DoM and HL LR
pdf
keyboard_arrow_up
School
University of Illinois, Urbana Champaign *
*We aren’t endorsed by this school
Course
102
Subject
Mechanical Engineering
Date
Apr 3, 2024
Type
Pages
9
Uploaded by DrBookPony31
Experiment one: Density of Matter
1.
Introduction:
The purpose of this experiment was to study the density of solid objects. The greater the
volume of an object, the smaller the density of an object as they have an inversely proportional
relationship. In this lab, density will be found from found masses and volumes calculated from
measurements taken during the lab.
The mathematical equation used to calculate the volume of cylindrical solids is:
V
=
(1)
Π𝑟
2
?
where V is the volume of the cylinder,
is the ratio of the circumference of a circle to its
Π radius, r is the radius of the cylinder, and l is the length of the cylinder.
The mathematical equation used to calculate the volume of a solid rectangular prism is:
(2)
𝑉 = ??ℎ
where V is the volume of the rectangular prism, l is the length of the rectangular prism, w
is the width of the rectangular prism, and h is the height of the rectangular prism.
The mathematical equation used to calculate the density of an object is:
(3)
ρ =
𝑀
𝑉
where
is the density of an object, M is the mass of the object, and V is the volume of an
ρ object.
2.
Experiment procedures:
The materials and equipment used for this lab included the following: 3 aluminum
cylinders of varied sizes, 3 cardboard rectangular prisms of varied sizes, a balance, and vernier
calipers.
Part 1:
-
Step 1: The balance was turned on and zeroed.
-
Step 2: The mass of a cylinder was measured on the balance.
-
Step 3: The radius and height of the cylinder were measured by putting the cylinder in
between the ends of the vernier calipers.
-
Step 4: The volume was found by multiplying the square of the radius by the height of
the cylinder by pi.
-
Step 5: The density was calculated by dividing the found mass of the cylinder by the
found volume of the cylinder.
-
Step 6: Steps 1-5 were repeated twice for two other cylinders.
Description: The aluminum used were smooth, opaque, silver cylinders.
Part 2:
-
Step 7: Steps 1 and 2 were repeated for the rectangular prism.
-
Step 8: The height, length, and width of the prism were measured by putting the prism in
between the ends of the vernier calipers.
-
Step 9: The volume was found by multiplying the length by the height by the width of the
cylinder.
-
Step 10: Step 5 was repeated.
-
Step 11: Steps 7-10 were repeated twice for the other rectangular prisms.
Description: The rectangular prisms used were made of cardboard. The largest was red, the
second largest was yellow, and the smallest was blue. They were hollow and opaque with a
semi-matte finish.
3.
Results, analysis, and questions:
Table 1: Table one shows the mass, length, radius, volume, and density of the aluminum
cylinders.
Column
1
mass
(grams)
length
(cm)
diameter
(cm)
radius (cm)
volume (m^3
x10^-6)
density
(kg/m^3)
cylinder
1
27.52
7.7
1.1
0.55
7.32
3760
cylinder
2
12.56
3.1
1.1
0.55
2.95
4258
cylinder
3
6.36
7.5
0.6
0.3
2.12
3000
Based on table 1, the graph illustrated the relationship between volume versus mass of the
cylinders.
Graph 1:
From graph 1, the slope of best fit was 0.000254, which demonstrates
(based on equation 3).
1
ρ
Therefore, the density of aluminum is theoretically 3,979 kilograms per meter cubed. The
average experimental density of the aluminum cylinders was found to be approximately 3,673
kilograms per meter cubed, which means that there was around a 7.69% error. The coefficient of
determination was calculated to be 0.981. This demonstrates that the data from this part of the
experiment was relatively accurate. A likely source of error was from measuring the cylinders
with the vernier calipers, where the cylinder may not have gripped tight enough for accuracy.
Table 2: Table 2 shows the mass, height, length, width, volume and density of the blocks.
