measurement of length, mass, volume, density, and time

Week 1, Report 2: Measurement

Title:

Measurement:

Length, Mass, Volume, Density, and Time

Laboratorial Report 2

Created to fulfill the assignment for Mechanic and heat EN222 subject

I Wayan Surya Aryana (2014370006)

Lecturers:

Lina J Diguna

Sampoerna University

Jakarta, June 8th, 2015

Abstract

Measurement is an essential activity that need to be presented in the physics experiment;

when the measurement is close to the perfect, the experiment is said to be success. In this second

physics laboratorial activity, the students are undergoing five activities toward the concept of

measurement. Determining length, sensing mass, calculating volume, comparing density, and

checking time are what the student have done in laboratory; by using the concept of percent error

and reading graph, the students are expected to be able to understand the basic concept of

measurement and its SI measurement unit.

Keyword: Length, Mass, Volume, Density, Time, Error, Slope, Graph.

Chapter I

Objective

1. Student is expected to be able to perform a basic measurement about distance, density, and

2. Student is expected to be able to use a proper unit in calculating the volume and density of an

object.

3. Student is expected to be able to construct graph using spreadsheet software due to the

relationship between the circumference of a circle and its diameter.

Chapter II

Methodology

1. Material

The materials that being used in the second physics lab-activity are as what they are shown in

the table 1 as follow:

Table 1. Materials

Source of Materials Label or Box Bag Quantity Item Description

Student

3 Box-like object

2 Pencil or pen

1 Chair or step tool

5 Circular object of different size

1 Computer and spreadsheet program

1 Lab partner

1 Cup filled with tap water

Laboratories

1 Cylinder, 25 ml

1 Ruler, Metric

1 Digital scale

1 Scale-spring-500 g

1 Digital Stopwatch

1 Tape measurement

Marble, bolt, and

Spring bag

1 Bolt, small metal

String and weight

1 4 meter string

2. Procedure

2.1. Activity 1: Length, Time, and Mass Measurement

Length

a. Setting the data-record table as shown below:

Table 2. Estimation of Various Measurement

Measurement Estimated Actual % Error

Length (m)

Time (s)

Mass (g)

b. Estimating the length of a meter by putting a pen or pencil at one end of the table and

placing a second pen or pencil about one meter away from the first.

c. Using the tape measurement to measure the actual length of your meter estimation.

d. Recording the length of your meter estimation.

e. Calculating the percent error.

a. Estimating a 30-s time period while someone else times you using a stopwatch.

b. Recording the actual time of your estimation.

c. Calculating the percent error of the estimation from the actual time.

a. Picking up a small paperback book or similar small object.

b. Estimating the mass of the object.

c. Determining the actual mass of the object using the 500-g spring scale.

d. Recording the estimation mass and the actual mass.

e. Calculating the percent error.

2.2. Activity 2: Measuring Using Instrument of Varying Degrees of Precision.

a. Choosing three object.

b. Setting three tables as shown below:

Table 3. Measurement of Object 1 Using Various Instrument

Length (cm) Width (cm) Height (cm) Volume (cm3)

Object Being Measured

Hand (hand unit)

Hand (cm)

Meter tape

Table 4. . Measurement of Object 2 Using Various Instrument

Hand (hand unit)

Hand (cm)

Meter tape

Table 5. Measurement of Object 3 Using Various Instrument

Hand (hand unit)

Hand (cm)

Meter tape

c. Using hand as what it is instructed below:

Spreading out your hand and use the measuring tape to measure the distance

from the tip of the thumb to the tip of the little finger in centimeter and record

the value

Using hand to measure the length, width, and height of the three rectangular

items.

Converting the hand unit to centimeter and record in the table 3.

d. Using metric ruler and meter tape as what it is instructed below:

Using the metric ruler to measure the length, width, and height of the same

objects in step c.

Recording the data in the table 4 by using the nearest half-millimeter

Measuring the length, width, and height if the box with the tape measure.

Recording the measurement data in the table 4.

e. Performing the calculation as follow:

Calculating the volume using three different set of measurement and record it.

