Tamara- AP Physics

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?

Our accuracy and precision were accurate and precise. Our objects of measurement were fairly easy to evaluate because their measurements were mostly to one decimal place. The accuracy can be better improved by using tools that are more specific and have less room for error. The tools can allow one to expand the number to more decimal places. The precision can be improved by making sure the tool is being used correctly and measuring the correct part of the object.

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 was predominately the same throughout the lab. Most of the measurements only needed two or three significant figures but the micrometer allowed us to go to three significant figures and show us that our first measurement was slightly off. We had two measurements that have one significant figure because the measurement is smaller than the other elements of the lab. The ruler allows us to go to three significant figures, as well as the caliper and micrometer. The micrometer is the most precise because it holds the object in place and takes the appropriate measurement. Likewise, the caliper is fairly precise because it touched the object, but it does not hold it in place. The ruler, however, is the least precise of the instruments because it is not the most reliable tool for measuring a round object and the circumference.

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.

My group rounded to a smaller decimal place which contributed to a slight difference in calculations. The graduated cylinder measurements seemed to be fairly close, while the aluminum square was a few decimals off. the square itself could have contributed to the problem, but if all the squares were the same size then human error is to blame. While comparing our measurements to the other groups, we were able to infer that our information is fairly accurate. The accuracy for the graduated cylinder better than the accuracy of the aluminum square. Considering that each group measured a different square and rounded to different figures, the outcome was fair.

4. Which instrument is more precise, the metric ruler, micrometer or caliper?

The micrometer is the most accurate, but not necessarily the most precise. The most precise measurements came from the ruler and the caliper. The micrometer allows one to go to more significant figures which allows for more error considering the groups differing significant figures. The caliper and the ruler almost always calculated to be the same measurement for our group. Most groups had close to the same calculations. Likewise, all of the tools allowed us to to compute fairly precise measurements.

**Sample Data Table (**you may use this one or create your own):

Graduated Cylinder

Dimensions 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 cm 10.4 cm

Volume 18.4 cm3 18.4 cm3

Aluminum Square

Dimensions 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 cm2 5.8 cm2 5.8 cm2

Volume 2.3 cm3 2.3 cm3 2.6 cm3

** **

Laboratory Exploration

· To introduce scientific measuring instruments.

· To practice measuring

· To achieve mastery in reporting measurements to the correct number of significant digits based on the

· Measurement kit containing: Vernier caliper, micrometer, depth gauge, metric ruler, aluminum square, plastic vial, graduated cylinder, steel ball.

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.

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.

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.

1. Compare and contrast

Our accuracy and precision were accurate and precise. Our objects of measurement were fairly easy to evaluate because their measurements were mostly to one decimal place. The accuracy can be better improved by using tools that are more specific and have less room for error. The tools can allow one to expand the number to more decimal places. The precision can be improved by making sure the tool is being used correctly and measuring the correct part of the object.

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 was predominately the same throughout the lab. Most of the measurements only needed two or three significant figures but the micrometer allowed us to go to three significant figures and show us that our first measurement was slightly off. We had two measurements that have one significant figure because the measurement is smaller than the other elements of the lab. The ruler allows us to go to three significant figures, as well as the caliper and micrometer. The micrometer is the most precise because it holds the object in place and takes the appropriate measurement. Likewise, the caliper is fairly precise because it touched the object, but it does not hold it in place. The ruler, however, is the least precise of the instruments because it is not the most reliable tool for measuring a round object and the circumference.

3. Compare your measurements and calculations with those of a classmate. Are they the same? Discuss sources of error in the

My group rounded to a smaller decimal place which contributed to a slight difference in calculations. The graduated cylinder measurements seemed to be fairly close, while the aluminum square was a few decimals off. the square itself could have contributed to the problem, but if all the squares were the same size then human error is to blame. While comparing our measurements to the other groups, we were able to infer that our information is fairly accurate. The accuracy for the graduated cylinder better than the accuracy of the aluminum square. Considering that each group measured a different square and rounded to different figures, the outcome was fair.

4. Which instrument is more precise, the metric ruler, micrometer or caliper?

The micrometer is the most accurate, but not necessarily the most precise. The most precise measurements came from the ruler and the caliper. The micrometer allows one to go to more significant figures which allows for more error considering the groups differing significant figures. The caliper and the ruler almost always calculated to be the same measurement for our group. Most groups had close to the same calculations. Likewise, all of the tools allowed us to to compute fairly precise measurements.

Graduated Cylinder

Dimensions 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 cm 10.4 cm

Volume 18.4 cm3 18.4 cm3

Aluminum Square

Dimensions 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 cm2 5.8 cm2 5.8 cm2

Volume 2.3 cm3 2.3 cm3 2.6 cm3