Mass
(grams)
Height (cm)
Length (cm)
Width (cm)
Volume (m^3 x
10^-3)
Density
(kg/m^3)
Block 1
(red)
134.18
303
74
150
3.36
40
Block 2
(yellow)
86.6
75
152
152
1.73
50
Block 3
(blue)
50.01
146
73
73
0.78
64
Based on table 2, the graph 2 illustrates the relationship between mass and volume of the blocks.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
From graph 2, the slope of best fit was 0.0308, which demonstrates
(based on equation 3).
1
ρ
Therefore, the density of cardboard was 32.47 kilograms per meter cubed. The average
experimental density was 51.3 kilograms per meter cubed, giving a 36.8% error. The coefficient
of determination was calculated to be 0.994. This demonstrates that the data from this part of the
experiment was precise, but not accurate. A source of error was likely due to the inexact
measuring of the blocks due to a tightened grip on the vernier calipers. It is possible that the
cardboard may have been compressed, making the measurements more inaccurate.
4.
Conclusion:
Through this experiment, the density of solid objects was studied. A deeper
understanding of laboratory procedures and precise measurements were also examined. The
density of solid objects was studied. One was calculated with the volume of a set of cylinders,
and the other was calculated using a set of cardboard blocks.
was used in both parts of the
ρ experiment to represent density. The errors in this lab stemmed from improper measuring. To be
repeated with greater accuracy, the lab should be redone with measurements taken on a flat
surface.
5.
Data Sheet:
Next Page under Density of Matter
Experiment one: Hooke’s Law
1.
Introduction:
The purpose of this experiment was to study Hooke’s Law and its properties. This
lab explores the opposing directions of force and the change in position of the spring.
Force and the change in distance (extension) of springs were found with differing
weights. The further a spring’s position changes from equilibrium, the greater the
resultant force will be.
The equation to calculate the change in distance (position) is:
(4)
∆? = ?
𝑓
− ?
𝑖
Where
is the change in position,
is the final position, and
is the initial position of
∆? ?
𝑓
?
𝑖 the spring.
The equation to calculate the force of a spring is:
(5)
𝐹 =− ?∆?
Where F is the spring force, k is the spring constant, and
is the change in position.
∆?
2.
Experimental Procedures:
Materials and equipment needed for this procedure are: a force sensor, 850
Universal Interface, PASCO Capstone software (on computer), 2 springs (with different
spring constants), and a set of weights.
-
Step 1: Connect the force sensor to the 850 Universal Interface.
-
Step 2: Open the PASCO Capstone software on a computer.
-
Step 3: Locate the TOOLS tab and click Hardware setup, then choose the port that
is connected to the force sensor, and select the correct sensor from the dropdown
menu.
-
Step 4: Find the Displays tab (far right of the window) and click “graph” twice for
a force versus time graph.
-
Step 5: Hook the 50 gram weight holder to the force sensor.
-
Step 6: Click “Record” to collect data.
-
Step 7: Press the tare button on the force sensor to set the sensor to zero.
-
Step 8: Measure the position of the spring as the initial position.
-
Step 9: Add 40 grams of weight to the holder, then measure the change in distance
once the spring has finished oscillation.
-
Step 10: Repeat step 9 four more times.
-
Step 11: With a different spring, repeat steps 7-10.
3.
Results, analysis, and questions:
Table 1: Table 1 shows the change in position and the spring force of Spring 1 with an
initial position of 0.449 meters from the force sensor when the 50 grams of the weight
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
holder on it. (40 grams is added each time to change the position of the spring.) The
calculated spring constant is also included.
Force (N)
Change in position (m)
Spring constant (k)
0.396
0.029
13.7
0.784
0.059
13.3
1.165
0.085
13.7
1.557
0.122
12.8
1.946
0.155
12.6
Based on table 1, graph 1 shows the relationship between the change in position and force
on Spring 1.
From graph 1, the line of best fit is 0.0814, which represents
(based on equation 4).
1
?
Therefore, the spring constant of Spring 1 is theoretically 12.3. The average experimental
spring constant of Spring 1 was found to be 13.2, which means that there was around a
7.32% error. The coefficient of determination was calculated to be 0.997. This
demonstrates that the data from this part of the experiment is relatively accurate. A
source of error is likely due to inexact estimations of the spring force from failing to
exactly determine the value on the computer.
Table 2: Table 2 shows the change in position and the spring force of Spring 2 with an
initial position of 0.464 meters from the force sensor when the 50 grams of the weight
holder is on it. (40 grams is added each time to change the position of the spring.) The
calculated spring constant is also included.
Force (N)
Change in position (m)
Spring constant (k)
0.423
0.067
6.31
0.816
0.125
6.53
1.203
0.192
6.27
1.608
0.239
6.73
1.995
0.307
6.5
Based on Table 2, graph 2 shows the relationship between the change in position and
spring force of Spring 2.
From graph 2, the slope of best fit was found to be 0.151, which represents
(based on
1
?
equation 4). Therefore, the spring constant of Spring 2 is theoretically 6.62. The average
experimental spring constant was calculated to be 6.41, meaning that there was a 3.17%
error. The coefficient of determination was calculated to be 0.997. This demonstrates that
the data from this experiment was very accurate. A possible source of error was likely
due to inexact estimations of the spring force from failing to exactly determine the value
on the computer.
4.
Conclusion:
Through this experiment, spring force and displacement were explored. The
slopes of the force versus change in position were
(as seen with equation 4). This law
1
?
determined that Hooke’s Law is dependent on which spring is used as springs have varied
properties, such as their durability and stiffness. Springs have different spring constants
that determine the amount of force needed to displace their position from equilibrium.
Hooke’s Law was found to not hold for larger forces as there is a point that a mass so
significant will be enacted on the spring that it either deforms it or will break the spring.
The errors in this experiment were due inexact estimations from computer rapid computer
readings. To increase the accuracy of the data, the lab should be repeated with spring’s
measurements being taken when the spring is completely done oscillating.
5.
Data sheet:
See above under Hooke’s Lab
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Documents
Related Questions
A block of metal measures 12 cm by 10 cm by 10 cm.
When the block is hung from a spring scale, as shown in
Figure 3a, the scale reads 30 kg. This is the "true mass"
of the block. Suppose we attempt to measure the block's
mass under water. The same mass, while hanging from
the same scale, is completely submerged in water, as
shown in Figure 3b. What is the reading (in kilograms)
on the spring scale? Show and explain your work.
Scale
Figure 3a
Figure 3b
arrow_forward
The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 12 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)
arrow_forward
1. Clouds can weigh thousands of pounds due to their liquid water content. Often this content
is measured in grams per cubic meter (g/m³). Assume that a cumulus cloud occupies a volume
of one cubic kilometer, and its liquid water content is 0.2 g/m³. (a) What is the volume of this
cloud in cubic miles? (b) How much does the water in the cloud weigh in pounds?
2. A tank of oil has a mass of 3 0 slugs. (a) Determine its weight in pounds and in newtons at the
earth's surface. (b) What would be its mass (in slugs) and its weight (in pounds) if located on
the moon's surface where the gravitational attraction is approximately one-sixth that at the
earth's surface?
3. If p is a pressure, V a velocity, and p a fluid density, what are the dimensions (in the MLT
system) of (a) p/p, (b) pvp, and (c) p/pV²?
4. The viscosity of a certain fluid is 5 x 104 poise. Determine its viscosity in both SI and BG units.
5. Crude oil having a viscosity of 9.52 X 10 lb-s/ft2 is contained between parallel…
arrow_forward
Use your weight in pounds (while standing on the surface of the Earth) to calculate your mass in the following units (1 kg weighs approx. 2.205 lb on the surface of the Earth). Show all your calculation, how you cancel the units and use the correct number of digits to get credit. Use scientific notation. Weight in pounds = 200 mass in grams = mass in kilograms = mass in teragrams = mass in picograms =
arrow_forward
Please do this carefully.
arrow_forward
The floor area of the model in the image below is 500 square inches, and the floor area of the house is
1,280 square feet. If the model has a room with a side length of 5 inches, then what is the scale factor for
the model to the actual floor?
©2018 AlessandoMassiniano / Getty mages Plus
O 5 in:8 ft
O 5 in:12 ft
O 5 in:36 ft
O 5 in:64 ft
arrow_forward
The unit for density found in many density tables is kg/m cube. At a certain temperature, the gasoline you pump into your car gas tank has a density of 732.22 kg/m cube. If your tank has a capacity of 14.0 gallons, how tank when it is full? How may pounds?
arrow_forward
Kayleigh loves fishing with her grandpa Kevin. Kayleigh was the first one to catch a fish and found out that it weighs 90 Newtons out of the river. When the fish was completely immersed in the river water, the tension of the fishing rod line was 55 N. Her grandpa Kevin proceeded to fish in the muddy part of the river and caught an almost identically sized fish. Kevin measured the tension of his rod line to be 30 N. What is the density of the water in the muddy part of the river?
Remember that the density of water is 997 kg/m³
arrow_forward
hello tutor, i have here questions that have answers. so i am requesting you to provide the necessary solution to come up with the given answer. I hope you help me. thanks
arrow_forward
Some scientists believe that the collision of one or more large asteroids with the Earth was responsible for the extinction of the dinosaurs. The unit of kiloton is used to describe the energy released during large explosions. It
was originally defined as the explosive capability of 1000 tons of trinitrotoluene (TNT) high explosive. Because that expression can be imprecise depending on the explosive's exact chemical composition, the kiloton
subsequently has been redefined as the equivalent of 4.186 x 1012 J. In the units of kiloton, calculate the kinetic energy of an asteroid that has the size (box-shaped, 13 x 13 x 25 km) and composition (density,
2.4 g/cm) of an asteroid. Kinetic energy is defined by
U. =
mv?
where m is the object's mass and v is its speed. Objects passing through the inner solar system generally have speeds in the range of 20 km/s.
(Express your answer using two significant figures.)
Uk =
x1011 kilotons
arrow_forward
What is the ABSOLUTE pressure at point 1 (P1) in kPa? The atmospheric pressure is 102 kPa. The specific gravity of Fluid 2 is
0.66. The heights of the fluids are:
h1 = 0.47 m
h2 = 0.97 m
h3 = 0.41 m
Report your answer to 3 decimal places.
Fluid 2
P2
Fluid 1:
h;
Argon Gas
P1
h2
Fluid 3:
Water,
25 deg C
arrow_forward
Answer this two questions. Thank you
arrow_forward
We have superheated steam at a pressure of 0.05 bar and temperature of 366.62 oC. What is the specific volume in units of m3/kg? Use the steam tables and report your answer to three decimal places.
Note that in the steam tables, the specific volume is reported in units of m3/kg.
arrow_forward
1. Please only use 3 sig fig for answer.
arrow_forward
Directions: Show your complete solutions and box your final answer. Do not round off in between the solutions but round off your final answer to the nearest ten thousandths place(4 decimal places).
1.Find the volume of the fluid in cm3 with a mass of 0.31 kgm and density of 30 lbm/ft3.
arrow_forward
Please solve the problem correctly with the formula.