2.3. Activity 3: Graphing Data and Determining π

a. Setting up the data table as what it is shown below:

Table 6. Determination of π

Object Diameter D (cm) Circumference C (cm) Slope % Error

b. Selecting five circular object of different size.

c. Using the metric ruler or tape measurement to measure the diameter D in centimeter

of each object to two decimal points and record the data in the table 6.

d. Using tape measurement, measure the circumference C in centimeter of each object

to two decimal point and record the data in the table 6.

e. Graphing C versus D using a computer spreadsheet program.

f. Using linear line fit command from the program menu to plot a best-fit line.

g. Recording the slope of each line in the table 6.

h. Calculating the percent error of the value obtained from the slope from the true value

of π.

i. Recording the percent error in the table 6.

2.4. Activity 4: Density Measurement.

a. Setting up the data like what it is shown below:

Table 7. Density Measurement

Measurement Value

Mass using scale (Ms)

Mass of displaced water (Md)

Volume using ruler (Vr)

Volume using displacement (Vd)

Density 1 (ρ1 = Ms/Vr)

Density 2 (ρ2 = Ms/Vd)

Density 3 (ρ3 = Md/Vr)

Density 4 (ρ3 = Md/Vd)

b. Finding the mass of the bolt using a digital scale and then compare this value to the

mass of the water displaced by bolt using the following steps:

Using the digital scale to find the mass (Ms) in gram of the metal bolt.

Filling the graduated cylinder to exactly the 10-ml line with water.till the

graduated cylinder at a 45 to 60 degree angle and allow the bolt to slowly slide

down the side of the graduated cylinder until it rest at the bottom. Be careful not

to allow any water to splash out of the graduated cylinder.

Calculating the final volume minus 10 ml. this is the amount of water displaced

by the bolt.

Determining the mass (Md) of the volume of water that was displaced by the bolt.

c. Taking a moment to compare the values for Ms and Md.

d. Finding the volume of the volt with ruler and with displacement by using the

following steps:

Using ruler to measure in millimeter the length, width, and the height of the metal

Calculate the volume (Vr).

Calculate the volume (Vd).

e. Taking a moment to compare the values of Vr and Vd.

f. Calculate the density of bolt.

g. Taking a moment to compare all the type of density and consider which density type

is more accurate.

2.5. Activity 5: Time Measurements.

Aye Opened

a. Setting the table as what it is shown below:

Table 8. Time Measurement Using Visual Cues

Drop time (s)

Trial 1

Trial 2

Trial 3

Average

b. Measuring and marking a verticals distance of 2 m from the floor up.

c. Standing on the chair and hold a small box or similar object at the marked height in

one hand and the stopwatch in the other hand.

d. Starting the stopwatch at the same instant time the releasing of the falling object.

e. Stopping the stopwatch when the object is hitting the floor.

f. Record the times to nearest tenth of a second in table 8.

g. Repeating the trial to three times.

h. Finding the average drop time of the object.

i. Recording it in the table 8.

Aye Closed

a. Setting the table as what it is shown below:

Table 9. Time Measurement Using Visual Cues

Drop time (s)

Trial 1

Trial 2

Trial 3

Average

b. Repeating the step of the eye opened activity, however in this time the eye is closed.

Chapter III

Result and Discussion

1. Experimental Theory

Physics is fundamentally an experimental science-based study that importantly aiming

at the flawless result of its measurement. In physics experiment, it is important to regard the

measurement process as an essential process that need to be precisely and accurately done;

every experiment, as a result, need to have a perfect-close result of its scientific measurement.

By using an international unit standard, every unit that involved in physics experiment is

consequently become well determined and therefore is expected to be able to create a

similarity in an international level standard. Regarding International System of Unit or

commonly called as SI is theoretically a modern form of the metric system that use the units

of ten as its basis in processing the experimental data number, therefore by aiming at the same

standard, the physics measurement is then expected not to have a vague result in every

different country indeed it should shows a resemblance and unity perception due to what

measurement means and aiming for.

Length, temperature, volume, mass, and density, as a result of the international

standardized, have been possessing an international unit. Length, as a variable that being used

to measure the length of something, is having meter as its SI unit. In line with length,

temperature has Kelvin as its SI unit. Volume has liter as its SU unit and mass has kilogram

as its SI. Density, since there are liquid form and solid form of an object, is sometimes

performed by using two different unit; the density of liquids are usually reported in grams per

milliliter (g/ml), the density of solid, however, are usually reported in grams per cubic

centimeter (g/cm3).

