EMPA style Q and A

Question 1

Now do you calculate the percentage uncertainty of a measured quantity?

Answer 1

Divide the uncertainty by the measured value and multiply by 100.

Question 2

How do you calculate the overall percentage uncertainty in the value for A/B if A = 1.3% and B = 2.6%?

Answer 2

The calculation uses one value of A and one of B so add these together to get 3.9%.

Question 3

How would you detect the presence of unreliable data from a graph?

Answer 3

It would be shown by a point (a reasonable distance) off the best fit line.

Question 4

Give a source of error when reading the length of a vertical object with a scale behind it (such as a volume of liquid or the length of a stretched spring). Suggest how to overcome this.

Answer 4

Parallax error when judging the level of liquid or stretch of spring against a ruler.
Must read at eye level. Add mirror behind the scale so that length/height hides its own reflection or look along a set square place in contact with vertical face of the ruler.

Question 5

Why can measured values of 0.023, 0.025 and 0.026 be given the mean value 0.0247?

Answer 5

The mean value can not be quoted to a greater precision than the least precise measurement. In this case 0.001 so the mean value is 0.025.

Question 6

How would it be possible to reduce the percentage uncertainty of a measured value?

Answer 6

Increase the quantity measured from the same measuring instrument.
Change the measuring instrument for one with less uncertainty.

Question 7

What does it mean to say a quantity can not be measured accurately?

Answer 7

Accuracy is determined by the amount of uncertainty in a measurement. The less the uncertainty the more accurate a measurement is. If the uncertainty is large, then the quantity can not be measured accurately.

Question 8

How would you determine the gradient of a curved line at a specified point?

Answer 8

Add a tangent to the curve at the point specified. Ensure the gradient of the straight lined tangent covers 8 semi-major squares on the y and x axes.

Question 9

State how you could read off your graph the point at which a spring has reached its elastic limit.

Answer 9

This is the point at which the gradient changes/decreases.

Question 10

Explain why recording more data points in an investigation is helpful.

Answer 10

More points plotted on the graph will reduce the impact of random error of the gradient and make it more reliable. You will also be able to identify and eliminate anomalous results.

Question 11

When measuring the extension of a spring, give one source of systematic error.

Answer 11

If the scale/ruler is not positioned at zero to mark the bottom of the U stretched spring then a zero error results. Each measurement of extension is out by exactly the same amount.

Question 12

You have measured 4 repeated values for the extension of a spring. They are 11mm, 13mm, 14mm and 12mm. Give the range and the uncertainty of your measurements.

Answer 12

Range = 11 - 14mm
Uncertainty is half the range = 3/2 = +- 1.5mm

Be careful to remove obvious anomalies.

Question 13

What does the gradient of a force extension graph for a stretched spring provide you with?

Answer 13

The spring constant.

Question 14

You have calculated from the gradient of your force extension graph that the spring constant of 4 springs, a pair in parallel with another pair is 20Nm^-1. Assuming all springs are the same when is the spring constant of one spring?

Answer 14

Each pair will have a spring constant of 10Nm^-1.
Each spring will have a spring constant of 20Nm^-1.
Add constants of springs in parallel, do the 1/k rule for those in series.

Question 15

How could you check for zero error on an instrument?

Answer 15

Digital or analogue measurer - switch on equipment with nothing connected to it. It should read zero.
Ruler - ensure zero measurement is positioned at the start of the length being measured. Remove parallax error to do this.

Question 16

How are random errors reduced in your measurements?

Answer 16

Repeat measurements a number of times for the same system. Calculate an average value after checking for any obvious anomalous readings. Ensure results contributing to the average value are consistent.

Question 17

You have recorded a measurement of a quantity using 2 different methods but the same measurement instrument. The first method gains larger values than the second. Which measurements have the smaller percentage uncertainty?

Answer 17

The first method. Larger measurements will have smaller percentage uncertainty assuming the measuring instrument is the same. The uncertainty is a smaller proportion of the overall measurement.

Question 18

When asked to comment on the reliability of the data you collected what would you reference when saying yes or no?

Answer 18

You could reference repeated readings all consistent.

Use your graph to comment on points relative to the best fit line. Close to or not close to?

Question 19

How does a zero error affect the gradient of a graph?

Answer 19

It doesn’t. All values will be the same value lower or higher and so gradient unaffected.

Question 20

How could a mean calculated value be more accurate?

Answer 20

Increase number of repeat readings.

Question 21

What does a curved line in a force extension graph show about a system?

Answer 21

The spring constant of that system is not constant at all loads applied. The system does not obey Hooke’s law with all loads applied.

Question 22

If using the expression X^2 (x squared) in a calculation and x has a percentage uncertainty of 1.6% what does x contribute to the overall % uncertainty?

Answer 22

2x 1.6 = 3.2%

Question 23

If a measuring instrument has a precision of 0.5mm and measured the extension of a spring at 34mm then what is the percentage uncertainty?

Answer 23

0. 5/34 x 100

1. 5%

Question 24

If the repeated readings of a measurement are equal then how do you determine the uncertainty?

Answer 24

Use the precision of the instrument as there is no range/spread so can’t do 1/2 spread of results.

Question 25

How would you tell if there was a zero error in the measurement of extension from a stretching of a spring experiment?

Answer 25

The straight line of a force extension graph would not go through the origin. It would intercept the x axis at a value greater or less than zero (this would be the value of zero error). The gradient would be unaffected. Same spring constant but not a directly proportional relationship between force and extension.

Question 26

How could you ensure there is no error when measuring the distance of one ruler under another connecting a system of springs in parallel.

Answer 26

Measure the vertical distance mid way between springs in parallel.
Use a spirit level to ensure each rule is perfectly horizontal.
Ensure there is no parallax error by measuring scale showing distance at eye level.
Use of set square from ruler to bench behind.

Question 27

If asked to discuss the validity of a predicted or estimated value, what would you do?

Answer 27

Compare it with the actual measured value given.
If different, suggest why. An unexplained systematic error, something not taken into account when finding the actual value measured.
Random error only given if uncertainty bigger than the difference between the predicted and actual measurements.

Question 28

What is a systematic error?

Answer 28

Errors which show a pattern or a bias.

An error which has the same value in all readings.

Question 29

How do you find the gradient of your straight line on the graph?

Answer 29

The change in y divided by the change in x.
Each change must be at least 8 semi-major squares.
Remember to add an appropriate unit if there is one!