Unit 1 Lab Report
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Yagmurov 1
Roman Yagmurov
Prof. Tuero
Phy2048L
1/28/2024
Unit 1: Measurement Lab Report
Abstract:
I measured the dimensions of a book that I had and of my room, after which I then calculated the mean, standard deviation, and relative error of my measurements of the book. I also used the mean data to calculate the volume of my book. I then calculated the volume of the room as well. Furthermore, interested in finding the weight of the air occupying my room, I decided to calculate it. After looking through various sources online, as well as my Physics textbook, I found that the density of air is 1.29 kg/m^3. This would be important as it would allow me to find the mass of the air in my room without actually having to weigh the air (I don’t think that’s possible yet with our technology). With this information in hand, I then calculated the weight of the air, which is just the measure of the force of gravity acting on it.
Yagmurov 2
Introduction:
In this lab, I will be measuring the dimensions of certain objects, calculating statistical values regarding those dimensions, as well as finding the weight of air that is in my room. For this, it is important to know that volume is the measure of the amount of stuff that can fit into an object, that density is a constant ratio for an object, and that there will always be inaccuracies in measurement due to human error or uncalibrated equipment. I will be measuring everything with either a 32-cm ruler or a meter stick. General Principles:
In this lab, I am measuring the dimensions of a book and the room that I am
in, as well as finding the volumes of those two objects. Along with finding the dimensions, another goal of this lab is to find the mean, standard deviation, and relative error of the data. The mean is just the average of the data, and it helps see what the true value of the measurement may be. The standard deviation shows how off the measurements are from the mean, which can be used to see if the measuring methods or equipment is sub-par. The relative error is the ratio of the standard deviation to the mean, which is useful to see inefficiencies in experimentation. Since
we are calculating volume of different objects in this lab, it is important to conceptualize what volume is. Volume is the physical measure of how much stuff can fit into an object based on its dimensions. Usually, to find out volume, you can either use water and a measuring cup or measure the object and do mathematical calculations, which is what I am using in this lab. Since I am measuring the volume of mostly rectangular shapes (a book and a flat-ceiling room), I will simply multiply the dimensions that I measure out. Furthermore, since the next part of the lab requires me to find out the weight of the air in the room that I will measure, I will need to use the
concepts of density and weight. Density is a set ratio of a material/object that compares its mass to its volume; it is always constant for a material/object but almost all things have different densities. Weight is the measure of an object’s mass under the effect of gravity. In other words,
Yagmurov 3
weight is just mass multiplied by the acceleration due to gravity. In this lab, density will be useful as I can’t directly measure the mass of air, but I can calculate it by multiplying its density by the volume of the room it occupies. With the found mass, I can then simply calculate the weight of the air by multiplying the mass by the acceleration due to gravity on Earth.
Methods:
I measured the book with a ruler and recorded the findings, after which I utilized the formulas to find the numbers I needed. To measure the room, I used a meter stick and my height as an approximation to the height of the room, after which I used the necessary formulas and numbers to calculate the weight of the air.
Results:
In this lab, I had to measure the thickness, length, and width of a book. Here are the results:
Measurement (cm)
Width
Length
Thickness
Trial 1
16
23.15
2.85
Trial 2
16.05
23.15
2.83
Trial 3
16.05
23.1
2.84
Trial 4
16.03
23.13
2.83
Trial 5
16.05
23.15
2.86
Trial 6
16
23.14
2.83
Trial 7
16.1
23.09
2.84
The mean values for each were calculated with the formula M
=
1
N
∑
i
N
M
i
where N is the number of trials. The deviations of each value were calculated with d
i
=
M
i
−
M
. The standard deviation was found using σ
i
=
√
1
N
√
∑
i
N
|
d
i
|
2
. The relative error of the data set was found using ε
L
=
σ
i
L
. Here are the results:
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Related Questions
The first length measured in a laboratory experiment is 2.5 ± 0.1 m and the second length is 3.4 ± 0.1 m.a. What is the sum of the lengths?b. What is the difference in the lengths?c. What is the percentage uncertainty in each a and b?