Due to the experiment, the formula that being used are as follows:

𝑀 𝑜𝑏𝑗𝑒𝑐𝑡

𝑀 𝑓𝑙𝑢𝑖𝑑 𝑙𝑜𝑠𝑡=

𝜌 𝑜𝑏𝑗𝑒𝑐𝑡

𝜌 𝐹𝑙𝑢𝑖𝑑

%𝐸𝑟𝑟𝑜𝑟 = ⃒𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒⃒

𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒× 100%

%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = ⃒𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 1 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 2⃒

𝐴𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒× 100%

𝜎 = √∑(𝑥 − x̅)^2

𝑁 − 1

2. Discussion 1: Length, Time, and Mass Measurement

Table 9. Estimation Result of Various Measurements

Measurement Estimated Actual % Error

Length (m) 14.0 13.8 1.45

Time (s) 30.00 30.62 2.02

Mass (g) 40 50 20

By using the formula of percent error the percent error of each prediction (length, time,

and mass) is recorded in the table; the calculations are shown as follows:

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ = ⃒14.0 − 13.8⃒

13.8× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ = 1.45%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 = ⃒30.00 − 30.62⃒

30.62× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒 = 2.02%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑛𝑔 𝑚𝑎𝑠𝑠 = ⃒40 − 50⃒

50× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑝𝑜𝑓 𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑛𝑔 𝑚𝑎𝑠𝑠 = 20%

Answering Question

The results shown in the table are basically based on the calculation performed under

the table 9. Based on the observations, the calculations are basically telling that, in physics

experiment, using an estimation or prediction to determine the value of certain object must

definitely resulting an error. This is fundamentally grounded by the essence of prediction

itself; the more the prediction is used by someone on a certain case, the least possibilities of

prediction error will be. Therefore, by looking at the result, it is reasonable to conclude that

predicting length is easier rather that predicting mass because some people have been getting

used to predicting length compared to predicting mass; and by that, it is also acceptable to say

that the data of length prediction is more reliable compared to the data of mass prediction.

In short, it is important to correctly perform an estimation (in this case length, time, and

mass) because the estimation itself is directly proportional to the value of the percent error in

the experiment. When the error is big (more than five percent), the data used in the experiment

is consequently said to be failed or unreliable; cannot be used to determine the value of the

result.

3. Discussion 2: Measuring Using Instrument of Varying Degree of Precision

Table 10. Measurement of Object 1 Using Various Instruments

Object Being Measured Book Book Book Book

Hand (hand unit) 1 5/4 1/6 0.208

Hand (cm) 18.50 23.10 3.00 1282.05

Ruler 18.60 23.20 2.00 863.00

Meter tape 18.6 23.3 2 866.80

Based on the table 10, the measurement using hand is really showing a visible error. By

determining the mater tape as an acceptable value, the error of the measurement using hand

and ruler are as follow:

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 ℎ𝑎𝑛𝑑 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 = ⃒1282.05 − 866.80⃒

866.80× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 ℎ𝑎𝑛𝑑 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 = 47.90%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 = ⃒863.00 − 866.80⃒

866.80× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 = 0.44%

Object Being Measured Hand phone Hand phone Hand phone Hand phone

Hand (hand unit) 3/4 1/3 1/10 0.02

Hand (cm) 13.90 6.20 1.85 159.40

Ruler 14.30 7.30 1.40 146.15

Meter tape 14.30 7.40 1.40 148.15

In line with the result shown by table 10, table 11 is also showing the bigger error of the

measurement using hand compared to using ruler. By determining the mater tape as an

acceptable value, the error of the measurement using hand and ruler are as follow:

148.15× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑚𝑒𝑛𝑡 = ⃒146.15 − 148.15⃒

148.15× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑚𝑒𝑛𝑡 = 1.35%

Object Being Measured Table Table Table Table

Hand (hand unit) 10/3 13/2 25/6 90.30

Hand (cm) 61.65 120.25 77.10 571574.10

Ruler 60.00 121.00 76.50 555390.00

Meter tape 60.00 120.00 78.50 565200.00

By observing the table, it can be shown that a hand measurement, in contrast to two

different trial above, reflecting less error comparing to the ruler measurement. By determining

the mater tape as an acceptable value, the error of the measurement using hand and ruler are

as follow:

565200.00× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑚𝑒𝑛𝑡 = ⃒555390.00 − 565200.00⃒

565200.00× 100%

%𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑟𝑢𝑙𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑚𝑒𝑛𝑡 = 1.70%

The three tables above, in conclusion, can basically reveal that, the percent error of an

experimental result is really depending on how accurate is the tool used in measuring the data. When

hand is being used to measure the length of a certain data, the precision of the data measurement is

lost while converting the “hand unit” of the data to be another unit (in this case another unit is SI).

