MARY JOSETTE ACADEMY, INC. Tigbe, Norzagaray, Bulacan
[email protected]
NAME: GRADE AND STRAND:
GRADE: 12 SEMESTER: FIRST SEMESTER SUBJECT TITLE: GENERAL PHYSICS 1 NO. OF HOURS/SEM: 80 hours/semester
GENERAL PHYSICS 1
Prepared by: LESLIE S. MERMELO
NOTE: Only the Activities, and Quiz in each learning Kit shall be returned/ submitted during the drop-off of the answered modules.
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Quarter 1 - Module 1
Introductory Concepts in Physics
Learning Competencies
• solve measurement problem involving conversion of units, expression of measurements in scientific notation, • differentiate accuracy from precision and random rando m errors from systematic errors, • estimate the uncertainty of a derived quantities; and • identify different variable relationship
A. Meas Measur urem emen entt
As discussed in the previous grades, measurement is the art of comparing unknown value to a standard, or the accepted set of values for a particular quantity.
Physical variables, such as time, temperature, and length, can be used to quantitatively describe physical phenomena. The standards in which the physical quantities are expressed are called units.. units Table 1 SI fundamental quantities and units
M E T T A L L
Physical Quantity Mass electric current Time temperature amount of substance length luminous intensity
Unit Kilogram (kg) Ampere (A) second (sec) Kelvin (K) mole (mol) meter (m) candela (cd)
Figure 2 Common Metric Conversion Factor Let’s try to Convert this! 960 cm - m
2.) 11 m2 – dm2 dm2 = 11m2 x 10 10dm dm 2 1m2 dm2 = 110dm2 2|Page
3.) 30 kg - g
m = 960cm x 1m 100cm m = 960cm x 1m m = 9.6m 100cm
Expression of Measurements in Scientific Notation
When physicists deal with either very large or very small numbers, they used scientific notation to facilitate recording and calculations. Generally, a scientific notation is expressed as follows: M x 10E Where the M is the mantissa, following the condition: 1 > M > 10 , the mantissa can be equal to 1 but must be less than 10. For Example: 1.) 980 000 000 000m 000m is is 9.8 9.8 x 108 m 2.) 0.006 0.006 J iiss 6 x 10 10-3 J Try this one a. 0.0000007 m b. 100cm
B. Uncerta Uncertainti inties es and Errors Errors in Measur Measureme ement nt
Accuracy and precision are related to the level of closeness of the values measured with the theoretical or accepted values, and vice versa. Accuracy means obtaining a measurement result that is close to the theoretical value. On the other hand, precision denotes getting a similar result when measurement of a certain object is repeated.
To illustrate, imagine a dartboard. The darts represent the accuracy ac curacy and precision of the player p layer in throwing, while the center of the dartboard represents the true/theoretical/accepted value.
Now, consider the following measurements made on particular material, which has true value of 10 inches. Table 1.2 Sample Values Measured
Set A 9.9 in, 10 in, 10 in,
Set B 7.8 in, 8.1 in, 8.2 in,
Set C 10 in, 9 in, 8 in,
Set D 3 in, 5 in, 7 in,
10 in, 9.9 in, 9.9 in
8.0 in, 8.2 in, 8.3 in
11 in, 12 in, 7 in
9 in, 11 in, 12 in
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Which set displays the highest levels of accuracy and precision?
Poor precision and/or accuracy in measurement lead(s) to potential errors. When the accuracy is poor and measurement is reproducible, the error is called a systematic error. Another type of error is the random error, which involve poor precision. Random Ran dom errors are usually more problematic than systematic, as tracing the source of error is more difficult.
