Model Answers - Working Scientifically - complete

Question 1

State all unit conversions in a chart

Answer 1

Question 2

Give the 5 base quantities and their units

Answer 2

Question 3

Give 4 examples of derived units

Answer 3

Force (N), acceleration(ms^-2), momentum(kgms^-1), pressure(Pa)

Question 4

Define accurate

Answer 4

How close a measured value is to the true value

Question 5

Define precise

Answer 5

How close repeated measurements are to one another

Question 6

Define resolution

Answer 6

The smallest measuring interval on a measuring instrument

Question 7

Define valid

Answer 7

A measurement is valid if it measures what it is supposed to be measuring

Question 8

Define repeatable

Answer 8

If measurements are repeated by the same person in the same laboratory with the same equipment the repeated results are close to each other

Question 9

Define reproducible

Answer 9

If measurements are repeated by a different person or using different techniques and the results are close to each other

Question 10

Define true value

Answer 10

The value that would have been obtained in an ideal measurement

Question 11

Define uncertainty

Answer 11

The internal within which the true value can be considered to lie with a given level of confidence

Question 12

Define error

Answer 12

The difference between the measurement result and the true value (NOT a mistake in the measurement)

Question 13

Explain why a measurement of 2.40V is NOT more precise than a measurement of 2.4V

Answer 13

A. Precision is a measure of the closeness of repeated measurements
b. Both 2.40V and 2.4V are single measurements so we cannot comment on their ‘precision’
c. The result 2.40V has been measured using a higher resolution multimeter
d. So 2.40V has a lower absolute uncertainty (=resolution/2 = 0.005V) compare to 2.4V (absolute uncertainty = 0.1/2 = 0.05V).

Question 14

Explain why doing repeat measurements increases the likelihood of an accurate measurement

Answer 14

Repeating measurements reduces the effect of random error

Question 15

Describe how data with a systematic error would affect the appearance of a line of best fit on a graph

Answer 15

It would adjust the value of the y or x intercept as every data point has the same error

Question 16

Describe how data with a random error would affect the appearance of a line of best fit on a graph

Answer 16

It would increase the spread of data around the line of best fit - both above and below the line

Question 17

Describe how to calculate absolute uncertainty in a single reading

Answer 17

Resolution / 2

Question 18

Describe how to calculate the absolute uncertainty in a set of repeated data

Answer 18

First exclude anomalies
Then calculate range
Absolute uncertainty = range/2

Question 19

State the formula for calculating % uncertainty

Answer 19

percentage uncertainty = (absolute uncertainty / mean value) x 100 – if we have repeats
b. percentage uncertainty = (absolute uncertainty / measurement) x 100 – if we have a single measurement

Question 20

Explain the experimental choices we should make to increase the likelihood of us getting an accurate result

Answer 20

We should aim to reduce the % uncertainty in the measurements
b. To do this we could choose equipment with a high resolution. This will have a low absolute uncertainty, resulting in a low % uncertainty
c. Or, where possible, we should increase the measurement we are taking. For the same absolute uncertainty this will reduce the % uncertainty (as % uncertainty = 100 x absolute uncertainty/measurement)

Question 21

To determine the acceleration due to gravity, a student drops a ball from an upstairs window instead of a lower one. Explain why this is more likely to produce an accurate result.

Answer 21

The time taken for the ball to fall will increase
b. Reducing the % uncertainty in the measurement of time

Question 22

Show how to calculate the absolute uncertainty in a measurement when given its percentage uncertainty:

Answer 22

absolute uncertainty = (percentage uncertainty / 100) x mean value

Question 23

State the range of values a measured value can take when given its percentage uncertainty eg. if resistance = 4.0Ω +/- 2% what is the range of resistance?:

Answer 23

calculate the absolute uncertainty first: (2/100) x 4 = 0.08.
b. So resistance = 4.0+/- 0.08 Ω

