1 Measurements and uncertainties
digital measuring device uncertainty
+ or - ATLEAST the smallest unit
Analog measuring device uncertainty
+ or - half of the smallest scale division e.g. uncertainty is ATLEAST + or - half a millimetre, therefore it is + or - 0.05 cm (uncertainty value must be 1 sig fig)
What causes uncertainties
- Measuring devices - Experimental procedures + technique flaws - Nature of the measurement itself e.g. speed of light is difficult
How can errors be reduced
- repeating readings will reduce random error - because systematic errors occur at each reading, repeating readings does not reduce their affect on the data.
Significant figures
-Non-zero digits are always significant. -Any zeros between two significant digits are significant. -A final zero or trailing zeros in the decimal portion ONLY are significant.
mass of an apple
10^-1 (Tenth of a kilogram)
Smallest and largest size
10^-15 to 10^25 metre (Subatomic particle to the extent of the visible universe)
Smallest and largest time
10^-24 to 10^18 seconds (time for light to cross a nucleus to the age of the universe)
Smallest and largest mass
10^-30 to 10^50 (mass of an electron to the mass of the universe)
How many significant figure in...
608 000: = 6.08e5 this has 3 sig figs 0.000 305 = 3.05e-4 this has 3 sig figs 0.005900 = 5.900e-3 this has 4 sig figs (zeroes at the end of the decimal are all significant)
ave heartbeats per minute
70
Accuracy
A measurement is said to be accurate if it has little systematic errors
Precision
A measurement is said to be precise if it has little random errors. If all values are almost the same, then they are precise. A measurement can be of great precision but be inaccurate (for example, if the instrument used had a zero offset error).
repeated measurements uncertainties
Average of all the values + or - half (max-min) value
Maximum gradient
From the bottom of the error bar of the first point, to the top of the error bar on the last point (The red line)
Minimum gradient
From the top of the error bar of the first point, to the bottom of the error bar on the last point (The blue line)
Vector quantity
Have a magnitude (size) and direction. e.g. Force, acceleration, displacement, velocity, momentum, electric field, magnetic field
Scalar quantity
Have a magnitude (size) only. No direction. e.g. Temp, mass, distance, speed, work, energy, voltage
SI unit for work
J
W
Js^-1
What are the 7 fundamental units
Metre Second Ampere Kelvin Mole Candela Kilogram
J
Nm
J =
Nm = kg m^2 s^-2
Pa
Nm^-2
adding / subtracting rule
Same amount of significant figures as the least put into the equation e.g. 2.4 + 0.56 = 2.96 = 3.0
Multiplying / dividing rule
Same amount of significant figures as the least put into the equation e.g. 4/3 =1.33 = 1
Ω
VA^-1
combining uncertainties eg3
Volume of a block *note: IB likes uncertainties to 1 sig fig therefor it would be + or - 10, rather than 14
V
WA^-1
Subtracting vectors
When subtracting vectors, we just add the magnitude in the opposite direction. e.g. lets say left is positive and right is negative. 6ms^-1 left minus 4ms^-1 right = 6ms^-1- - 4ms^-1) = 6ms^-1+ 4ms^-1)= 10ms^-1
Random errors & examples
an error which affects a reading at random. Sources of random errors include: - The observer being less than perfect - The readability of the equipment - External effects on the observed item
Systematic errors & examples
an error which occurs at each reading. Sources of systematic errors include: - The observer being less than perfect in the same way every time - An instrument with a zero offset error - An instrument that is improperly calibrated
terminal velocity
the maximum speed an object reaches when it falls freely under the influence of gravity. continues to accelerate until the upward force due to air resistance equals the downward force of gravity.
Energy =
work done = force x distance = mass x acceleration x distance