However, it is in contrast to ruler and meter tape; considering that those two measurement tools are

being used without converting its unit to another units, the percent error of their results is consequently

less than the hand measurement tool.

Answering Questions

Besides revealing the percent error due to the measurement tool that is being used, the three

tables are also implicitly stating that the influence of the measurement tool to determine the percent

error is decreasing when the measurement is done to the bigger object. By doing observation, it can be

shown that, when the hand is used to measure the small object (hand phone) the error is bigger rather

that when the hand is used to measure a bigger object (table). In short, hand is adequate to be used as

a measurement tool is when hand is used to measure a big object.

When a variables of a calculation are altered by the chance of error, the value of the finals result

of the calculation will also be shifted toward a bigger error. Therefore when the length, width, and

height of a calculation is being off a little, the value of the volume will be changed toward an error.

4. Discussion 3: Graphing Data and Determining π

Table 13.Determination of π

Object Diameter D (cm) Circumference C (cm) Slope % Error

Dumble 2.50 8.00 3.20 1.85%

Cap of a bottle 3.10 10.50 3.40 8.20%

Betray 3.30 10.80 3.25 3.40%

Glass 6.40 21.40 3.20 1.80%

Chair 28.20 60.30 2.10 33.16%

Based on table, the graph of circumference versus diameter is as follow:

Based on the observation, the shape of the graph is not linear; this is basically because the graph

is made up of lines that has different slope. Besides the difference of the slope regard the graph as a

nonlinear graph, the difference of the slope in each line is also regard the error that is contained in each

data taken. Since the slope of each line is indicating the π (and the value of the π is ideally constant

which is 3.142), therefore when the graph is performing a nonlinear line, the graph is

consequently indicating an error. The value of the error is basically calculated by comparing

the difference between slope and π to the value of π which is 3.14.

810,5 10,8

2,5 3,1 3,3 6,4 28,2

Diameter

Graph Circumference Versus Diameter

5. Discussion 4: Density Measurement

Table 14. Density Measurement

Measurement Value

Mass using scale (Ms) 8.00 × 10-3 kg

Mass of displaced water (Md) 2.00 × 10-3 kg

Volume using ruler (Vr) 3.30 cm3

Volume using displacement (Vd) 1.50 cm3

Density 1 (ρ1 = Ms/Vr) 2.40 g/cm3

Density 2 (ρ2 = Ms/Vd) 5.30 g/cm3

Density 3 (ρ3 = Md/Vr) 0.60 g/cm3

Density 4 (ρ3 = Md/Vd) 1.30 g/cm3

The density that is being showed in the table are basically determined by using the calculation

bellow:

ρ1 = Ms/Vr

ρ1 = 8.00 × 10-3 kg /3.30 cm3

ρ1 = 2.40 g/cm3

ρ2 = Ms/Vd

ρ1 = 8.00 × 10-3 kg /1.50 cm3

ρ1 = 5.30 g/cm3

ρ3 = Md/Vr

ρ3 = 2.00 × 10-3 kg /3.30 cm3

ρ3 = 0.60 g/cm3

ρ3 = Md/Vd

ρ3 = 2.00 × 10-3 kg /1.50 cm3

ρ3 = 1.30 g/cm3

Answering Question

In the experiment, especially when measuring the displaced water, the error is occurred;

it is basically grounded by the limitation of the scale of the graduated cylinder. When the

displaced water is too small and the graduated cylinder cannot precisely read the displaced

water scale, the experiment is consequently said to be occurring an error. Therefore the

accurate value of calculation is came from the data that is not gotten from the displaced water

data. As a result the most accurate density value is the first density which is ρ1 = 2.40 g/cm3

The Archimedes principles is stating that the raising force of the fluid is equal to the

weight of the object.