Mech-engg
arrow_forward
Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre = 43,560 ft2, 1 mile = 5280 ft). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Related Questions
- A block of metal measures 12 cm by 10 cm by 10 cm. When the block is hung from a spring scale, as shown in Figure 3a, the scale reads 30 kg. This is the "true mass" of the block. Suppose we attempt to measure the block's mass under water. The same mass, while hanging from the same scale, is completely submerged in water, as shown in Figure 3b. What is the reading (in kilograms) on the spring scale? Show and explain your work. Scale Figure 3a Figure 3barrow_forwardThe number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 12 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)arrow_forward1. Clouds can weigh thousands of pounds due to their liquid water content. Often this content is measured in grams per cubic meter (g/m³). Assume that a cumulus cloud occupies a volume of one cubic kilometer, and its liquid water content is 0.2 g/m³. (a) What is the volume of this cloud in cubic miles? (b) How much does the water in the cloud weigh in pounds? 2. A tank of oil has a mass of 3 0 slugs. (a) Determine its weight in pounds and in newtons at the earth's surface. (b) What would be its mass (in slugs) and its weight (in pounds) if located on the moon's surface where the gravitational attraction is approximately one-sixth that at the earth's surface? 3. If p is a pressure, V a velocity, and p a fluid density, what are the dimensions (in the MLT system) of (a) p/p, (b) pvp, and (c) p/pV²? 4. The viscosity of a certain fluid is 5 x 104 poise. Determine its viscosity in both SI and BG units. 5. Crude oil having a viscosity of 9.52 X 10 lb-s/ft2 is contained between parallel…arrow_forward
- Use your weight in pounds (while standing on the surface of the Earth) to calculate your mass in the following units (1 kg weighs approx. 2.205 lb on the surface of the Earth). Show all your calculation, how you cancel the units and use the correct number of digits to get credit. Use scientific notation. Weight in pounds = 200 mass in grams = mass in kilograms = mass in teragrams = mass in picograms =arrow_forwardPlease do this carefully.arrow_forwardThe floor area of the model in the image below is 500 square inches, and the floor area of the house is 1,280 square feet. If the model has a room with a side length of 5 inches, then what is the scale factor for the model to the actual floor? ©2018 AlessandoMassiniano / Getty mages Plus O 5 in:8 ft O 5 in:12 ft O 5 in:36 ft O 5 in:64 ftarrow_forward
- The unit for density found in many density tables is kg/m cube. At a certain temperature, the gasoline you pump into your car gas tank has a density of 732.22 kg/m cube. If your tank has a capacity of 14.0 gallons, how tank when it is full? How may pounds?arrow_forwardKayleigh loves fishing with her grandpa Kevin. Kayleigh was the first one to catch a fish and found out that it weighs 90 Newtons out of the river. When the fish was completely immersed in the river water, the tension of the fishing rod line was 55 N. Her grandpa Kevin proceeded to fish in the muddy part of the river and caught an almost identically sized fish. Kevin measured the tension of his rod line to be 30 N. What is the density of the water in the muddy part of the river? Remember that the density of water is 997 kg/m³arrow_forwardhello tutor, i have here questions that have answers. so i am requesting you to provide the necessary solution to come up with the given answer. I hope you help me. thanksarrow_forward
- Some scientists believe that the collision of one or more large asteroids with the Earth was responsible for the extinction of the dinosaurs. The unit of kiloton is used to describe the energy released during large explosions. It was originally defined as the explosive capability of 1000 tons of trinitrotoluene (TNT) high explosive. Because that expression can be imprecise depending on the explosive's exact chemical composition, the kiloton subsequently has been redefined as the equivalent of 4.186 x 1012 J. In the units of kiloton, calculate the kinetic energy of an asteroid that has the size (box-shaped, 13 x 13 x 25 km) and composition (density, 2.4 g/cm) of an asteroid. Kinetic energy is defined by U. = mv? where m is the object's mass and v is its speed. Objects passing through the inner solar system generally have speeds in the range of 20 km/s. (Express your answer using two significant figures.) Uk = x1011 kilotonsarrow_forwardWhat is the ABSOLUTE pressure at point 1 (P1) in kPa? The atmospheric pressure is 102 kPa. The specific gravity of Fluid 2 is 0.66. The heights of the fluids are: h1 = 0.47 m h2 = 0.97 m h3 = 0.41 m Report your answer to 3 decimal places. Fluid 2 P2 Fluid 1: h; Argon Gas P1 h2 Fluid 3: Water, 25 deg Carrow_forwardAnswer this two questions. Thank youarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY