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Topic #01 Physics - A Mathematical Science

Topic 1 Concepts and Skills

Vocabulary, Variables and Equations

Review Questions

Application Questions

Problem Set 01

Topic #01 Concepts and Skills

Link to "Concepts and Skills"
 

Vocabulary, Variables and Equations

metric system: A set of standards of measurement where units of different sizes are related to by powers of ten

SI: International standards of measurement adapted from the metric system

base unit(s): The seven fundamental SI units of measure 

meter: The SI base unit of length

second: The SI base unit of time

kilogram: The SI base unit of mass

mks system: A system of measurements that are based upon the meter, kilogram and the second. 

fundamental unit(s): A term referring to any of the of the seven base units in the SI standards of measurement

derived unit(s): A unit of a measurement that is defined by the combination of two or more fundamental (base) units

scientific notation: The expression of numbers as powers of ten

factor-label method: The method of converting a quantity expressed in one unit to that quantity in another unit

precision: The degree of exactness with which a quantity is measured using a given instrument (measuring tool) 

accuracy: How well the results of an experiment agree with the measured measured accepted value. (This also applies to measurements made in situations other than experiments.)

parallax: The apparent shift in position of an object when it is seen from differet angles (This is important to know about when making measurements)

significant digits: All valid digits in a measurement (There are rules about this; know them)

metric prefixes: Define the following.prefixes.
tera, giga, mega, kilo, hecto, deca, deci, centi milli, micro, nano, pico, femto
 

Review Questions:

Reviewing Concepts
Questions:
1. Define Physics in your own words.

2. Why is mathematics important to science?

3. Assume for a moment that the theory of matter held by some of the ancient Greeks is correct.  How does this theory explain the motion of the four elements?
 

Application Questions:

Chapter 1
Applying Concepts

Questions

4. Give some examples of applications that resulted from work done by 
Physicists.

5. Give some examples of application s that have resulted from work done by 
Physicists on the exploration of space.

6. Research the aspects of nature investigated by each of the following 
kinds of scientists: astrophysicists, astronomers, biophysicists, 
Exobiologists, and geophysicists.

7. Some of the branches of physics that you will study in this course 
investigate motion, the properties of materials, sound, light, and electricity 
and magnetism, properties of atoms, and nuclear reactions.  Give at least 
one example of an application of each branch.

8. What reason might the Greeks have had not to question the evidence that 
heavier objects fall faster than lighter objects?  Hint: did you ever 
question which falls faster?

9. Is the scientific method a clearly defined set of steps and procedures? 
Support your answer.

10. Why will the work of a physicist never be finished?

 

Word Problems:

Problem Set #1:  Follow the written directions unless indicated otherwise by your instructor.

1. Convert each of the following length measurements to its equivalent in meters.
 a. 1.1 cm   b. 76.2 pm   c. 2.1 km  d. 0.123 mm

2. Rank the following mass measurements from smallest to largest.
 11.6 mg 1021 mg  0.6 cg          0.31 mg

Problems 3-9 Convert each value to scientific notation. 

3.  a. 5,800 m  b. 450,000 m  c. 302,000,000 m d.86,000,000,000 m

4.  a. .000508 kg b. 0.0000045 kg c. 0.0036 kg  d. 0.004 kg 

5.  a. 300,000,000 s b. 186,000 s  c. 93,000,000 s

6.  a.0.0073 m  b. 0.00087m  c. 0.0032 m

7. a. 5,000,000,000,000,000,000,000,000 m  b. 0.000000000000000000166 m    [ 0.{18 zeros}166]

    c. 2,033,000,000 m  d. 0.0000001030 m

8. a. 65,000 kg  b. 5,000,000 s  c. 226 m d.  4500 s

9. a. 0.025 m  b.  0.00025 m  c. 0.0006 s d. 0.00000000000019 s

Note: Express your answers in scientific notation.  [Note:  2.5x10^2 represents 2.5 x 10 raised to the second power. If you find it more comfortable to rewrite the numbers written in this way before solving the problems, do so.]

