Physics 9702/22 — May/June 2010

Background Concept

A systematic error shifts all readings in the same direction by (approximately) the same amount. A common systematic error in length instruments is zero error: when the true length is zero, the instrument does not read zero.

For a micrometer screw gauge, zero error occurs if the thimble and sleeve zero marks do not align when the jaws are fully closed. If you do not check this, every diameter reading will be too large or too small by the same offset.

Understanding the Question

This part asks how the instrument from (a) (a micrometer) should be checked to avoid systematic error. The most relevant systematic issue is a micrometer’s zero error.

Approach

Before measuring the wire, test the instrument at a known true value (here, (0\ \text{mm}) when fully closed). If it does not read that value, record the offset and apply a correction to subsequent measurements.

Step-by-Step Reasoning

• Gently close the micrometer jaws so they just touch (use the ratchet to avoid over-tightening).
• Read the micrometer.
• If the reading is not (0.00\ \text{mm}), there is a zero error.
• Apply a correction to every measurement:
  • If the micrometer reads (+e) at zero, subtract (e) from all readings.
  • If it reads (-e) at zero, add (e) to all readings.

Key Takeaways

• Systematic errors are checked by calibration/zero checks.
• A micrometer’s main systematic issue is zero error; checking it avoids consistently biased results.

Common Mistakes

• Saying “take repeats” for systematic error (repeats reduce random error, not zero offset).
• Closing the jaws tightly by hand (can damage the instrument or compress the object, introducing further systematic bias).

Things to Be Careful About

• Use the ratchet to achieve a consistent gentle contact when checking zero.
• State both: (1) check for zero error and (2) correct for it if present, since the question asks about avoiding systematic error.

Background Concept

Random errors cause readings to vary unpredictably about a mean value (due to judgment, slight instrument variation, surface irregularities, etc.). Unlike systematic errors, random errors are reduced by taking many measurements and averaging.

For a wire, additional scatter can come from:

• Slight changes in diameter along its length.
• The wire not being perfectly circular (so the measured diameter depends on orientation).

Understanding the Question

You must describe how to use the micrometer so that random errors are reduced. Since it is worth 2 marks, you typically need two clear, creditworthy actions.

Approach

Use repetition and averaging, and ensure readings sample possible variations in the wire (different places and directions) so the mean is more reliable.

Step-by-Step Reasoning

1. Repeat measurements:

   • Measure the diameter multiple times rather than once.
   • This gives a set of values with some spread due to random effects.

2. Measure in different places/directions:

   • Take readings at several points along the wire.
   • Rotate the wire (e.g. by (90^\circ)) and measure again to account for any slight oval shape.

3. Average the readings:

   • Calculate the mean diameter:

$$\bar{d} = \frac{d_1 + d_2 + \cdots + d_n}{n}$$

Averaging reduces the effect of random fluctuations, giving a better estimate of the true diameter.

Key Takeaways

• Random errors are reduced by repeats and averaging.
• For real objects, measuring at multiple positions/orientations improves reliability.

Common Mistakes

• Describing a zero check (that targets systematic error, not random error).
• Taking only two readings (often too few to convincingly reduce random scatter).
• Writing “be careful” or “avoid parallax” without a concrete method (micrometer readings generally do not involve parallax in the same way as analogue pointer instruments).

Things to Be Careful About

• Random error reduction is about the method: multiple readings + mean.
• If you only measure at one point, you may get an unrepresentative value if the wire is slightly uneven.
• Keep the micrometer contact consistent (use the ratchet) so you do not introduce extra variability by changing the squeezing force.