2 Nature of quantities Units and measurements Flashcards
What the S.I Base units for mass, length and time
Kilogram, Kg
Metre, m
seconds, s
What the S.I Base units for current, temperature and amount of substance
ampere, A
kelvin, K
mole, mol
Define Homogenity of units
Units in an equation must always be the same on both sides
Mulitple of unit for pico
p 1×10^-12
Mulitple of unit for nano
n 1×10^-9
Mulitple of unit for micro
µ 1×10^-6
Mulitple of unit for milli
m 1×10^-3
Mulitple of unit for centi
c 1×10^-2
Mulitple of unit for deci
d 1×10^-1
Mulitple of unit for Kilo
K 1×10^3
Mulitple of unit for mega
M 1×10^6
Mulitple of unit for giga
G 1×10^9
Mulitple of unit for tera
T 1×10^12
Accuracy
Accuracy-How close the mean value of your measurement is to the true value
Human error
Mistake made by a person, results in an anomolous result
Systematic error
caused by mistake in calibration of the measuring equippment. affects accuracy not precision
zero error
type of systematic error where the equipment gives a reading when it should read zero
random error
casued by fluctuations in the object you are measuring or the equipment. can affect accuracy and precision
How do you add or subtract data with uncertainties?
Q. A wire is stretched from 0.3 ±0.1 cm to 0.5 ±0.1 cm. Calculate the extension of the wire
Add the absolute uncertainties
A. 0.5 - 0.3=0.2
0.1 + 0.1 =0.2
so Extension in wire is 0.2 ±0.2 cm
How do you multiply or divide data with uncertainties?
Q. A force of 15 N ±3% is applied to a stationary object which has a mass of 6.0 ±0.3 Kg.
Calculate the the acceleration of the object and state the % uncertainty in this value
Add the percentage uncertainties
A. a=f/m
15/6=2.5ms^-2
%uncertainty in mass=(0.3/6)×100=5%
Total uncertainty= 3% + 5%
so acceleration = 2.5ms^-2 ±8%
How do you find %uncertainty for data with powers?
Q. The radius of a circle is r=40cm ±2.5%. What will the %uncertainty be in the area of this circle (πr^2)
Multiply the %uncertainty by the power
A. 2.5% × 2=5%
For single readings what is the absolute uncertainty?
The actual uncertainty and is the same as the resolution of the measuring instrument
For single readings what’s the percentage uncertainty?
(absolute uncertainty/measured value) ×100
For multiple readings what’s the absolute uncertainty?
(largest value-smallest value)/2
For multiple readings whats the precentage uncertainty?
(absolute uncertainty/mean) ×100
What’s an error bar?
Shows the absolute uncertainty of individual points on a graph. It ca be plotted in x and y direction
How do you calculate %uncertainties of final results from a line of best fit?
- Add error bars to each point (usually the same)
- Draw line of best fit, max line and min line (worst lines)
3.Calculate: uncertainty= (grad of best fit - grad of worst fit)
Or (max grad - min grad)/2 - %Uncertainty=(uncertainty/grad of best fit) ×100
Precision
Precision-How close together repeat values are
How do you work out %uncertainties in the intercept from the max and min gradients?
- draw line of best fit and extrapolate it to find the ‘best value of the y intercept”
- Draw max and min grads and extrapolate them to get max and min value for the y intercept
- Determine the diffrence between the max and min values then halve it to find the uncertainty in the y intercept
- %uncertainty= (uncertainty/best y intercept value) x 100
What is the resolution of a measuring equipment
The smallest change it can read
callibrated
an accurate scale has been established by comparison to a known standard
