Science Skills Flashcards
uncertainty
An estimate of the range of values where the true value lies
absolute uncertainty
How high above or below a measurement can be from the true value; the amount by which the value is uncertain
if a is a measurement, what is Δa?
The absolute uncertainty of a
precision of a measuring instrument = ?
its resolution
precision of lots of measurements = ?
the range of the values
What does the typical precision of a device mean?
The precision of the values it measures i.e. the range of readings you’d get from measuring a certain value
What is the typical precision of a datalogger with a resolution of 0.01s?
Resolution = 0.01s
So, for a certain value, the measured time could be 0.01s above or below the true value
Precision = 0.01 + 0.01 = 0.02s
I think - not 100% sure, so don’t quote me
What is the typical precision of a micrometer?
Resolution = 0.01mm
Absolute uncertainty = ± 0.01mm
So, for a certain value, the measured length could be 0.01mm above or below the true value
Precision = 0.01 + 0.01 = 0.02mm
I think - not 100% sure, so don’t quote me
difference between a reading and a measurement (+ example)
Reading = 1 measured value e.g. mass
Measurement = 2 measured values e.g. length
formula for absolute uncertainty for a:
a) reading
b) measurement
a) ± half of resolution
b) resolution
formula for absolute uncertainty for lots of readings e.g. when you’ve taken repeats
± range / 2
need to check
formula for absolute uncertainty for a mean
± range / 2
What absolute uncertainty are human-recorded time measurements limited to? Why?
Time is limited to an absolute uncertainty of ± 0.2-0.5s due to human error
A force is measured to be 2N. What is the uncertainty?
1 / 2 = ± 0.5
How is the percentage uncertainty determined from a single reading whose value is a?
absolute uncertainty / measured value (a) × 100 = εa
epsilon a = percentage uncertainty
need to check
How can you calculate the fractional uncertainty?
absolute uncertainty / measured value
Combining
uncertainties should
always make the
uncertainty ____.
increase
When adding or subtracting data with uncertainties, how do you calculate the absolute uncertainty?
Add the absolute uncertainties
When multiplying or dividing data with uncertainties, how do you calculate the uncertainty?
check this FC
Add the percentage uncertainties - this gives you a percentage uncertainty e.g. ± 9.25%
When raising data with an uncertainty to a power, how do you calculate the uncertainty?
Multiply the percentage uncertainty by that power (i.e. you’re adding the uncertainty that many times)
When multiplying data with an uncertainty by a constant, how do you calculate the a) absolute uncertainty and b) the percentage uncertainty?
a) multiply the absolute uncertainty by that constant - any error in measurement is amplified by the constant
b) you don’t multiply the percentage uncertainty by the constant (it stays the same) - both the absolute uncertainty and the true value/mean would be multiplied by the constant, so there would be no overall change???
don’t fully understand how the percentage uncertainty changes
What are the two different instruments that you can use to measure length more accurately?
- Caliper (can measure internal & external widths) - resolution of 0.1mm
- Micrometer (used in class, has two measuring cylinder things) - resolution of 0.01mm
Does a micrometer or vernier caliper have the greater resolution?
Micrometer - it has a resolution of 0.01mm compared to the vernier caliper’s resolution of 0.1mm
What are the two different instruments that you can use to measure mass more accurately?
- Spring balance (like in shops for measuring the mass of fruit) - resolution of 0.1g
- Top-pan balance - resolution of 0.01g
How many decimal places should you quote errors to?
1 or 2 d.p.s
How many decimal places should you quote results to?
The same number of d.p.s as the error
Neville measures the length of a metal block to be 32.67 ± 0.1mm. Is this ok? Explain your answer.
No - it should be 32.7 ± 0.1mm as results & errors should be written to the same power e.g. 10-2 when givien in standard form / decimal places as in the case here
Liliana is drawing a table. In a column for temperature, she has 8.5°C, 9.7°C, 10.3°C and 12.0°C. Is this ok? Explain your answer.
Yes - when changing from one power of 10 to another in a table column, keep the number of d.p.s the same to not change the accuracy of the results
What do the values of y and x mean in the equation of a straight line?
y = dependent variable
x = independent variable
What does the value of m mean in the equation of a straight line?
m = gradient, the constant (of proportionality)
How would you plot s = ut + 1/2 at2 on a graph? What does each term represent?
s = ut + 1/2 at2
variables = s and t
to get rid of the repeated variable t, you divide the whole equation by t:
s/t = 1/2 at + u
s/t goes on the y-axis as it’s the dependent variable, t on the x-axis as it is the independent variable, 1/2a is the gradient (constant) and u is the y-intercept
How could you draw a graph and then use this to calculate the height of a cylinder from the formula for its volume?
V = π r2 h
1) Rearrange for h
h = (V/r2) / π
2) Plot one variable over the other on a graph, ignoring constants i.e. V on y-axis and r2 on the x-axis
3) Calculate the gradient of the line
4) Multiply the gradient by the constant i.e. 1 / π
How could you draw a graph and then use this to calculate Young’s modulus from the formula E = (Fl0) / (xA)? State which values you would also need to measure.
where E is Young’s modulus
F is the load added (independent variable)
l0 is the initial length of the wire
x is the extension (dependent variable)
and A is the cross-sectional area
E = (Fl0) / (xA)
1) Rearrange for E with extension on the numerator and force on the denominator (due to the specified independent/dependent variables)
E = (xA) / (Fl0)
2) Draw an extension-force graph, ignoring constants i.e. extension on y-axis and force on the x-axis
3) Calculate the gradient of the line (this will be equal to x/F)
4) Multiply the gradient by the constants of initial length of the wire and cross-sectional area (these would need to be measured separately)
i.e. E = gradient * A * (1/l0)
You believe two values are inversely proportional. How can you plot a straight line graph to confirm the relationship between the two?
y = k/x
Plot y against 1/x, making the gradient k.
You believe that some data you have collected is quadratic. How can you plot a straight line graph to confirm the relationship between the two?
Not sure if you need to know this.
y = kx2
Plot y against x2, making the gradient k.
You believe that some data you have collected have an inverse square relationship. How can you plot a straight line graph to confirm the relationship between the two?
Not sure if you need to know this.
y x2 = k
y = k (1/x2)
Plot y against 1/x2, making the gradient k.
When plotting y against x on a graph, you get a concave line of best fit. How can you plot a straight line graph to confirm the relationship between the two?
Not sure if you need to know this.
Plot y2 against x, making the gradient k.
6 base quantities
- Length
- Mass
- Time
- Current (not charge)
- Temperature interval
- Amount of substance
What is the amount of substance measured in?
moles
What is a temperature interval measured in, in SI units?
Kelvins, K
NOT DEGREES KELVIN
room temperature in kelvins
20°C = 20 + 273 = 293K
Derive the unit for energy from the base quantities.
Ek = 1/2m v2
= 1/2m (s / t)2
units:
J = kg (ms–1)2 = kg m2 s-2
Alternatively, you could you E = mc2
Derive the unit for potential difference from the base quantities.
Derive energy first:
Ek = 1/2m v2
= 1/2m (s / t)2
V = E / Q
V = 1/2m (s / t)2 / (I t)
V = (m s2) / (2I t3)
units:
V = kg m2 s-3 A-1
Alternatively, you could you E = mc2
Derive the unit for resistance from the base quantities.
R = VI
Potential difference derivation:
Derive energy first:
Ek = 1/2m v2
= 1/2m (s / t)2
V = E / Q
V = 1/2m (s / t)2 / (I t)
V = (m s2) / (2I t3)
Putting it all together:
R = (m s2) / (2I t3) / I
units:
Ω = kg m2 A -3 s-3
Alternatively, you could you E = mc2
Explanation: https://www.thestudentroom.co.uk/showthread.php?t=4671416
Derive the unit for frequency from the base quantities.
f = 1/T
Hz = 1/s = s-1
How do you reduce random errors?
repeat readings
How do you reduce systematic errors?
calibrating equipment
How do you improve accuracy?
reduce systematic errors -> calibrate equipment
How do you improve precision?
reduce random errors -> take repeat readings
Liliana measures the angle of refraction of some light rays. Some of her data were: 27.94°, 27.90°, 27.82° and 27.78°. Explain why these results couldn’t have been obtained with a normal protractor.
The data has a higher resolution than a normal protractor, so the normal protractor wouldn’t be able to measure the difference between these results.
Some students investigate the properties of the waves generated in a ripple tank with a shallow and deeper region.
Student A says, ‘the waves move water from one end of the tank to the other’.
Student B says, ‘that’s wrong. Only the waves move, not the water’.
Suggest what the students could do to decide which of them is correct. [2]
Place a floating object / plastic duck on the surface of the water (1) - it will stay in the same place or only bob up and down if the water doesn’t move (1)
Figure 5 shows a curve, where the maximum value of ε corresponds to the curve’s maximum, the turning point.
A graph of the gradient of figure 5 against θ is plotted in Figure 6 (this is a linear graph with a negative gradient).
The neutral temperature θn is the temperature corresponding to the maximum value of ε.
θn can be determined using either Figure 5 or Figure 6. Explain why a more accurate result for θn may be obtained using Figure 6. [1 mark]
θn in Figure 6 is just the x-intercept (because maximum ε = a gradient of 0) making it easy to read off the value of θn
OR
Using Figure 5 would give a range of values
Rewrite (1.4 * 10-14</sub>)m with a suitable unit.
14 fm
How can you quickly convert between unit prefixes? e.g. for (28 * 10-11</sub>)s
(28 * 10-11</sub>)s
= (280 * 10-12</sub>)s
280ps
What do you do for a question that asks you to show that a value is e.g. 1.52?
Calculate the value to at least one more d.p. than the given value (i.e. 3 d.p.s in this example)
Not verified by mark scheme yet
