The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in the figure below. Mass Best-fit line Ax Volume Best-fit line equation: y = mx + b b=y-intercept m = slope

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
icon
Related questions
Question

a. how will you calculate the value of the slope of this best-fit line?

b. How will the value of the slope help you identify the unknown material that the cylinders are made of?

The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of
the line, and b represents the y-intercept. This is illustrated in the figure below.
Mass
Best-fit line
+
Ax
Volume
Ay
The y-intercept (b) is the point on the y-axis where the line crosses the axis. In this experiment, the
value of b should be equal to zero. This is because if there is no mass, the volume must also be zero.
However, note that your best-fit line might not pass exactly through the origin (0,0) due to experimental
error - but it should be quite close.
The slope of the line (m) is the change in the y-axis values divided by the change in x-axis values (or,
rise over run):
m=
m =
Best-fit line equation: y = mx + b
b=y-intercept
m = slope
AyY₁-Y₂
=
x₁ - x₂
Ax
Since Ay is really the change in mass (Amass), and Ax is really the change in volume (Avolume), this
means that the slope of the best-fit line yields the density of the unknown material:
Ay
Ax
Amass
Avolume
Once the density is determined in this manner, it will be used to identify the unknown material analyzed.
= density
Transcribed Image Text:The equation of this best-fit line will have the familiar form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. This is illustrated in the figure below. Mass Best-fit line + Ax Volume Ay The y-intercept (b) is the point on the y-axis where the line crosses the axis. In this experiment, the value of b should be equal to zero. This is because if there is no mass, the volume must also be zero. However, note that your best-fit line might not pass exactly through the origin (0,0) due to experimental error - but it should be quite close. The slope of the line (m) is the change in the y-axis values divided by the change in x-axis values (or, rise over run): m= m = Best-fit line equation: y = mx + b b=y-intercept m = slope AyY₁-Y₂ = x₁ - x₂ Ax Since Ay is really the change in mass (Amass), and Ax is really the change in volume (Avolume), this means that the slope of the best-fit line yields the density of the unknown material: Ay Ax Amass Avolume Once the density is determined in this manner, it will be used to identify the unknown material analyzed. = density
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Slope and Deflection
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY