Purpose:
- To introduce scientific measuring instruments.
- To practice measuring accurately with these instruments.
- To achieve mastery in reporting measurements to the correct number of significant digits based on the precision of the instruments.
Materials:
Measurement kit containing: Vernier caliper, micrometer, depth gauge, metric ruler, aluminum square, plastic vial, graduated cylinder, steel ball.
Measurement kit containing: Vernier caliper, micrometer, depth gauge, metric ruler, aluminum square, plastic vial, graduated cylinder, steel ball.
Procedure:
Inner and outer diameters (a.k.a. internal and external diameters)
Inner and outer diameters (a.k.a. internal and external diameters)
- Measure the outer diameter of the plastic graduated cylinder.
- Place the plastic graduated cylinder on the lab table. Hold the cylinder with one hand.
- Using the ruler, measure the distance across the top of the cylinder. Record the distance from the outer edge of one side to the outer edge of the opposite side.
- Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
- Measure the outer diameter with the caliper. Using the ridged lines on the lower part of the Vernier caliper, open up the caliper all the way. Place the caliper over the outside edges of the cylinder.
- Carefully slide the sliding scale of the caliper until the lower parallel sides of the caliper touch the cylinder. Observe where the last line on the moveable section of the caliper lies directly under another line. Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
- Place the plastic graduated cylinder on the lab table. Hold the cylinder with one hand.
- Measure the inner diameter of the plastic graduated cylinder.
- Place the graduated cylinder on the lab table. Hold it in one of your hands.
- Using the ruler, measure the distance across the top of the cylinder from the inner edge of one side to the inner edge of the opposite side.
- Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
- Measure the inner diameter of the cylinder with the caliper. Invert the caliper so the upper part of the caliper is inserted into the inside of the cylinder. Place your thumb on the ridged section. Slowly move the caliper until the parallel parts for the internal measurement are touching the sides of the cylinder.
- Carefully observe the inside bottom of the caliper to take your measurement in centimeters. Observe the last line of the bottom of the moveable part of the caliper to determine the internal measurement of the cylinder.
- Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
- Place the graduated cylinder on the lab table. Hold it in one of your hands.
- Calculating circumference and volume
- Determine the circumference of the cylinder based on the outer diameter obtained from the ruler in centimeters.
- Repeat the calculation using the diameter obtained from the caliper in centimeters. Record your answers in the correct number of significant figures.
- Determine the depth of the cylinder using the depth gauge accessory on the caliper. Record your answer in centimeters using the correct number of significant figures.
- Calculate the total volume of the cylinder in cubic centimeters using the measurements taken with the ruler and with the measurements taken with the caliper and depth gauge. Record your answer with the correct number of significant figures.
- Determine the circumference of the cylinder based on the outer diameter obtained from the ruler in centimeters.
- Measure the length, width and height.
- Obtain the aluminum square. Using the ruler, measure and record the length, width and height of the aluminum square. Record your answer in centimeters using the correct number of significant figures.
- Calculate and record the area of the face of the aluminum square. Calculate and record the volume of the aluminum square. Record all data using the correct number of significant figures.
- Measure and record the length, width and height measurements with the caliper. Calculate and record the area of the face of the aluminum square. Calculate and record the volume of the aluminum square. Record all data using the correct number of significant figures.
- Obtain the aluminum square. Using the ruler, measure and record the length, width and height of the aluminum square. Record your answer in centimeters using the correct number of significant figures.
- Obtain measurements with a micrometer.
- Remove the micrometer from the measurement kit.
Your micrometer is a precise instrument and should never be over tightened. Place the handle of the cylinder in one hand, and with the other hand, hold the rounded bottom. Turn the revolving barrel counterclockwise. Observe the units of measurement on the rounded shaft. Turn the moveable barrel counterclockwise or clockwise until the 0 line is perfectly horizontal to the horizontal line. Note that one turn of the barrel represents one millimeter.
- Carefully turn the micrometer in a counterclockwise direction until it is opened wider than the height of the aluminum square. Carefully slide the aluminum square into the micrometer. Turn the barrel clockwise until it is touches the aluminum square. Turn the knurled knob on the end of the micrometer one “click” to achieve the desired tightness for measurement – remember: do not over tighten. Record the height of the aluminum square with the correct number of significant figures.
- Calculate the area of the face and volume of the square using the caliper length and width measurements and the micrometer height measurement. Record the area and volume using the correct number of significant figures.
- Remove the micrometer from the measurement kit.
Graduated Cylinder
Dimension
Outer diameter
Inner diameter
Circumference
Depth
Volume
Outer diameter
Inner diameter
Circumference
Depth
Volume
Metric ruler
1.6 cm
16 mm
1.3 cm
13 mm
5.0 cm
10.5 cm
21 cm3
1.6 cm
16 mm
1.3 cm
13 mm
5.0 cm
10.5 cm
21 cm3
Caliper
1.50 cm
15.0 mm
1.30 cm
13.0 mm
4.7 cm
10.5 cm
18.6 cm3
1.50 cm
15.0 mm
1.30 cm
13.0 mm
4.7 cm
10.5 cm
18.6 cm3
Aluminum Square
Dimension
length
width
height
Area
Volume
length
width
height
Area
Volume
Metric ruler
2.2 cm
2.3 cm
0.9 cm
5.06 cm2
4.554 cm3
2.2 cm
2.3 cm
0.9 cm
5.06 cm2
4.554 cm3
Caliper
2.14 cm
2.345 cm
.92 cm
5.02 cm2
4.6 cm3
2.14 cm
2.345 cm
.92 cm
5.02 cm2
4.6 cm3
Micrometer
n/a
n/a
1.053 cm
5.02 cm2
5.28 cm3
n/a
n/a
1.053 cm
5.02 cm2
5.28 cm3
Analysis:
1. Compare and contrast accuracy and precision. Consider how one could improve the accuracy of a measurement? the precision of a measurement?
