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Lecture 2

# Lecture 2 - Motion + Error Analysis, in 2 columns for easy printing+reading, includes diagrams I drew on the computer

by OC3700

Department

PhysicsCourse Code

PHY131H1Professor

Jason HarlowLecture

2This

**preview**shows half of the first page. to view the full**3 pages of the document.**PHY131H1 Summer Lecture #2

Error Analysis + Motion

The 4 Equations of Constant Acceleration

For zero acceleration:

Acceleration

-Can be negative, zero, or positive if the object is

stopped (even momentarily)

-SI unit = m/s per second = m/s2

Graphically:

Motion at Constant Acceleration

Ex. Free-fall, projectiles (ignore air resistance)

Errors

Rules: 1) Quote errors to 1 or 2 sigfigs

2) Make sure both number and error have the

same # of digits after the decimal place

(Basically, make sure they both end in the

same column, ex. Hundredths)

3) For other numbers, assume the error is

half the value of the last column

(ex. Error = 0.005 if the last column of the

number is the hundredths)

-Eliminate need to report measurements w/ “

approximately / ”

-Give quantitative way or stating your confidence

level in the measurement

-Answer = x ±

o = error

o68% sure the actual # is btwn – and +

o95% sure the actual # is btwn-2 and +2

Ex. Answer = 10 ± 2

o68% sure the actual # is btwn 8 and 12

o95% sure the actual # is btwn 6 and 14

Ex. Period of a Pendulum

-t5 = time for 5 oscillations

-Period = t5÷5

-A. Would be error if:

oSmaller scatter

oOnly 1 measurement taken

oOr if each measurement was 7.53_s, but

the stopwatch only shows up to the

hundredth place

-B. Is the best estimate for the error, since:

oIs almost half the range of the

measurements,

oAnd is for repeated measurements

-t5, avg = 7.45250s

-est = 0.0634429s = 0.06s A ÷ 83

Propagation of Errors

Sum/Difference Rules:

If z = x + y or z = x – y

∆z =

Product/Division Rules:

If z = x*y or z = x / y

If z = A*x

∆z = A∆x

Exponent Rule:

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