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A. Volume Measurement
Problem: You have 3 empty containers. One container holds 3L, a second holds
5L and a third, holds 9L. How can you use these containers to measure
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Follow the steps and write what you did to get 7L.
Frame on Volume Measurement
Step
1
2
3
5
3-L container
5-L container 9-L container Total number of
Liters
To get exactly 7liters from 3 containers holding 3L, 5L and 9L, I did these steps:
First,
Second,
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Question 8
A student obtains a set of measurements for the mass, and size (length, width and
height) of a iron anvil. They then compared their results with the known value for the
anvil.
They find that their results were off by about 20%. The student then repeats the
measurements multiple times, average all of the results and find that now their results
are only off by about 2%.
In this case, which of the follow statements best describes the experimental
uncertainty?
Systematic uncertainty
Random uncertainty
Human error
O Broken equipment
Question 9
The same student obtains a new set of measurements for the mass, and size (length,
width and height) of a different iron anvil and compared their results with the known
value for that anvil.
They find that their new results were off, again, by about 20%. The student then
repeats the measurements multiple times, average all of the results and find that their
results are STILL off by the same amount.
In this case, which of the follow…
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Kevin (nm)
Sally (nm)
107.0
Trial No.
Tom (nm)
1.
103.7
107.7
2.
105.6
101.1
107.5
3.
106.9
105.4
107.9
Mean
105.4
104.5
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None of the given options
Tom's measurement is most precise, and Kelly's measurement is most accurate.
Sally's measurement is most precise, and Kelly's measurement is most accurate.
Kevin's measurement is most precise, and Tom's measurement is most accurate
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Question 8
A student obtains a set of measurements for the mass, and size (length, width and
height) of a iron anvil. They then compared their results with the known value for the
anvil.
They find that their results were off by about 20%. The student then repeats the
measurements multiple times, average all of the results and find that now their results
are only off by about 2%.
In this case, which of the follow statements best describes the experimental
uncertainty?
Human error
Broken equipment
Random uncertainty
Systematic uncertainty
Question 9
The same student obtains a new set of measurements for the mass, and size (length,
width and height) of a different iron anvil and compared their results with the known
value for that anvil.
They find that their new results were off, again, by about 20%. The student then
repeats the measurements multiple times, average all of the results and find that their
results are STILL off by the same amount.
In this case, which of the follow statements…
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The accepted value of the density of aluminum at standard temperature and pressure is 2.70 g/cm³ What is the discrepancy
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Is this
discrepancy significant?
QUESTION 9
The accepted value of the density of aluminum is 2.70 g/cm³ while our computed value is 2.8 g/cm³ What is the percent
uncertainty of our experimental density (observing correct significant figures)?
a. 0.037
Ob.37
c.3.70
d.4
0.5 poin
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Question 2
The following figure shows a balance used to measure the mass of an orange cylinder.
Read the value of that mass from the balance scale.
40
50
60
O a. m= (44± 2) gram
O b. m= (44+1) gram
Ocm=(42±1) gram
O d. m= ( 43 +2) gram
A Moving to the next question prevents changes to this answer.
Tearis
DAT (2)
O Type here to search
Lenovo
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Question 7
In a measurement of B two results were obtained,
B₁ = (2x10^-3) T and B₁ = (1.00x10^-4) T
B2 = (2.0x10^-3) T and B₂ = (7.00x10^-4) T
The result of the comparison test is
Report your answer to 1 significant figures.
Note: Your answer is assumed to be reduced to the highest power possible.