10.  a. 5x10^7 m + 3x10^7 m       b. 6x10^8 m +2x10^8 m 
       c. 4.2x10^4 m + 3.6x10^4 m         d.  1.8x10^9 m + 2.5x10^9 m

11.  a. 5x10^-7 kg + 3x10^-7 kg        b. 4x10^-3 kg +3x10^-3 kg 
       c. 1.66x10^-19 kg + 2.3x10^-19 kg        d. 7.2x10^-12 kg - 2.6x10^-12 kg

12.  a. 6x10^8 cm - 4x10^8 cm       b. 3.8x10^12 cm - 1.9x10^12 cm
       c. 5.8x10^9 cm - 2.8x10^9 cm       d. 6.25x10^4 cm - 4.5x10^4 cm
 

13.  a. 6x10^-8 m2 - 4x10^-8 m2.       b. 3.8x 10^-12 m2 - 1.9x10^-11 m2.
       c. 5.8x10^-9 m2 - 2.8x10^-9 m2.       d. 2.26x10^-18 m2 - 1.80x10^-18 m2.

14  a. 6x10^8 kg + 4x10^7 kg      b. 7x10^4 kg + 2x10^3 kg
      c. 4x10^4 kg + 3x10^5 kg      d. 6x10^10 kg + 5x10^11 kg

15  a. 5x10^-7 cg + 4x10^-8 cg      b. 6x10^-3 cg + 2x10^-4 cg
      c. 3x10^-14 cg + 2x10^-15 cg      d. 4x10^-12 cg + 6x10^-13 cg

16  a. 5x10^-7 L - 4x10^-8 L      b. 6x10^-3 L - 2x10^-4 L
      c. 3x10^-14 L - 2x10^-15 L      d. 8.2x10^-16 L - 4.5x10^-17 L

17  a. 6x10^8 m + 3x10^8 m      b  2.2x10^4 m + 3.6x10^4 m
      c. 5x10^8 m + 6x10^7 m      d  9.8x10^5 m + 2x10^4 m

18  a. 8.4x10^-8 g - 3.2x10^-8 g      b. 5.4x10^7 g - 3.4x10^7 g
      c. 6x10^-8 g - 6x10^-9 g      d. 2.2x10^12 g - 8x10^11 g

Solve each problem expressing the answer in scientific notation.

19. a. (2x10^4 m) (4x10^8 m)
      b. (3x10^4 m) (2x10^6 m)
      c. (6x10^-4 m) (5x10^-8 m)
      d. (2.5x10^-7 m) (2.5x10^16 m)

20. a. 6x10^8 kg / 2x10^4 m3.
      b. 6x10^8 m / 2x10^-4 s
      c. 6x10^-8 kg / 2x10^4 m3. 
      d. 6x10^-8 m / 2x10^-4 s

21. a. (3x10^4 kg) (4x10^4 m) / 6x10^4 s
      b. (2.5x10^6 kg) (6x10^4 m) / 5x10^-2 s2.

In problems 22 and 23 state the number of significant digits for each value.

22. a. 2804 m   b. 2.84 m  c. 0.0029 m
      d. 0.003068 m  e. 4.6x10^5 m  f. 4.06x10^5 m 

23. a. 75 m   b. 75.00 cm  c. 0.007060 kg
      d. 1.87x10^6 m   e. 1.008x10^8 m f.  1.20x10^-4 m

Using the rules for working with significant digits, solve the following problems.

24. Add 6.201 cm, 7.4 cm, 0.68 cm, and 12.0 cm

25. Add 28.662 m, 32.34 m, and 17.5 m. 

26. Add 26.38 kg, 14.531 kg, 30.8 kg.

27. The sides of a quadrangular plot of land are measured. Their lengths are found to be 
      132.68 m, 48.3 m, 132.736 m, and 48.37 m. What is the perimeter of the plot of land as can
       best be determined from these numbers.

28. Subtract 8.264 g from 10.8 g.

29. Subtract 26.82 mL from 44.12 mL.

30. A water tank has a mass of 3.64 kg when empty and a mass of 51.8 kg when filled to a
      certain level.  What is the mass of the water in the tank?
 

Solve the following problems using the rules for significant digits.

31. a. 131 cm x 2.3 cm
      b. 6.87 cm x 2.2 cm
      c. 3.2145 km x 4.23 km

32. a. 20.2 cm / 7.41 s
      b. 3.1416 cm /  12.4 s
      c.  64.39 m / 13.6 s

33. A rectangular floor has a length of 15.72 m and a width of 4.40 m. Calculate the area of the 
      floor to the best possible value using these measurements.