Science Skills

Question 1

uncertainty

Answer 1

An estimate of the range of values where the true value lies

Question 2

absolute uncertainty

Answer 2

How high above or below a measurement can be from the true value; the amount by which the value is uncertain

Question 3

if a is a measurement, what is Δa?

Answer 3

The absolute uncertainty of a

Question 4

precision of a measuring instrument = ?

Answer 4

its resolution

Question 5

precision of lots of measurements = ?

Answer 5

the range of the values

Question 6

difference between a reading and a measurement (+ example)

Answer 6

Reading = 1 measured value e.g. mass
Measurement = 2 measured values e.g. length

Question 7

formula for absolute uncertainty for a:
a) reading
b) measurement

Answer 7

a) ± half of resolution
b) resolution

Question 8

formula for absolute uncertainty for lots of readings e.g. when you’ve taken repeats

Answer 8

± range / 2

need to check

Question 9

formula for absolute uncertainty for a mean

Answer 9

± range / 2

Question 10

What absolute uncertainty are human-recorded time measurements limited to? Why?

Answer 10

Time is limited to an absolute uncertainty of ± 0.2-0.5s due to human error

Question 11

A force is measured to be 2N. What is the uncertainty?

Answer 11

1 / 2 = ± 0.5

Question 12

How is the percentage uncertainty determined from a single reading whose value is a?

Answer 12

absolute uncertainty / measured value (a) × 100 = εa

epsilon a = percentage uncertainty

need to check

Question 13

How can you calculate the fractional uncertainty?

Answer 13

absolute uncertainty / measured value

Question 14

Combining
uncertainties should
always make the
uncertainty ____.

Answer 14

increase

Question 15

When adding or subtracting data with uncertainties, how do you calculate the absolute uncertainty?

Answer 15

Add the absolute uncertainties

Question 16

When multiplying or dividing data with uncertainties, how do you calculate the uncertainty?

check this FC

Answer 16

Add the percentage uncertainties - this gives you a percentage uncertainty e.g. ± 9.25%

Question 17

When raising data with an uncertainty to a power, how do you calculate the uncertainty?

Answer 17

Multiply the percentage uncertainty by that power (i.e. you’re adding the uncertainty that many times)

Question 18

When multiplying data with an uncertainty by a constant, how do you calculate the a) absolute uncertainty and b) the percentage uncertainty?

Answer 18

a) multiply the absolute uncertainty by that constant
b) you don’t multiply the percentage uncertainty by the constant (it stays the same???).

not really sure how the percentage uncertainty changes

Question 19

What are the two different instruments that you can use to measure length more accurately?

Answer 19

• Caliper (can measure internal & external widths) - resolution of 0.1mm
• Micrometer (used in class, has two measuring cylinder things) - resolution of 0.01mm

Question 20

Does a micrometer or vernier caliper have the greater resolution?

Answer 20

Micrometer - it has a resolution of 0.01mm compared to the vernier caliper’s resolution of 0.1mm

Question 21

What are the two different instruments that you can use to measure mass more accurately?

Answer 21

• Spring balance (like in shops for measuring the mass of fruit) - resolution of 0.1g
• Top-pan balance - resolution of 0.01g

Question 22

How many decimal places should you quote errors to?

Answer 22

1 or 2 d.p.s

Question 23

How many decimal places should you quote results to?

Answer 23

The same number of d.p.s as the error

Question 24

Neville measures the diameter of a metal block to be 32.67 ± 0.1mm. Is this ok? Explain your answer.

Answer 24

No - it should be 32.7 ± 0.1mm as results & errors should be written to the same power e.g. 10^-2

Question 25

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.

Answer 25

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

Question 26

What do the values of y and x mean in the equation of a straight line?

Answer 26

y = dependent variable
x = independent variable

Question 27

What does the value of m mean in the equation of a straight line?

Answer 27

m = gradient, the constant (of proportionality)

Question 28

How would you plot s = ut + 1/2 at² on a graph? What does each term represent?

Answer 28

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

Question 29

How could you draw a graph and then use this to calculate the height of a cylinder from the formula for its volume?

Answer 29

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

Question 30

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

Answer 30

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)

Question 31

You believe two values are inversely proportional. How can you plot a straight line graph to confirm the relationship between the two?

Answer 31

y = k/x
Plot y against 1/x, making the gradient k.

Question 32

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.

Answer 32

y = kx²
Plot y against x², making the gradient k.

Question 33

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.

Answer 33

y x² = k
y = k (1/x²)
Plot y against 1/x², making the gradient k.

Question 34

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.

Answer 34

Plot y² against x, making the gradient k.

Question 35

6 base quantities

Answer 35

• Length
• Mass
• Time
• Current (not charge)
• Temperature interval
• Amount of substance

Question 36

What is the amount of substance measured in?

Answer 36

moles

Question 37

What is a temperature interval in?

Answer 37

Kelvins, K

Question 38

Derive the unit for energy from the base quantities.

Answer 38

E_k = 1/2m v²
= 1/2m (s / t)²

units:
J = kg (ms^–1)² = kg m² s^-2

Alternatively, you could you E = mc²

Question 39

Derive the unit for potential difference from the base quantities.

Answer 39

Derive energy first:
E_k = 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

Question 40

Derive the unit for resistance from the base quantities.

Answer 40

R = VI

Potential difference derivation:
Derive energy first:
E_k = 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