Your Answer:
Answer
x10
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tabletop
91.41m±0.05m
cube ruler
clipper
micrometer Triple beam balai digital balance
3.30cm±0.05cm 2.184±0.001cm 27.310±0.005mm 64.42±0.05g 64.58±0.01g
2.92m±0.05m 2.71cm±0.05cm 2.482±0.001cm 25.251+0.005mm
216.20m±0.05m 2.50cm±0.05cm 3.136±0.001cm 34.140±10.0005mm
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UNCERTAINTIES IN MEASUREMENT:
1.the dimensions of a metal cylinder were measured three times and yielded the following result:
-height=5.50cm,5.48cm,5.48cm
-diameter=2.50cm,2.54cm,2.54cm
Find:
a) True value (height) of the cylinder
b) True value (diameter ) of the cylinder
c) relative uncertainty of the height of the cylinder
d)the percentage uncertainty of its diameter
e)the volume of the cylinder based on the true values of its dimensions
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Physics
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Question Details
SerEssen1 1.P.027. [35052
Estimate the number of 1.8 cm radius Ping-Pong balls that would fit into a 10 ft by 11 ft room with a ceiling 8 ft high
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balls
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Q2 /
unit cell of a hypbthfetioaing figure shows the-
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1. The following data are the measurements of the dimensions of a box: l = 8.6 ± 0.5 cm
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a. What is the absolute uncertainty for the following measurements? 5.8 cm, 5.6 cm, 5.7 cm, 5.4 cm, 5.4 cm, 5.6 cm
b. Determine the fractional uncertainty in part a.
c. Determine the percentage uncertainty in part a.
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Q 6 please
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C. leas t del Niu
3. Three students make measurements (in m) of the length of a rod using a meter stick. Each
student's measurements are tabulated in the table below. Using your calculator in statistic
mode calculate the mean L, standard deviation S and uncertainty u of the measurements.
Student
L1
L3
L2
1.4711
L4
1.4715
SD
u
Student 1
1.4717
1.4722
1,4716
t.4754
1.4710
1.4753
1.4759
1.4756
1.4749
Student 2
Student 3
1.4719
1.4723
1.4705
1.4719
Note that the actual length of the rod is determined by a laser measurement technique to be
1.4715 m (this should be considered the standard value).
a) State how one determines the accuracy of a measurement. Apply your idea to the
measurements of the three students above and state which student has the most
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2.) A typical person has an average heart rate of 69.0 beats/min. Calculate the given questions. How many beats does she have in 7.0 years? How many beats in 7.00 years? And finally, how many beats in 7.000 years? Pay close attention to significant figures in this question.
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12.
DETAILS
PREVIOUS ANSWERS
OSCOLPHYS2016 1,3.P.015.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Suppose that a person has an average heart rate of 98.4 beats/min. (Express your answers to problems in this section to the correct number of significant figures and proper units.)
(a) How many beats does he or she have in 4.0 y?
4.0
X Your answer cannot be understood or graded. More Information beats
(b) How many beats does he or she have in 4.00 y?
4.0
Check the number of significant figures. More Information. beats
(9) How many beats does he or she have in 4.000 y?
4.0
Check the number of significant figures. More Information. beats
Enter a number with the correct number of significant figures.
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15
1.75
13
1.63
11
1.5
9
1.35
7
1.19
5
1.01
3
0.78
A. Graph these data
B. Describe the graph
C. Using the data, calculate 1/2t^2 and complete
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b)the relative uncertainty of the mass of the liquid
c)the percentage uncertainty of its mass
d)the density of the liquid
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YOUR TEACHER
PRACTICE ANOTHER
Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Hosteller formula gives one way of estimating body surface
area B, in square meters. The formula uses the welight w, in kilograms, and the height h, in centimeters. The relation is
/hw
Consider a man who weighs 80 kilograms
(a) write a formula for B as a function of h.
60
(b) what height range will resut in a body surface area range from 1.7 to 2 souare meters?
Ohsi80.00 cm
Ons130.0s cm or h a 160.00 cm
O no solution
130.05 cmshs180.00 cm
On2130.05 cm
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