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physics Advanced Subsidiary (AS) Level Physics.
 
Solved problems for the chapter:
 

Errors

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Detailed solution steps are available at:
 
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Example 1.

Which experimental technique reduces the systematic error of the quantity being investigated?


  • adjusting an ammeter to remove its zero error before measuring a current

  • measuring several internodal distances on a standing wave to find the mean internodal distance

  • measuring the diameter of a wire repeatedly and calculating the average

  • timing a large number of oscillations to find a period

    
Example 2.

A fixed quantity is measured many times in an experiment that has experimental uncertainty. A graph is plotted to show the number of times that a particular value is obtained. Which graph could be obtained if the measurement of has a large systematic error but a small random error?


    
3.

A steel rule can be read to the nearest millimetre. It is used to measure the length of a bar whose true length is . Repeated measurements give the following readings.


length / mm
892, 891, 892, 891, 891, 892

Are the readings accurate and precise to within ?


 
results are accurate
to within 1 mm
results are precise
to within 1 mm
 
A
no
no
 
B
no
yes
 
C
yes
no
 
D
yes
yes
 
    
4.

A student uses a micrometer screw gauge to measure the diameter of a wire. He fails to notice that the reading is not zero with the gauge fully closed.


  • State and explain whether the omission introduces a random error or a systematic error into the readings of the diameter.


  • Explain why the readings are precise but not accurate.

    
5.

  • For each of the following, tick [✓] one box to indicate whether the experimental technique would reduce random error, systematic error or neither. The first row has been completed as an example.


     random errorsystematic errorneither
    keeping your eye

    in line with the

    scale and the

    liquid level for a

    single reading of

    a thermometer    		 ✓ 
    averaging many

    readings of the

    time taken for a

    ball to roll down a

    slope    		   
    using a linear

    scale on an

    ammeter    		   
    correcting for

    a non-zero

    reading when a

    micrometer screw

    gauge is closed    		   

  • The measurement of a particular time interval is repeated many times. The readings are found to vary. The results are shown in the figure below.


    Fig 17



    The true value of the time interval is .


    • State how the readings on Fig. 17 show the presence of


      • a systematic error,

      • a random error.


    • State the expected changes to Fig. 17 for experimental measurements that are

      • more accurate,

      • more precise.

    
6.

A well has a depth of from ground level to the surface of the water in the well, as shown in the figure.


not scale



A student wishes to find the depth of the well. The student plans to drop a stone down the well and record the time taken from releasing the stone to hearing the splash made by the stone as it enters the water.


  • Assume that air resistance is negligible and that the stone is released from rest. Calculate the time taken for the stone to fall from ground level to the surface of the water.


  • The time recorded by the student using a stop-watch is not equal to the time in (a). Suggest three possible reasons, other than the effect of air resistance, for this difference.


  • The student repeats the experiment three times and uses the results to calculate the depth of the well. The values are shown in the table.


     1st experiment2nd experiment3rd experiment 
    depth/m54.453.954.1 

    The true depth of the well is . Explain why these results may be described as precise but not accurate.


    
7.

A clock lags by 2.00 seconds per hour. Does the clock have a systematic or random error?

A time period of ten seconds is measured using the clock.

What will be the measurement uncertainty?

How much time do we actually measure?

    
8.

Determine which of the following measurements has a systematic error and which is random.


  • A length of 20 meters is measured using a meter scale, which is moved during the measurement.

  • The meter used to measure a length is 2 mm too short.

  • The balance used to measure a mass has an accuracy level of 1 %.

  • The kitchen scale shows accurate results only at room temperature . It is used to weigh a mass at an outdoor temperature of .

  • We measure time with a lagging clock.

    

9.

How many significant figures does each of the data below have?








    
10.

Calculate the value of each of the expressions below and give the result in a standard form.








    
11.

Jack and Ella measure the length of a pole. Jack measures 4.6 m and Ella 4.60 m. Determine whether the statement is correct:

  • Both measured the same length.

  • The results of both measurements represent the true length of the pole.

  • Both made the same measurement error.

  • There is not enough data to determine the absolute uncertainty of both measurements.

  • Percentage uncertainty of Jack's measurement is greater than that of Ella's measurement.