Transcript 1.3 Measurement of Length
Discover PHYSICS for GCE ‘O’ Level Science
Unit 1: Measurement
1.1 What is Physics?
• • Physics is the study of Matter and Energy.
› › › › › › › This includes sub-topics like: General Physics Thermal Physics Light Waves Sound Electricity Magnetism
Figure 1.1 What is Physics - a pictorial overview
1.2 Physical Quantities and SI units
• • • In this section, you’ll be able to: understand that all physical quantities consist of a numerical magnitude and a unit recall the seven base quantities and their units use prefixes and symbols to indicate very big or very small SI quantities
1.2 Physical Quantities and SI units What is a Physical Quantity?
A physical quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit.
1.2 Physical Quantities and SI units
The 7 base quantities and 7 base SI units are shown in the table below.
Table 1.1 The seven base quantities and their SI units
1.2 Physical Quantities and SI units
All other physical quantities can be derived from these seven base quantities. These are called derived quantities.
Table 1.2 Some common derived quantities and units
1.2 Physical Quantities and SI units
Some common SI prefixes are listed in the table below.
Table 1.3 Common SI prefixes
1.2 Physical Quantities and SI units Worked Example 1.1
Donovan Bailey broke the 100 m sprint world record at the 1996 Atlanta Olympics, with a time of 9.84 s. In contrast, a dog runs at a speed of 30 km h up with him?
–1 . If the dog chases Donovan Bailey, will the dog catch
1.2 Physical Quantities and SI units Solution
First, we calculate the average speed of Donovan Bailey.
Average speed = distance time = 100 9.84
m s = 10.2
m s 1
1.2 Physical Quantities and SI units Solution (Continued)
In order to make meaningful comparisons of speed, the units must be the same. So Bailey’s speed should be converted to km h –1 .
10.2
m s 1 = 10.2
1 m s 1 = 10.2
1 1 m s 1 km 1000 m 1 60 s min = 36.7
km h 1 60 1 min h Since Bailey’s speed of 36.7 km h – 1 > 30 km h – outrun the dog over a distance of 100 m.
1 , Bailey will
1.2 Physical Quantities and SI units
• • •
Key Ideas
A physical quantity has a numerical magnitude and a unit.
The are seven base quantities: length, mass, time, electric current, temperature, luminous intensity and amount of substance.
The units of these seven base quantities are known as the SI base units: m, kg, s, A, K, cd, mole
1.2 Physical Quantities and SI units Test Yourself 1.2
1. Express the weight of a ‘Quarter Pounder’ in grams, given that 2.205 pounds (lb) is equal to 1 kilogram (kg).
Figure 1.5 Quarter Pounder 2. The world’s smallest playable guitar is 13 Express the length in standard form.
m long. Figure 1.6 Nanoguitar
1.2 Physical Quantities and SI units Solutions 1.
1 4 lb = 1 4 lb 1 kg 2.205
lb 1000 1 kg g = 113.3
g 2. 13 m = 13 10 = 1.3 -6 m 10 -7 m (in standard form)
1.3 Measurement of Length
• • • In this section, you will be able to: Have a good sense of the orders of magnitude Describe how to measure a variety of lengths using the appropriate instruments (e.g. metre rule, vernier calipers, micrometer) Use a vernier scale
1.3 Measurement of Length
The SI unit for length is the metre (m).
Figure 1.7 There is a wide range of lengths in the natural world.
1.3 Measurement of Length
• • • • • Some of the common instruments that we use to measure lengths are the: Metre rule Tape measure Calipers Vernier Calipers Micrometer screw gauge
1.3 Measurement of Length
Metre rules can measure lengths up to 1 m.
Figure 1.11 Using a metre rule to measure the depth of a pond Tape measures can measure lengths up to a few metres.
Figure 1.9 Tape measure Figure 1.10 Using a tape measure to measure the width of a pond
1.3 Measurement of Length Precision of an Instrument
The precision of an instrument is the smallest unit that the instrument can measure.
What is the precision of the metre rule? The smallest unit the metre rule can measure is 0.1 cm or 1 mm.
Hence, we say that the metre rule has a precision of 0.1 cm.
1.3 Measurement of Length Avoiding Reading Errors
When using the metre rule, position your eye directly above the markings to avoid parallax errors. By taking several readings and taking the average, you will minimise reading errors.
Figure 1.12(a) No parallax errors Figure 1.12(b) Inaccurate measurement due to parallax errors
1.3 Measurement of Length
Calipers – An instrument for measuring the diameters of cylinders or circular objects.
Figure 1.13(a) Inverting the jaws of the calipers to measure inner diameters
1.3 Measurement of Length
Figure 1.13(b) Calipers used to measure outer diameters.
1.3 Measurement of Length Vernier Calipers
A useful instrument to measure both internal and external diameters of objects. It consists of a main scale and a sliding vernier scale.
The vernier calipers has a precision of 0.01 cm.
1.3 Measurement of Length
Figure 1.14 Parts and uses of the vernier calipers
1.3 Measurement of Length Using the Vernier Calipers
Before using the vernier calipers, it is important to check the instrument for zero error.
This is to check that the zero mark on the main scale coincides with the zero mark on the vernier scale when not measuring anything between the jaws.
Table 1.4 of the textbook shows how to deal with zero errors.
1.3 Measurement of Length Guide to Using Vernier Calipers
Figure 1.15 Using the vernier calipers to measure the diameter of a ball bearing.
1.3 Measurement of Length
Table 1.4 Checking and correcting zero errors when using vernier calipers
1.3 Measurement of Length Micrometer Screw Gauge
This instrument can measure to a precision of 0.01 mm. It is used to measure the diameters of wires or ball bearings.
