6.8 Evaluating Experiments

• The accuracy of an experiment can be increased by repeating measurements and using mean values
• Methods seeking to reduce systematic errors result in increased accuracy
• Sometimes, additional apparatus can be used to improve the experiment, by reducing errors
• Some changes to the method could be:
  • Timing over multiple oscillations
  • Using a fiducial marker

Example: Oscillations

• The time period of oscillations is commonly measured using a stopwatch
  
  • Reaction time is a common error when measuring time
• Uncertainty in a measurement of periodic time can therefore be reduced by:
  • Measuring many oscillations to calculate the average time for one oscillation
  • Increasing the total time measured for multiple swings

• It would be ideal to measure the time taken for the pendulum to complete 10 (or more) oscillations and divide this time by 10 to determine the time period of one oscillation

One complete oscillation of a pendulum

• The student should make sure the amplitude of the oscillations is large so the time period is longer
  • This would reduce the effect of the human reaction time which causes a slight error when using a stopwatch
• The student should measure the time period over 10 oscillations and divide the time by 10 for the time period of one oscillation
  • However, due to damping effects, the amplitude of all the oscillations, and therefore their time periods, will not be the same
  • This effect is reduced if there is a large amplitude for the first oscillations
• The spring must not exceed its elastic limit at any point of the experiment
  • If the spring is stretched too much, it will not go back to its original un-stretched position therefore affecting the oscillations
• The student must make sure the oscillations are all completing vertical
  • This effect will the time period if the mass is pulled down at a slight angle, or pushed one way or another during the experiment

• A set square is a right-angled triangle plane used for drawing lines and determining whether two pieces of apparatus are perpendicular to teach other
• In physics, it is used to determine whether:
  • An object is vertical
  • Two objects are at right angles to each other
  • Two lines are parallel
• A plumb line can also be used to determine if a setup is vertically aligned accurately

A plumb line and set square used to make sure the setup is completely vertical

• Another example is using a set square to determine whether a ruler is vertical to aid the measurement of the extension of a spring
  
  • The right-angle side of a set square is aligned with the ruler and the bottom of the spring
  • This ensures the spring and the ruler are parallel to each other (or in other words, a line joining them both is horizontal)
• If this set up is not correctly checked with a set square, the ruler could be at an angle, thus providing an inaccurate reading of the extension, which can often be very small

Diameter of a Cylinder

• Two set squares can be used to measure the diameter of a cylinder
  • Since a cylinder has a circular cross-section, this is the diameter of its cross-section
• If a ruler is placed directly next to the ends of the cylinder, it is subjective to measure the start and end of the line joining the diameter by eye
• Two set squares are placed on either side of the cylinder
  • These ensure that the ruler and the edges of the cylinder are perpendicular to each other to read the most accurate result

Additional Apparatus

• A fiducial marker is a useful tool to act as a clear reference point, such as when measuring the time period of a pendulum using a stopwatch
• This improves the accuracy of a measurement of periodic time by:
  • Making timings by sighting the pendulum as it passes the fiducial marker
  • Sighting the pendulum as it passes the fiducial marker at its highest speed. The pendulum swings fastest at its lowest point and slowest at the top of each swing

A fiducial marker is used to mark the centre of the oscillation of the pendulum