figures: https://www.youtube.com/watch?v=iorZdz4dsBU • Adding and Subtracting with Significant Figures: https://www.youtube.com/watch?v=xHgPtFUbAeU • Complete Worksheets 2 and 3 3. Converting Units of Measurements • View videos – take notes! • Metric vs. Imperial Systems of Measurement: https://www.youtube.com/watch?v=sNn_qsgBuM0 • How to Convert Units Within the Metric System: https://www.youtube.com/watch?v=w0nqd_HXHPQ
• •
How to Convert Units Across the Metric and Imperial System: https://www.youtube.com/watch?v=1wQYWUKruoQ Complete Worksheets 5 and 6
When completing Worksheet 5, please refer to the conversation chart included at the end of your summer assignment packet. It would be wise to keep this chart in your physics binder to refer to at any time during the school year. Note that the chart refers to English or Imperial Units as “American Units” and SI units as “metric”.
If you have any questions about this assignment, please email me at my school Google account:
[email protected].
Welcome to Physics First Honors. first day of classes.
I look forward to meeting you on the
Exponents:
Scientific Notation
By using exponents, we can reformat numbers. This can be helpful, in much the same way that it’s helpful(that is, easier) to write “twelve trillion” rather than 12,000,000,000,000 or “thirty nanometers” rather than “0.00000003”. For very large or very small numbers, it is sometimes simpler to use “scientific notation” (so called, because scientists often deal with very large and very small numbers). The format for writing a number in scientific notation is fairly simple: (first digit of the the number) followed by (the decimal point) and then (all the rest of the digits of the number) times (10 to an appropriate power): Format: First_digit 10appropriate_power Example:
.
rest_of_digits
x
4.56 x 108
Converting numbers is fairly simple. It’s easiest to learn by example. Let’s convert 124 to scientific notation. It’s not a very large number, but it will work nicely as an example. First, we move the decimal point two spaces to the left to fit the Format above, 124 becomes 1.24 But, this is not the number we started with, we need to multiply it by 102 to get back to 124. 100 is 102 so our number becomes 1.24 x 102 Let’s try a bigger number such as 3,566,879,990 Step 1:
Move the decimal point 9 spaces to the left:
3.566879990
Step 2: Round off the number to 2 places (we’ll learn more about this in the next section of the summer assignment): 3.57 Step 3: Multiply by 10 to the power you moved the decimal over: 3.57 x 109 How do we handle a number smaller than 1? Since you are moving the decimal point to the right, the power becomes a negative number. Example:
0.00000044522
becomes 4.45 x 10-7
Converting between scientific notation to “regular” notation is easier – you just need to move the decimal place over the number of spaces indicated by the power. If the power is positive, you move the decimal point to the right, if it is negative, you move the decimal point to the left. Example:
3.60 x 1012
becomes 3,600,000,000,000
Example:
8.77 x 10-5
becomes 0.0000877
General Examples Example 1: 0.0000000000436 becomes 4.36 x 10-11 Example 2: 4.2 x 10-7 becomes 0.00000042 Example 3: 0.00000000578 becomes 5.78 x 10-9 Example 4: 93,000,000 becomes 9.3 x 107
Practice Set 1:
Converting Scientific Notation
Convert from scientific notation to standard form 1. 4.83 x 10-3
________________
2. 9 x 103
________________
3. 8.2 x 100
________________
4. 8.291 x 10-3
________________
5. 1.939 x 103
________________
6. 3.4 x 10-3
________________
7. 4.37 x 106
________________
8. 1 x 10-5
________________
9. 4 x 104
________________
10. 1.9 x 1011
________________
Convert from standard form to scientific notation 1. 8589.32
________________
2. 0.0000076
________________
3. 0.00038
________________
4. 0.002898
________________
5. 25,000,000,000
________________
6. 980,000
________________
7. 0.700
________________
8. 11,800
________________
9. 0.0764
________________
10.0.000044
________________
Practice Set 2:
Adding and Subtracting Scientific Notation (answer using scientific notation)
1. 2.5236 x 103 + 9.8575 x 101 =
______________
2. 5.6083 x 101 + 6.3616 x 103 =
______________
3. 5.70 x 103 + 2.66 x 101 =
______________
4. 4.1056 x 105 + 5.1742 x 106 =
______________
5. 4.3891 x 100 + 5.9501 x 102 =
