SPH 4U1

Physics

Essential Skills

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Reference: Appendices

Units are extremely IMPORTANT in this course.  Always show them in your calculations.

 

Significant Digits

·         Non-zero numbers are significant digits ( i.e. 23.4 has 3 sig. digits).

·         Zeros before other digits are not significant (i.e. 0.0003 has 1 sig. Digits).  Zeroes between other digits are significant (i.e. 20003 has 5 sig. Digits). Zeroes after other digits behind a decimal are significant (i.e. 70.00 has 4 sig. Digits).

Significant Digit Rules for Calculations

Multiplication and Division:

The answer will have the same number of significant digits as the measurement with the least number of significant digits.

Addition and Subtraction:

The answer will have the same number of decimal places as the measured value with the fewest decimal places.

Rounding:

·        Always round off answers to the least # of decimals in the original measurements.

·        If digit dropped is 4 or less leave preceding digit unchanged.

·        Round up if digit dropped is > 5 or if it is a 5 followed by at least one non-zero digit (i.e. 7.751 rounds to 7.8).

·        If digit to be dropped is a lone 5 or a 5 followed by zeros, the preceding digit is not changed if it is even, but is increased if it is odd (i.e. 6.675 rounds to 6.68 & 6.465 rounds to 6.46). In other words make the preceding digit even. AS PER NELSON TEXTBOOK

 

Know how to convert units to Base SI Units

 

 

Error Analysis (remember to apply in lab write-ups) :

All counted quantities are exact. All measured quantities have a built in uncertainty which is determined by the measuring instrument.  Scientists agree that the uncertainty in a measured quantity is ˝ of the value of the smallest division on that instrument.

Example: A ruler with only cm divisions will have an uncertainty of

 

Accuracy/Reporting Error: Accuracy is how close a measured value is to the accepted value.

Absolute Error = Experimental Value – Accepted Value

% Error is more useful than absolute error

 

% Difference (% Deviation) is used in cases where the Accepted Value isn’t known so scientists compare trials.

 

 

 

Trial

Time for 10 cycles(s)

Time for 1 cycle (s)

SOLVE

Difference in values

ANSWER

% Difference (from trial 1)

1

20.

2.0

 

 

2

21.

2.1

0.1

5.0 %

3

22.

2.2

0.2

10. %

4

20.

2.0

0.0

0.0 %

5

18.

1.8

0.2

10. %

6

19.

1.9

0.1

5.0 %

7

20

2.0

0.0

0.0 %

                        Average of Values = 2.0