Fraise = W object

ρ fluid × g ×v object in fluid = ρ object × g × v object

In other word the formula can be expressed as follow:

𝑀 𝑜𝑏𝑗𝑒𝑐𝑡

𝑀 𝑓𝑙𝑢𝑖𝑑 𝑙𝑜𝑠𝑡=

𝜌 𝑜𝑏𝑗𝑒𝑐𝑡

𝜌 𝐹𝑙𝑢𝑖𝑑

The principle is basically used in this experiment; when the object is slid down slowly

to the graduated cylinder, the water in the graduated cylinder is raised with an amount that is

equal to the volume of the object. Based on the formula, it can be seen that the floating objects

displaced a mass of fluid that is equal to its own mass, and the mass of a submerged object is

diminished by the mass of the displaced fluid.

6. Discussion 5: Time Measurements

Table 15. Aye Opened Time Measurement

Drop time (s)

Trial 1 1.0

Trial 2 0.9

Trial 3 1.1

Average 1.0

Based on the table, it can be shown that, between the first trial, the second trial, and

the third trial, the time take of the object to reach the floor is not too visible in difference.

Therefore, by seeing the average of the time taken which is one second, the data can be said

to be accurate.

Table 16. Aye Closed Time Measurement

Drop time (s)

Trial 1 1.6

Trial 2 1.8

Trial 3 1.2

Average 1.5

Differ from what it is shown in the table 15, table 16 is showing an irregular difference

between each trial. By considering that the observation is limited by just hearing the sound of

the falling object (without seeing it as what it is done in the table 15), the data taken in the aye

closed observation is having a greater error compared to the aye opened observation.

Answering Question

In an experiment, individual data is said to be inaccurate; by assuming that the

possibilities of an error may occurred in an individual data, therefore the data taken is done

more than once. After getting several individual data, those data then can be proceed

(compering to each other); therefore, by finding the average of the data, the result then can be

said to be perfect-close data. In short the average data is more accurate compared to the

individual data due to the possibilities of error that may contained by individual data.

When the many trial are run and then recorded, the possibilities of having the highest

data and the lowest data to be disregarded may be occurred; in this case, the highest data and

the lowest data is said to be vanishing each other. When this is happened the technique can

still be used (it has no effect to the final result) because the data taken is so many. When the

two data is disregarded, there are still several data that can be used to determine the final result

or average.

In doing an observation due to the data taken process, the technique that is being used

in observing/getting the data may be different. Some may be visual, some may be aural, or

some may be both (visual and aural). Those technique are having their own weaknesses and

therefore one of those technique may not be used in a certain experimental. In the case of the

time measurement, the different between those three are as follows:

Visual Aural Both

Since the data take can be

seed directly, therefore the difference between the time

when the object reach the floor and the time when the

observer see the object reach

the floor is just slightly difference (small error)

Since the data cannot be seen

directly and the movement of the sound vibration need

time to be heard in the observer ear, therefore the

difference between the time

when the object reach the floor and the time when the

observer see the object reach the floor is bigger compared

to the visual technique

(grater error)

Since the observer can see

and hear the object fall and reach the floor, this

techniques may be the best in measuring the time

Less disturbance Grate sound disturbance

(due to another student activities in the same place)

Independent to the material

in the current place.

The data may be difference if

the material that is being used by the sound vibration

is difference also.

Chapter IV

Conclusion

1. Conclusion

a. Distance/length measurement is using meter as its SI unit; Mass measurement is using

kilogram as its SI unit; Density measurement is using g/cm3 or g/ml as its SI unit; and

time measurement is using second as its SI unit.

b. Calculation in determining volume and density is commonly using both manual

calculation and Archimedes principle; the acceptance density of the object being

measured is ρ1 = 2.40 g/cm3.

c. Graph is shown in the discussion 3.

2. Recommendation

a. Due to the vague steps, the experiment would be better if the procedure is clearly stating

the calculation steps of the experiment.

References

(2015). Experimental Error and Uncertainty Guidance. South Jakarta: Lonestar Collage (Sampoerna

University). Retrieved June 12, 2015

Physicsjhs. (2010, October 13). Archimedes low. Retrieved from Physics For Junior High School:

https://physicsjhs.wordpress.com/2010/10/13/archimedes-low/

measurement of length, mass, volume, density, and time

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