Question 24

23. State the equation for % difference and explain what it can tell us about a measurement

Answer 24

a. % difference = 100 x (measured value – true value) / true value
b. This is a measure of the accuracy of the experiment as it is quantifying the difference between the true value and the measurement

Question 25

Describe examples of things that may have caused a result to be inaccurate

Answer 25

Parallax error introduces random error (if the viewer is looking at the scale from different angles each time) or systematic error (if the viewer is looking at the scale from a consistently wrong angle)
b. Zero error may have introduced systematic errror

Question 26

Describe what is meant by zero error and explain how to correct for it

Answer 26

Zero error is a systematic error that occurs when a measuring instrument does not display exactly zero when no object is being measured
b. To correct for it you should subtract or add the zero error

Question 27

Explain why a digital thermometer is a better choice of a device than an in glass thermometer to measure temperature

Answer 27

digital thermometer will have a higher resolution, leading to a measurement with a lower absolute uncertainty and therefore lower % uncertainty
b. A digital thermometer also avoids parallax error

Question 28

Describe 5 things to identify when criticising a table of results

Answer 28

All data in a column should be to the same number of decimal places as the resolution of an instrument
b. All data that has been calculated from raw data should be to the same number of significant figures as the raw data
c. Repeats should be evident
d. The range of the independent variable should be high
e. At least 6 sets of results should be taken (important note – this does not mean you should only take 6 sets of results in your required practicals/future experiments. 6 is a minimum, more will achieve a result that is more likely to be closer to the true value.)

Question 29

Answer 29

All values of current should be given to the same number of decimal places
b. All values of potential difference should be given to the same number of decimal places
c. All values of resistance should be given to the same number of significant figures as the raw data it was calculated from: ie. As the pd and current so all resistance values should have 2sf
d. There are only 4 sets of results – there should be at least 6
e. There is no evidence of repeats
f. The range of values of the current is too small
Key point: notice how the rules above have been applied to the table with specifics – I do not just say ‘all data in a column should be to the same dp’, I say specifically ‘all current values should be to the same dp’. I do not just say ‘there are not enough sets of results’, I say ‘there are only 4 sets of results – there should be at least 6’.

Question 30

. Define directly proportional and describe its graphical appearance

Answer 30

Two quantities are directly proportional if when one increases by a certain factor the other increases by the same factor
b. It will be a straight line through the origin

Question 31

Draw a graph illustrating the relationship between two quantities that are inversely proportional

Answer 31

Question 32

explain why we should always seek to plot a straight line grab in physics

Answer 32

it is only through converting equations into y = mx + c form and drawing straight line graphs that the validity of equations can be tested and constants determined
- an inverse proportion graphs looks very similar to (fro example) an inverse square graph - it is difficult to ‘spot’ the relationship when drawing curves

Question 33

A student wants to determine the value of the acceleration due to gravity. He measures the time taken for a ball to fall a distance s. He substitutes his measured values into the equation g = 2s/t^2. Another student changes the displacement through which the ball falls, s, and measures the time taken in each case. She plots a graph of t2 against s, draws a line of best fit and determines the gradient = 2/g. She calculates g as 2/gradient. Explain which result is likely to be more accurate.

Answer 33

The student who plots a graph is likely to get a more accurate result

o Because the line of best fit averages the results

o This reduces the effect of random error

Question 34

Describe, by rearranging the equation into y = mx + c form, what should be plotted on each axis to give a straight line graph for the following equations
a. EMF = V + Ir (changing I and measuring V)

b. s = ½ g t2 (changing s and measuring t)

c. T = 2π √(𝑙/𝑔) (changing l and measuring T)

d. E = hc / λ (changing λ and measuring E)

e. ρ = RA / l (changing l and measuring R)

Answer 34

V = - r I + EMF

y = m x + c

b. t2 = 2/g s

y = m x

c. T2 = 4 π2/g l

y = m x

d. E = hc x 1/ λ

y = m x

e. R = ρ/A l

y = m x

Question 35

31. Explain why a graph of R against l would produce a straight line graph through the origin

Answer 35

The equation linking R and l can be rearranged into the form:

o R = ρ/A l

§ y = m x

o Where the gradient is ρ/A . As both ρ and A are constants, the gradient is a constant and so the graph should be a straight line.

o The line should pass through the origin as the y-intercept (c) is zero.

