A student measures the circumference of a circular pipe. He wraps a length of string around the pipe five times and marks it with ink, as shown in the photograph.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/252145/xpgqm9jjvgw1hxlpsxyb.png)
(a) The student unwraps the string and holds it against a ruler with a centimeter scale. The next photograph shows the first two ink marks on the string.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/252145/rope_length_txqkh1.png)
(i) Estimate the circumference of the pipe, using the photograph of the string and the centimeter scale. Give your answer to two significant figures.
→ Because the student left marks for every wrap around the pipe, the distance between the two marks is approximately the circumference of the pipe.
→ 47.3 - 41.9 = 5.4 cm
(ii) The student finds that the total length of string for 5 turns is 25.6 cm. Calculate the average (mean) circumference of the pipe using this value.
→ 5 turns means 5 circumferences.
→ average circumference = 25.6 / 5 = 5.12 cm
(iii) The student measures the diameter of the pipe using a digital caliper.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/252145/gnaivtg5khcp70f5cuxz.png)
The caliper shows that the diameter is 15.10 mm. Calculate the circumference of the pipe using the formula circumference = diameter × π
→ circumference = 15.10 x π = 47.44 mm = 4.744 cm
(b) The student uses two methods to find the circumference
- averaging, using a measured length of string
- calculating, using the digital caliper reading
Explain why the two methods are likely to give different results.
Possible answers:
- The equation to calculate the circumference of the pipe is valid only for circles; the pipe may not be perfectly circular.
- The width of the pen mark may affect the readings.
- There may be parallax error when using the ruler; the readings may be different when viewed from different angles.
- The caliper may not be properly calibrated and give results with errors.
- Caliper and ruler have different precision.
- The caliper may not have been placed at right angles.
- The thickness of the string will make the diameter bigger.
- The string may have stretched during the experiment.