Measurements in Physics
Laboratory Exploration
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.
Procedure:
Inner and outer diameters (a.k.a. internal and external diameters)
1. Measure the outer diameter of the plastic graduated cylinder.
1.1 Place the plastic graduated cylinder on the lab table. Hold the cylinder with one hand.
1.2 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.
1.3 Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
1.4 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.
1.5 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.
2. Measure the inner diameter of the plastic graduated cylinder.
2.1 Place the graduated cylinder on the lab table. Hold it in one of your hands.
2.2 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.
2.3 Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
2.4 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.
2.5 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.
2.6 Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
3. Calculating circumference and volume
3.1 Determine the circumference of the cylinder based on the outer diameter obtained from the ruler in centimeters.
3.2 Repeat the calculation using the diameter obtained from the caliper in centimeters. Record your answers in the correct number of significant figures.
3.3 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.
3.4 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.
Length, Width, Area and Volume
4. Measure the length, width and height.
4.1 length
width
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. 4.2 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.
4.3 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.
5. Obtain measurements with a micrometer.
5.1 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.
5.2 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.
5.3 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.
Challenge (optional, as time allows):
6. Measure and record the volume of pulp required to manufacture a sheet of notebook paper. Record your measurements and calculations using the correct number of significant figures.
Analysis:
1. Compare and contrast accuracy and precision. Consider how one could improve the accuracy of a measurement? the precision of a measurement? Accuracy is how close the calculated value was to the true value. Precision is how close all of the calculated values are to each other. To improve the accuracy of a measurement, one would need to measure more carefully. If one's values are all precise but not accurate, chances are all of the instruments are being used wrong, on the wrong tool or on the wrong part of the tool. To improve the precision of all of the calculations, one would need to make sure that all of the values are being calculated at the same part of the object. Since precision is all based on calculated values, one could have perfect precision but not good accuracy. Both accuracy and precision are imperitive parts of calculating values for an experiment.
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. The number of significant figures when a value was calculated with a ruler were the same as when calculated with the caliper. The micrometer was the only tool that gave an answer past the tenths place of the decimal. Most answers had two significant figures. The precision of the ruler and the caliper was high. The micrometer also had high precision with the other tools but it was not as precise as the ruler and caliper. Although not exactly the same, all of the tools were very precise.
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. When compared to the calculations of another group (Jackie and Emily), our (Tamara, Elise, Katie) calculations seemed to have less significant figures. This could have been for many reasons. For one, our group could have measured and then rounded instead of guess to one more decimal number. This seemed like the case in many of the first measurements, especially in the caliper. Other than that, the graduated cylineder measurements were fairly precise. In the aluminum square, the measurements became less and less precise. Even with significant figures aside, the measurements were off anywhere from .1 to .3 off, or more. With such a difference, the aluminum squares may have been a different size, slightly off. If the squares were exactly the same than it was most likely human error on one of our parts.
4. Which instrument is more precise, the metric ruler, micrometer or caliper? The caliper and the metric ruler seemed to be more precise when our group calculated the values by ourselves. Those values were almost always the same. The micrometer seemed to be more accurate only because we aquired values with more significant figures. In the end, though, all tools gave us close enough values that they could all be considered precise.
Table:
Graduated Cylinder:
Dimension Metric Ruler Caliper
Outer Diameter 1.5 cm 1.5 cm
15 mm 15 mm
Inner Diameter 1.3 cm 1.3 cm
13 mm 13 mm
Circumference 4.7 cm 4.7 cm
Depth 10.4
Volume 18.4 cm 18.4 cm
Aluminum Square:
Dimension Metric Ruler Caliper Micrometer
Length 2.4 cm 2.4 cm 2.4 cm
Width 2.4 cm 2.4 cm 2.4 cm
Height 0.4 cm 0.4 cm 0.45 cm
Area 5.8 cm^2 5.8 cm^2 5.8 cm^2
Volume 2.3 cm^3 2.3 cm^3 2.6 cm^3
Laboratory Exploration
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.
