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 a person reads a measurment, while precision is how close the instument measures an object. One could improve accuracy by simply looking closer or paying more attention, but the only way to improve precision is to get a better instrument.
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 precision of the instruments increased as we went through them (i.e. the ruler, then the caliper, then the micrometer in that order).
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.
The measurment were generally the same. Any errors were probably due to the fact that we were measuring different cylenders and aluminium squares.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer was the most precise.
Sample Data Table (you may use this one or create your own):
Graduated Cylinder
Dimension
Metric ruler
Caliper
Outer diameter
1.5cm
1.53cm
15mm
15.3mm
Inner diameter
1.3cm
1.3cm
13mm
13mm
Circumference
1.77cm
1.84cm
Depth
10.4cm
10.43cm
Volume
18.408cm3
19.1912cm3
Aluminum Square
Dimension
Metric ruler
Caliper
length
2.5cm
2.54cm
height
0.1cm
0.17cm
width
2.5cm
2.52cm
Area
6.25cm2
6.40008cm2
Volume
0.55cm3
1.08836cm3
Height (with micrometer)
0.137cm
Volume (with micrometer)
0.877cm3
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 a person reads a measurment, while precision is how close the instument measures an object. One could improve accuracy by simply looking closer or paying more attention, but the only way to improve precision is to get a better instrument.
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 precision of the instruments increased as we went through them (i.e. the ruler, then the caliper, then the micrometer in that order).
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.
The measurment were generally the same. Any errors were probably due to the fact that we were measuring different cylenders and aluminium squares.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer was the most precise.
Sample Data Table (you may use this one or create your own):
Graduated Cylinder
Dimension
Metric ruler
Caliper
Outer diameter
1.5cm
1.53cm
15mm
15.3mm
Inner diameter
1.3cm
1.3cm
13mm
13mm
Circumference
1.77cm
1.84cm
Depth
10.4cm
10.43cm
Volume
18.408cm3
19.1912cm3
Aluminum Square
Dimension
Metric ruler
Caliper
length
2.5cm
2.54cm
height
0.1cm
0.17cm
width
2.5cm
2.52cm
Area
6.25cm2
6.40008cm2
Volume
0.55cm3
1.08836cm3
Height (with micrometer)
0.137cm
Volume (with micrometer)
0.877cm3
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 a person reads a measurment, while precision is how close the instument measures an object. One could improve accuracy by simply looking closer or paying more attention, but the only way to improve precision is to get a better instrument.
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 precision of the instruments increased as we went through them (i.e. the ruler, then the caliper, then the micrometer in that order).
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.
The measurment were generally the same. Any errors were probably due to the fact that we were measuring different cylenders and aluminium squares.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer was the most precise.
Sample Data Table (you may use this one or create your own):
Graduated Cylinder
Dimension
Metric ruler
Caliper
Outer diameter
1.5cm
1.53cm
15mm
15.3mm
Inner diameter
1.3cm
1.3cm
13mm
13mm
Circumference
1.77cm
1.84cm
Depth
10.4cm
10.43cm
Volume
18.408cm3
19.1912cm3
Aluminum Square
Dimension
Metric ruler
Caliper
length
2.5cm
2.54cm
height
0.1cm
0.17cm
width
2.5cm
2.52cm
Area
6.25cm2
6.40008cm2
Volume
0.55cm3
1.08836cm3
Height (with micrometer)
0.137cm
Volume (with micrometer)
0.877cm3
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 a person reads a measurment, while precision is how close the instument measures an object. One could improve accuracy by simply looking closer or paying more attention, but the only way to improve precision is to get a better instrument.
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 precision of the instruments increased as we went through them (i.e. the ruler, then the caliper, then the micrometer in that order).
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.
The measurment were generally the same. Any errors were probably due to the fact that we were measuring different cylenders and aluminium squares.
4. Which instrument is more precise, the metric ruler, micrometer or caliper?
The micrometer was the most precise.
Sample Data Table (you may use this one or create your own):
Graduated Cylinder
Dimension
Metric ruler
Caliper
Outer diameter
1.5cm
1.53cm
15mm
15.3mm
Inner diameter
1.3cm
1.3cm
13mm
13mm
Circumference
1.77cm
1.84cm
Depth
10.4cm
10.43cm
Volume
18.408cm3
19.1912cm3
Aluminum Square
Dimension
Metric ruler
Caliper
length
2.5cm
2.54cm
height
0.1cm
0.17cm
width
2.5cm
2.52cm
Area
6.25cm2
6.40008cm2
Volume
0.55cm3
1.08836cm3
Height (with micrometer)
0.137cm
Volume (with micrometer)
0.877cm3
