2.1.5 Absolute and Percentage Uncertainties

Question 1

Define absolute uncertainty.

Answer 1

Shows how large the uncertainty actually is: and has the same units as the quantity being measured. When dealing with singular measurements, it is usually given as the resolution of the equipment used.

Question 2

Define percentage uncertainty.

Answer 2

(Absolute unc / measured value) x100

Question 3

Why may measurements change? Produce two suggestions.

Answer 3

1. Lack of sensitivity in the instrument we use and

2. Skill level of the person conducting the experiment;

Question 4

Why is it hard to take uncertainty into account when measuring with stopwatches? How do scientists overcome this?

Answer 4

1. Human reaction times

2. We take the human reaction time of 0.5s to be the absolute uncertainty.

Question 5

Three measurements : 78+/-1cm, 43+/-1cm and 57+/-1cm. How would one add and subtract these values? What would the total percentage uncertainty be?

Answer 5

1. One would add the integers and the uncertainties as separate values.
2. One would subtract the integers and add the uncertainties to achieve a total uncertainty value.
3. 4/45 x 100 = 9%

Question 6

How would one calculate percentage uncertainty? What is special about this value?

Answer 6

1. uncertainty (total resolution of equipment) / measured value x100;
2. It must be left correct to 1sf.

Question 7

What is the process of calculating percentage uncertainty from a table?

Answer 7

1. Write down the repeat values in the table.
2. Find and record the mean of these readings.
3. Find the range of the repeat readings: highest value - the smallest value;
4. Halve the range to find the absolute uncertainty.
5. Find the percentage uncertainty by dividing the uncertainty value by the mean value and multiplying it by 100 to give percentage unc.
   STATE THIS VALUE TO 1SF

Question 8

How do you find absolute uncertainty of readings from a table?

Answer 8

The absolute uncertainty in the repeat readings is given by half the range of the values.

Question 9

For a compound quantity of the form y=ab,

%uncertainty in y =?

Answer 9

%uncertainty in y =%uncertainty in a + % uncertainty in b

Question 10

For a compound quantity of the form y=a/b,

%uncertainty in y =?

Answer 10

%uncertainty in y =%uncertainty in a + % uncertainty in b

Question 11

For a compound quantity of the form a^2,

%uncertainty in y =?

Answer 11

%uncertainty in y = 2 x %uncertainty in a

Question 12

For a compound quantity of the form a^n,

%uncertainty in y =?

Answer 12

%uncertainty in y = n x %uncertainty in a

Question 13

What do you do to the uncertainty values in the Young modulus?

Answer 13

Add them: stress/strain = a/b - add values in a/b for uncertainty value.

Question 14

What do you do for the uncertainty values in volume?

Answer 14

Do 3x the % uncertainty in length - as v=a^3