1.3 Measurement of Length
Figure 1.16 Step by step guide to using the micrometer screw gauge
1.3 Measurement of Length
Table 1.5 Checking and correcting zero errors when using the micrometer screw gauge
1.3 Measurement of Length Key Ideas
1. Instruments with their range and precision.
1.3 Measurement of Length
2. Errors to take note for each instrument
1.3 Measurement of Length Test Yourself 1.3
1. Figure 1.17 shows a voltmeter with a strip of mirror mounted under the needle and near the scale. Suggest how this may help to reduce errors when taking a reading.
Figure 1.17 Voltmeter scale with mirror mounted under the needle Answer: When taking a reading, ensure that your vision is placed directly above the needle so that the image of the needle coincides with the needle. This helps to reduce parallax error.
1.3 Measurement of Length
2. Vernier calipers are used to measure the diameter of a ball bearing. What is the reading of the vernier scale?
Answer:
Step 1: Main scale reading: 2.5 cm Step 2: Vernier coincides with 3 rd line. Vernier reading is 0.03 cm.
Step 3: Reading of diameter = 2.5 + 0.03 cm = 2.53 cm
1.3 Measurement of Length
3. The diameter of a wire is measured using a micrometer screw gauge. A student takes an initial zero reading and then a reading of the diameter. What is the corrected diameter of the wire in mm?
A 3.37 B 3.85 C 3.89 D 3.87
Answer:
The zero reading Z = +0.02 mm The diameter reading D = 3.87 mm Hence the corrected diameter reading: D corrected = D – Z = 3.87 – (+0.02) = 3.85 mm Therefore the answer is B.
1.4 Measurement of Time
• In this section, you’ll be able to: Describe how to measure periods of time using the pendulum, stopwatch and other appropriate instruments.
1.4 Measurement of Time Using a Pendulum to Measure Time
• • A simple pendulum consists of a bob attached to a string.
A complete to-and-fro motion from R to S and back to R is one complete oscillation.
The period T is the time taken for one complete revolution.
Figure 1.22 A pendulum completes one full oscillation when the bob moves from R to S and back to R.
1.4 Measurement of Time
• •
Instruments for Telling Time
All instruments use some kind of periodic motion to tell time e.g. mechanical watches or clocks use the oscillations of springs, quartz watches use the natural vibrations of crystals. Stopwatches can measure time to a precision of 0.1 s. Digital stopwatches can show readings to two decimal places of a second. However, human reaction time introduces an error of about 0.3–0.5 s.
1.4 Measurement of Time Experiment 1.1
Objective: To calibrate a simple pendulum to measure time in seconds.
Apparatus: pendulum, stopwatch, metre rule, retort stand and clamp
1.4 Measurement of Time Procedure:
1. Fasten the metre rule vertically.
2. Tie the pendulum to the clamp and measure the length of the string,
l
in metres.
3. Measure the time taken t for the pendulum to make 20 oscillations.
4. Vary the length
l
between 60 cm and 100 cm.
Figure 1.24
1.4 Measurement of Time
Complete the table below.
Plot a graph of period T/s against
l
/m and find the length of pendulum with a period of one second.
Plot also a graph of T 2 /s 2 against length
l
/m.
1.4 Measurement of Time Results:
Figure 1.25(a) Graph of T/s vs.
l
/m Figure 1.25(b) Graph of T 2 /s 2 vs.
l
/m The length of pendulum with a period of 1 second can be read off the graph.
1.4 Measurement of Time
Question 1: Why do we need to take the average time of 20 oscillations?
Answer: We take the average to account for human reaction time. Human reaction time is about 0.3 s for most people. It would not be accurate to stop a stopwatch to measure the time taken for just one oscillation.
1.4 Measurement of Time
Question 2: What can you observe about the graph of T/s vs.
l
/m?
Answer: The period of the pendulum, T, increases with length
l
, but not linearly.
1.4 Measurement of Time
Question 3: What does the plot of T 2 /s 2 vs.
l
/m tell us?
Answer: It tells us that the square of the period, T 2 is directly proportional to the length,
l
. This gives rise to the straight line graph when we plot T 2 /s 2 against
l
/m. By extending the straight line graph, we can easily predict the period of the pendulum for lengths that are not included in the graph we have plotted.
1.4 Measurement of Time
• • • •
Key Ideas
Time intervals are measured by observing events that repeat themselves.
Clocks can be used to measure time intervals in minutes or hours.
Stopwatches can be used to measure time intervals to a precision of 0.1 s.
The period T is the time taken for the pendulum to swing from one end to the other and back again to its starting position.
1.4 Measurement of Time Test Yourself 1.4
1. How can you measure the average time taken by a bus to travel from home to school?
Answer: At the beginning of the week e.g. Monday,record the time on your watch when you board the bus. Record the time when you alight the bus. The difference between the two times is the time taken for the journey. Repeat steps 2-3 over the course of the week until Friday. Take the average of the time taken during the journey over the 5 days.
1.4 Measurement of Time
2. How can you determine the period of the swing in the playground?
Answer: Start the swing in its to-and-fro motion.
When the motion is steady, start the stopwatch when the swing is at one end of its motion. Stop the stopwatch after 20 oscillations. Record the time t 1 .
Repeat steps 2-3 for another set of reading t 2 .
Take average t = (t 1 + t 2 2 ) The period T is given by T =
t
20
1.4 Measurement of Time
3. Figure 1.26 shows an oscillating pendulum. If the time taken for the pendulum to swing from A to C to B is 3 s, what is the period of the pendulum?
Answer:
Moving from A to C to B only covers three-quarters of the oscillation. Hence, 3 4
T
= 3 s
T
= 3 4 3 = 4 s
Figure 1.26