Both accuracy and precision relate to the exactness of a measurement, but they relate to different topics of exactness. Accuracy is concerned with one's ability to register the value of a measurement, whereas precision relates to how exact an instrument is in its measurements. For example if one were to read the measurement of a ruler, accuracy relates to whether he or she is able to read the markings correctly, and precision relates to how exact the measurements of the ruler are.
One can improve his or her accuracy of a measurement by reading it at eye level or by placing something—like a piece of paper—behind the instrument so he or she can distinguish the markings of the instrument more clearly. One can increase the precision of his or her measurements by using more precise instruments—such as using a caliper instead of a metric ruler.
2. Compare the number of significant figures in the calculations and measurements taken with the ruler to the measurements taken with the caliper and micrometer. Discuss the differences in precision of these instruments.
Each of the instruments used—the metric ruler, the caliper, and the micrometer—were different in their precision because of their relative uses. When using the ruler the maximum number of significant figures that could be attained was two because its uses are for less exact measurements. Because the measurements were restricted to two significant figures, the calculations using the ruler were also restricted to two significant figures. The caliper was more precise than the ruler because it could be used to calculate three significant figures. However, the micrometer was more precise than both the caliper and the ruler with its ability to take a measurement with four significant figures.
Between these instruments, the micrometer was the most precise, the caliper was the next precise, and the ruler was the least precise. This precision of these instruments is rooted in the size of an object they are each able to measure. The ruler, being able to measure much larger objects, loses its precision because if it included enough detail it would be difficult to read. The caliper is still able to measure slightly large objects, but not as large as the ruler, and it gains precision in its loss of the ability to measure size. The micrometer is very precise, but its precision comes from the size of things it can measure; since it measures such delicately small measurements, it is limited in the sizes it can measure.
3. Compare your measurements and calculations with those of a classmate. Are they the same? Discuss sources of error in the accuracy of the measurements.
Our measurements were slightly different with those of our classmate but only by a millimeter or other small value. They were not exactly the same because our measurements held a different accuracy from those of the classmate we compared with. In measuring the graduated cylinder, we may have read the readings on the ruler or caliper differently than our classmate; this could be an error on either of our parts. In measuring the aluminum square, we measured a different aluminum square than our classmate, so our differences in measurement were more due to the different object we measured than anything. However, if we had measured the same square, our measurements would have differed slightly anyway just because of the differences in our accuracy.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer is the most precise of the three instruments because of its ability to calculate the most significant figures of the three instruments. Like its name, the micrometer can measure an object to the nearest micrometer, whereas the caliper can only measure to the nearest tenth of a millimeter and the metric ruler to the nearest millimeter.
Both accuracy and precision relate to the exactness of a measurement, but they relate to different topics of exactness. Accuracy is concerned with one's ability to register the value of a measurement, whereas precision relates to how exact an instrument is in its measurements. For example if one were to read the measurement of a ruler, accuracy relates to whether he or she is able to read the markings correctly, and precision relates to how exact the measurements of the ruler are.
One can improve his or her accuracy of a measurement by reading it at eye level or by placing something—like a piece of paper—behind the instrument so he or she can distinguish the markings of the instrument more clearly. One can increase the precision of his or her measurements by using more precise instruments—such as using a caliper instead of a metric ruler.
2. Compare the number of significant figures in the calculations and measurements taken with the ruler to the measurements taken with the caliper and micrometer. Discuss the differences in precision of these instruments.
Each of the instruments used—the metric ruler, the caliper, and the micrometer—were different in their precision because of their relative uses. When using the ruler the maximum number of significant figures that could be attained was two because its uses are for less exact measurements. Because the measurements were restricted to two significant figures, the calculations using the ruler were also restricted to two significant figures. The caliper was more precise than the ruler because it could be used to calculate three significant figures. However, the micrometer was more precise than both the caliper and the ruler with its ability to take a measurement with four significant figures.
Between these instruments, the micrometer was the most precise, the caliper was the next precise, and the ruler was the least precise. This precision of these instruments is rooted in the size of an object they are each able to measure. The ruler, being able to measure much larger objects, loses its precision because if it included enough detail it would be difficult to read. The caliper is still able to measure slightly large objects, but not as large as the ruler, and it gains precision in its loss of the ability to measure size. The micrometer is very precise, but its precision comes from the size of things it can measure; since it measures such delicately small measurements, it is limited in the sizes it can measure.
3. Compare your measurements and calculations with those of a classmate. Are they the same? Discuss sources of error in the accuracy of the measurements.
Our measurements were slightly different with those of our classmate but only by a millimeter or other small value. They were not exactly the same because our measurements held a different accuracy from those of the classmate we compared with. In measuring the graduated cylinder, we may have read the readings on the ruler or caliper differently than our classmate; this could be an error on either of our parts. In measuring the aluminum square, we measured a different aluminum square than our classmate, so our differences in measurement were more due to the different object we measured than anything. However, if we had measured the same square, our measurements would have differed slightly anyway just because of the differences in our accuracy.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer is the most precise of the three instruments because of its ability to calculate the most significant figures of the three instruments. Like its name, the micrometer can measure an object to the nearest micrometer, whereas the caliper can only measure to the nearest tenth of a millimeter and the metric ruler to the nearest millimeter.
| measurements_in_physics_lab.doc |
