Learning outcomes
- Measure spring extension accurately.
- Investigate force–extension relationships.
- Time oscillations with reduced reaction-time uncertainty.
- Identify a complete oscillation.
- Control amplitude and reference position.
14.1 Spring extension
Measure original length with no added load, then measure new length for each load. Extension is the difference, not the total length. Use a fixed ruler close and parallel to the spring with a thin pointer.
Add masses gently and wait for oscillations to stop. Stay within the elastic limit. Increase and, if time allows, decrease the load to look for failure to return to the original length.
14.2 Force and load
Convert mass to weight when the graph requires force, using W = mg and the value of g stated or assumed by the question. Include the mass of the hanger if it contributes to the load.
A straight force–extension graph through the origin supports proportionality in the elastic region. The gradient depends on which variable is plotted on which axis.
14.3 Timing oscillations
One complete oscillation returns to the starting position moving in the same direction. Time 10 or 20 oscillations from a central fiducial marker, where the bob moves fastest and the crossing is easiest to define.
Start and stop on the same directional crossing. Divide total time by the number of oscillations. Repeat and average.
14.4 Pendulum controls
Measure length from pivot to centre of the bob. Keep the release angle small and constant, use the same bob and avoid pushing it. The swing should remain in one vertical plane.
A long pendulum gives a longer period and lower percentage timing uncertainty, but the length must fit safely in the available space.
14.5 Motion measurements
For rolling or falling objects, define start and finish lines. Measure distance between the same reference points and use a release mechanism rather than pushing.
Short intervals are difficult to time manually. Increase the travel distance, repeat, or use light gates if provided. Ensure the slope and surface are controlled.
Worked examples
Extension
Original length 12.4 cm; loaded length 18.9 cm. Extension = 6.5 cm.
Period
Time for 20 oscillations = 31.6 s. Period T = 31.6/20 = 1.58 s.
Practical focus
Investigation or training activity
Investigate force against extension for a spring, then use a pendulum to compare timing one oscillation with timing 20. Calculate the percentage effect of a 0.2 s reaction-time uncertainty in both cases.
Examination guidance
- Extension is loaded length minus original length.
- Include the hanger in the load if appropriate.
- Time many oscillations.
- Measure pendulum length to the centre of the bob.
- Release without pushing and use a small amplitude.
Check your understanding
- What is spring extension?
- How is one complete oscillation defined?
- Why time at the central marker?
- How is pendulum length measured?
Answers
- Loaded length minus original length.
- Return to the starting state with the same direction of motion.
- The crossing is sharp and the bob moves fastest.
- From pivot to the centre of the bob.
