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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

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

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter1: Introduction To Statics
Section: Chapter Questions
Problem 1.12P: A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance...
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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
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