C. Uncerta Uncertainty inty of Deriv Derived ed Quantit Quantities ies
In order to account for the uncertainty of derived quantities, we shall look at the four basic operations to illustrate how the uncertainties can be calculated. Consider two measurements: X = 5 + 0.2 cm and Y = 4.5 + 0.3 cm For addition addition 1.) First First,, prepare prepare the follow following ing table. table. Measurement X Y X+Y
Minimum value (cm) 4.8 4.2 9
Average (cm)
Maximum value
5 4.5 9.5
5.2 4.8 10
2.) Subtract the average value of the sum from its maximum value. Get the difference. 10 – 9.5 = 0.5 3.) Alternatively, we can subtract the minimum minimum value of the sum from from its average value. 9.5 – 9 = 0.5 From what is illustrated, the uncertainty of the derived units is simply the sum of the uncertainties. For subtraction subtraction 1.) Simil Similar ar to what has been done in addition, addition, prepare the following following table. table. Measurement X Y X-Y 4|Page
Minimum value (cm) 4.8 4.2 0.6
Average (cm)
Maximum value
5 4.5 0.5
5.2 4.8 0.4
2.) Subtract the average value of the dif difference ference from the minimum value of the differences in measurement. 0.6 – 0.5 = 0.1 3.) Alternatively, we can subtract the maximum value of the difference from the average value of the difference to get the uncertainty. 0.5 – 0.4 = 0.1 This means that the uncertainty is 0.1
For Multiplication Multiplication
1.) Prepar Preparee the the table table.. Measurement X Y XY
Minimum value (cm) 4.8 4.2 20.16
Average (cm)
Maximum value
5 4.5 22.5
5.2 4.8 24.96
2.) Subtract the product of the average values from the product of the maximum maximum values. Get the the difference. 24.96 – 22.5 = 2.46 3.) We can also subtract the product of the minimum values from the product of the maximum values. 24.96 – 20.16 = 4.80 In this case, the uncertainty is the one with the larger value : 4.80
D. Variabl Variablee Relation Relationship shipss
There are common relationship that can be linearly established between a pair of variables. These are two direct and inverse relationships. Direct Proportion
As one quantity increases, the other quantity also increases proportionally. The graph of a direct d irect proportion is a slanted straight line.
Inverse Proportion
As one quantity increases, the other quantity decreases. The graph of the inverse proportion is a parabola. 5 | P a g e
NAME: GRADE AND STRAND: SUBJECT TITLE: GENERAL PHYSICS 1
Activity 1.1
Express the following examples in scientific notation. 1.) 2.) 3.) 4.) 5.)
300 m - ______ __________ _______ ______ ___ 758 000 000 mL - _______________ __________________ ___ 990 000 00 000 0 000 miles miles - _________ _________________ _________ _ 0.001 0.001 kg kg - ________ ____________ ________ _____ _ 1 500 000 Watts Watts - ___________ _______________ ____
Activity 1.2
Identify the levels of accuracy and precision of the following sets of values. Put a check (/) on the blank(s) to describe the set it/they follow(s). 1.) Theore Theoretic tical al value value : 1 kg Set A 996 g 324 g 762 g accuracy: ______ precision: ______
Set B 989 g 1 045 g 1 132 g accuracy: ______ precision: ______
Set C 768 g 783 g 792 g accuracy: ______ precision: ______
Set D 997 g 994 g 998 g accuracy: ______ precision: ______
Activity 1.3
Following the process of determining the uncertainty of derived d erived quantity, complete the following table. X = 5 + 0.2 cm and Y = 4.5 + 0.3 cm Measurement X Y X/Y
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Minimum value (cm) 4.8 4.2
Average (cm)
Maximum value
5 4.5
5.2 4.8
NAME: GRADE AND STRAND: SUBJECT TITLE: GENERAL PHYSICS 1
QUIZ 1
Direction : Write True if the Statement is Correct and False it’s not. ________ 1.) Direct proportion means when the one quantity increases, the other quantity also increases proportionally. ________ 2.) When physicists deal with either very large or very small numbers, they used scientific calculator to facilitate recording and calculations. ________ 3.) When accuracy is poor and measurements are reproducible, the error is called systematic error. ________ 4.) Another type of error is the random error, which involves poor accuracy. ________ 5.) Accuracy means obtaining a measurement result that is not close to the theoretical value. ________ 6.) precision denotes getting similar result when measurement of a certain object is repeated. ________ 7.) Mantissa (M) can be equal to 1 upto 10. ________ 8.) The scientific notation for 86 000 000 J is 86 x 106 J. ________ 9.) Measurement is the art of comparing unknown values to a standard, or the accepted set of values for a particular quantity ________ 10.) 10 cm is equal to 100 mm.
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