Procedure:
Inner and outer diameters (a.k.a. internal and external diameters)
1. Measure the outer diameter of the plastic graduated cylinder.
1.1 Place the plastic graduated cylinder on the lab table. Hold the cylinder with one hand.
1.2 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.
1.3 Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
1.4 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.
1.5 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.
2. Measure the inner diameter of the plastic graduated cylinder.
2.1 Place the graduated cylinder on the lab table. Hold it in one of your hands.
2.2 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.
2.3 Record your measurement correctly in centimeters. Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
2.4 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.
2.5 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.
2.6 Convert your centimeters into millimeters. Remember to record the correct number of significant figures.
3. Calculating circumference and volume
3.1 Determine the circumference of the cylinder based on the outer diameter obtained from the ruler in centimeters.
3.2 Repeat the calculation using the diameter obtained from the caliper in centimeters. Record your answers in the correct number of significant figures.
3.3 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.
3.4 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.
Length, Width, Area and Volume
4. Measure the length, width and height.
4.1 length
width
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. 4.2 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.
4.3 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.
5. Obtain measurements with a micrometer.
5.1 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.
5.2 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.
5.3 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.
Challenge (optional, as time allows):
6. Measure and record the volume of pulp required to manufacture a sheet of notebook paper. Record your measurements and calculations using the correct number of significant figures.
Analysis:
1. Compare and contrast accuracy and precision. Consider how one could improve the accuracy of a measurement? the precision of a measurement? Accuracy is how close the calculated value was to the true value. Precision is how close all of the calculated values are to each other. To improve the accuracy of a measurement, one would need to measure more carefully. If one's values are all precise but not accurate, chances are all of the instruments are being used wrong, on the wrong tool or on the wrong part of the tool. To improve the precision of all of the calculations, one would need to make sure that all of the values are being calculated at the same part of the object. Since precision is all based on calculated values, one could have perfect precision but not good accuracy. Both accuracy and precision are imperitive parts of calculating values for an experiment.
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. The number of significant figures when a value was calculated with a ruler were the same as when calculated with the caliper. The micrometer was the only tool that gave an answer past the tenths place of the decimal. Most answers had two significant figures. The precision of the ruler and the caliper was high. The micrometer also had high precision with the other tools but it was not as precise as the ruler and caliper. Although not exactly the same, all of the tools were very precise.
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. When compared to the calculations of another group (Jackie and Emily), our (Tamara, Elise, Katie) calculations seemed to have less significant figures. This could have been for many reasons. For one, our group could have measured and then rounded instead of guess to one more decimal number. This seemed like the case in many of the first measurements, especially in the caliper. Other than that, the graduated cylineder measurements were fairly precise. In the aluminum square, the measurements became less and less precise. Even with significant figures aside, the measurements were off anywhere from .1 to .3 off, or more. With such a difference, the aluminum squares may have been a different size, slightly off. If the squares were exactly the same than it was most likely human error on one of our parts.
4. Which instrument is more precise, the metric ruler, micrometer or caliper? The caliper and the metric ruler seemed to be more precise when our group calculated the values by ourselves. Those values were almost always the same. The micrometer seemed to be more accurate only because we aquired values with more significant figures. In the end, though, all tools gave us close enough values that they could all be considered precise.
Table:
Graduated Cylinder:
Dimension Metric Ruler Caliper
Outer Diameter 1.5 cm 1.5 cm
15 mm 15 mm
Inner Diameter 1.3 cm 1.3 cm
13 mm 13 mm
Circumference 4.7 cm 4.7 cm
Depth 10.4
Volume 18.4 cm 18.4 cm
Aluminum Square:
Dimension Metric Ruler Caliper Micrometer
Length 2.4 cm 2.4 cm 2.4 cm
Width 2.4 cm 2.4 cm 2.4 cm
Height 0.4 cm 0.4 cm 0.45 cm
Area 5.8 cm^2 5.8 cm^2 5.8 cm^2
Volume 2.3 cm^3 2.3 cm^3 2.6 cm^3
