Sources of Uncertainty or Limitations

At first, I’ll explain how to calculate percentage uncertainty. Following this calculations, I will give you some examples and talk about possible errors and uncertainties.

A) How to calculate percentage uncertainty:

E.g. A thermometer can measure up to the nearest degree ºC. Your measurement reads  ΔT=23ºC

The uncertainty must then be ±0.5ºC. You will multiply this by two. Remember that the measurement is taken twice so the uncertainty doubles.

Therefore you have :

1)   (0.5 x 2)  / ΔT 

2)    1 / ΔT 

3)    0.04347(8)…. x 100 = ±, 4.35% percentage uncertainty – Overall uncertainty of 4.35% x 2.

More examples here:

B) Examples of experiments.

1) Apparatus: Two weights hanging from a pulley. You have to measure height and time.

This is how it would look
This is how it would look

Limitations and Uncertainties

  1. Friction – state the sources of friction (between weights and the air; between the pulley and the holder)
  2. Height can’t be measured precisely/ Difficult to measure hight due to motion.
  3. Stopping the timer at the exact instant a mass touches the ground is impossibru.
  4. Less than five(5) measurements is not enough.


  1. Lube the pulley (real good yeah) – Do not write ‘real good yeah’
  2. Clamp a metre stick with smaller divisions next to the apparatus.
  3. Either use a laser portal timer or a camera timer
  4. Take more measurements and calculate more values of whatever they wanted you to calculate the first time. I guess K or smth. like that. / or / Take more measurements and plot a graph.

(if you miss anything after that ‘and‘ you won’t get the points lol).


2) Apparatus – An apparatus where you can test for turning forces (e.g. a  stick bored at the middle hanging from a metal stand).  See paper 9702/35/O/N/10 Exp 2.

Limitations and Uncertainties

  1. Difficult to balance because , be prepared, there’s a fan in the room. There’s a window open or It is very unstable.
  2. Difficult to judge when the stick is parallel to the ground/table (in equilibrium).
  3. Mass value might be inaccurate.
  4. They’ll make you take 1-2 measurements. Obviously not enough. ( I won;t mention this one any more from now on cos you’ll remember it).


  1. Drill hole higher up in the stick , and :)) don’t forget to move the fans away from the lab.
  2. Use a clamped metre rule to ensure equivalent distances between both ends of the stick to the ground.
  3. Use a balance to weight the masses.
  4. Take more measurements and calculate more values of whatever they wanted you to calculate the first time. I guess K or smth. like that. / or / Take more measurements and plot a graph.


3. Apparatus: A rubber band, attached to a holder on a metal stand, to which a mass hanger is added. You are to check for how much time it takes for the weights to return to their original Direction A, as you turn the weights so that they point towards direction B (Just like turning a swing).

See paper 9702/34/M/J/11

Limitations and Uncertainties 

  1. Difficult to judge the end of an oscillation
  2. Masses may not be accurate
  3. Diameter of mass hanger not accurate


  1. Use a video timer, and draw a line on the mass with a marker
  2. Use a balance to measure the masses accurately
  3. Use a screw gauge to measure the diameter


4. Apparatus: A metal strip hanged parallel to the ground from a stand. You attach the spring to the metal strip in a way that that a part of the string is above the strip. You are to investigate how the motion of the spring depends on its length.


Limitations and Uncertainties

  1. Difficult to measure the diameter D, because of the rings which get in the way.
  2. The Volume calculated is not accurate because D is not the inner diameter.
  3. Times are too small, and cannot obtain an accurate value
  4. Difficult to judge a complete oscillation, and the spring might move to the sides
  5. Metal strip bends
  6. Don’t forget that two measurements aren’t enough 🙂


  1. Use a micrometer to measure D
  2. Measure thickness using micrometer
  3. Use bigger mass, and laser/light portal/gate.
  4. Use camera timer, or sensor.
  5. Use stiffer strip.


5. Apparatus – A beaker, a bowl, a thermometer, and a ruler. You are to investigate how the cooling rate of a hot liquid depends on the surface area of the liquid exposed to air.

If you’d like to try this, it’s paper 9702/33/M/J/2012 ; the 2nd experiment.

Limitations and Uncertainties 

  1. Heat lost through the sides and the bottom.
  2. Temperature change is too small (ΔT)
  3. Large percentage % (perpenny haha) uncertainty in ΔT
  4. Difficult to measure the diameter of the bowl and beaker
  5. Water in bowl barely covers the bulb of thermometer


  1. Insulate the blow and beaker (polystyrene container)
  2. Wait a longer time ( e.g. 10 min instead of just two)
  3. Use an electronic thermometer
  4. Use a screw gauge or a better method
  5. Increase the volume of the water

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