______________
6. 1.7107 x 101 + 3.4978 x 104 =
______________
7. 8.071 x 102 + 7.629 x 101 =
______________
8. 2.72 x 103 + 4.33 x 103 =
______________
9. 2.5236 x 103 – 9.8575 x 101 =
______________
10. 5.6083 x 101 – 6.3616 x 103 =
______________
11. 5.70 x 103 – 2.66 x 101 =
______________
12. 4.1056 x 105 – 5.1742 x 106 =
______________
13. 4.3891 x 100 – 5.9501 x 102 =
______________
14. 1.7107 x 101 – 3.4978 x 104 =
______________
15. 8.071 x 102 – 7.629 x 101 =
______________
16. 2.72 x 103 – 4.33 x 103 =
______________
Practice Set 3:
Multiplying and Dividing Scientific Notation (answer using scientific notation)
1. 2.5236 x 103 x 9.8575 x 101 =
______________
2. 5.6083 x 101 x 6.3616 x 103 =
______________
3. 5.70 x 103 x 2.66 x 101 =
______________
4. 4.1056 x 105 x 5.1742 x 106 =
______________
5. 4.3891 x 100 x 5.9501 x 102 =
______________
6. 1.7107 x 101 x 3.4978 x 104 =
______________
7. 8.071 x 102 x 7.629 x 101 =
______________
8. 2.72 x 103 x 4.33 x 103 =
______________
9. 2.5236 x 103 / 9.8575 x 101 =
______________
10. 5.6083 x 101 / 6.3616 x 103 =
______________
11. 5.70 x 103 / 2.66 x 101 =
______________
12. 4.1056 x 105 / 5.1742 x 106 =
______________
13. 4.3891 x 100 / 5.9501 x 102 =
______________
14. 1.7107 x 101 / 3.4978 x 104 =
______________
15. 8.071 x 102 / 7.629 x 101 =
______________
16. 2.72 x 103 / 4.33 x 103 =
______________
Practice Set 4: 1.
Significant Figures
Indicate how many significant figures are in each of the followed measured values
246.32
______
14.600
______
1.0000
______
107.854
______
0.0001
______
320001
______
1.008
______
700,000
______
0.678
______
0.00340
______
350.670
______
100.3
______
2. Calculate the answer to the following problems using the appropriate number of significant figures.
+
32.567 135.0 1.4567
+
246.24 238.278 98.3
+
658.0 23.5478 1345.29
3. Calculate the answer to the appropriate number of significant digits a. 23.7 x 3.8 =
e. 43.678 x 64.1 =
b. 45.76 x 0.25 =
f. 1.678 x 0.42 =
c. 81.04 x 0.010 =
g. 28.376 x 3.74 =
d. 6.47 x 64.5 =
h. 4278 x 1.006 =
Practice Set 5:
Unit Conversions
Convert the following using conversation factors found in the conversion table handout attached to this packet. Express your answers in scientific notation where appropriate. 1.
83 cm into meters
7. 2.0 miles into inches
2. 459 L into milliliters
8. $25 into dimes
3. 2.5 mm into micrometers
9. 10 weeks into minutes
4. 12 yards into feet
10. 0.00378 kg into grams
5. 10 hours into seconds
11. 12.1 mm into centimeters
6. 15 quarters into pints
12. 6.8 gallons into milliliters
13. Aluminum costs $5.25 per pound. aluminum cost?
How much would 10.0 kg of
14. Arrange the following from shortest to longest a. 1.21 meters of chain b. 75 inches of rope c. A 3 foot – 5 inch rattlesnake d. A yardstick
_________
__________
________
_________
15. What is your height?
(in feet and inches)
_________________
a. Determine your height in inches b. Determine your height in centimeters c. Determine your height in yards d. Determine your height in meters e. Determine your height in miles (use scientific notation)
Practice Set 6:
Converting Rates
In the following problems, rates are given to you using some units. Please convert these rates to the desired units. Show your work as demonstrated in the first problem. 1. 55 km/hr into km/min 𝑘𝑚 1 ℎ𝑟 𝑘𝑚 55 ( ) ( ) = 0.92 ℎ𝑟 60 𝑚𝑖𝑛 𝑚𝑖𝑛 2. 5 ft/minute into ft/s
3. 2 L/km into L/m
4. $1.50/kg into $/g
5. $100/day into $/hour
6. 3,000 m/s into m/min
7. $2.50/g into dimes/g
8. 20 g/L into g/ml
9. $5/kg into quarters/kg
10. $2 L into nickels/L
11. 54 km/hr into m/s
In the following situation, which rates are the best deal or best situation? Circle the correct answer. 12. Wasting 2 L of gas per km or 0.003 L of gas per m? 13. Paying $1.30 per L of gas or $1.30 per quart of gas? 14. Paying $10,000/yr. at Harvard or $800/month at Princeton? 15. Receiving a salary of $100/day or $4.50 /hour? 16. Renting a game for $5/day or $36/week? 17. Andrew receives $480 per day working on a project. David receives $22 per hour for working on the same project. Who gets the better salary? 18. You are late for school. The bus driver can either drive at 70 km/hr or 1.1 km/minute. What speed is faster? 19. Sprinter #1 is running at a speed of 8 ft/s and sprinter #2 is running at 475 feet/min. Who will win the race?