Question 36

State the rules for finding the total uncertainty in a quantity calculated from the addition of 2 other quantities eg. what is absolute uncertainty in A = B + C when B and C have absolute uncertainties

of +/- 0.5mm each:

Answer 36

when combining quantities using addition, always add the absolute uncertainties.

o The absolute uncertainty in A would be 0.5 + 0.5 = 1.0mm

Question 37

34. Explain how to make a judgement about whether your result is accurate or not

Answer 37

EITHER:

i. If the % difference is less than the % uncertainty, the result is accurate.

ii. Ensure to compare actual values – stating the fact is not good enough. Eg. ‘% difference = 5% which is less than % uncertainty of 8% therefore result is accurate’.

b. OR

i. Absolute uncertainty should be determined from the % uncertainty and the value. Eg. if x = 10 m and % uncertainty is 10% then absolute uncertainty = 1 m. So the range of x is 9 m ≤ x ≤ 11 m (always include units!).

ii. After stating this, you would then compare the true value to the maximum/minimum result. Eg. if the true value of x was 12 m, then you would explicitly state, 12 m is greater than the maximum value for x, 11 m, so the result is inaccurate (note how the actual numbers have been compared).

c. OR

i. If (and only if) you do not know anything about the % uncertainty, compare the % difference to 5%

Question 37

5. Explain using a diagram how to use a micrometer scale to measure the size of an object

Answer 37

First read the main scale on the sleeve: identify how many whole millimeters there are and

if there are any 0.50mm present too.

o Then add the number shown on the thimble – where the horizontal line on the main scale intersects the thimble scale this is the number.

o So this reading would be 23mm + 0.15mm = 23.15mm

Question 38

6. Explain using a diagram, how to use a vernier scale to measure the size of an object

Answer 38

First identify the line on the main scale just left of the 0 on the Vernier scale

o In this case this is 1.1cm

o Then identify where the Vernier scale line aligns with the main scale line

o In this case it’s 6 on the Vernier scale

o Add this to the main scale reading: 1.16cm. Note it is NOT 1.7cm because the Vernier scale indicates the 1/10 mm division

Question 39

The jaws of a Vernier calliper are closed without an object present. This is the scale reading observed. What is the zero error?

Answer 39

Vernier scale is to the left of the 0 line so therefore this is a negative zero error. The Vernier

scale lines up with the main scale at 0.04cm so the zero error is -0.04cm. Any measurement taken with this instrument would be 0.04cm less than the true value. To correct this zero error we would have to add 0.04cm to the measured value.

o General rule: for negative zero errors, add the zero error to the measured value

o For positive zero errors, subtract the zero error from the measured value

Question 40

31. Explain why a graph of R against l would produce a straight line graph through the origi

Answer 40

o The equation linking R and l can be rearranged into the form:

o R = ρ/A l

§ y = m x

o Where the gradient is ρ/A . As both ρ and A are constants, the gradient is a constant and so the graph should be a straight line.

o The line should pass through the origin as the y-intercept (c) is zer

Question 41

. State the rules for finding the total uncertainty in a quantity calculated from the multiplication or division of 2 other quantities eg. what is percentage uncertainty in A = BC2/D4 when each B, C and D have % uncertainties of 5%?:

Answer 41

when combining uncertainties for quantities that are multiplied or divided, always add the percentage uncertainties.

o When a quantity is raised to a power, multiply by the number in the power.

o So in this case %U(A) = %U(B) + 2%U(C) + 4%U(D)

o = 5 + 2 x 5 + 4 x 5 = 35%