(a)
The position of fourth experimental point from the top from the best fit straight line as the difference in y-axis co-ordinate.
(a)
Answer to Problem 51P
The position of fourth experimental point from the best fit straight line is
Explanation of Solution
The experimental point is denoted by a circle and the point under consideration is the one which lies near the point
Write the equation to find mass equivalent from vertical separation.
Here,
Conclusion:
Substitute
Therefore, the position of fourth experimental point from the best fit straight line is
(b)
Find the percentage equivalent of part (a).
(b)
Answer to Problem 51P
Percentage equivalent is
Explanation of Solution
The y-coordinate of point on best fit line so closer to the fourth experimental point from the top is
Write the expression to calculate the percentage equivalent of vertical difference between the point and curve fit line.
Here,
Conclusion:
Substitute
Therefore, the percentage equivalent is
(c)
The slope of line.
(c)
Answer to Problem 51P
The slope of line is
Explanation of Solution
To find the slope, consider the points
Write the expression to find the slope.
Here,
Conclusion:
Substitute
Therefore, the slope of line is
(d)
The inferences from the shape of graph and results of part (a) and (b).
(d)
Answer to Problem 51P
The shape of graph tells that the mass is directly proportional to area and the value of proportionality constant is
Explanation of Solution
The graph is a straight line with mass on y-axis and area on x-axis. The straight line indicates that the quantity plotted on y-axis is linearly proportional to the quantity plotted on x-axis. The proportionality constant will be the slope. It is found that in part (c), the slope is
Therefore, the shape of graph tells that the mass is directly proportional to area and the value of proportionality constant is
(e)
Check whether the result of part (d) can be expected theoretically or not.
(e)
Answer to Problem 51P
The result of part (d) holds theoretically only if the density and thickness of paper is uniform in the limits of experimental uncertainty.
Explanation of Solution
For result in part (d) to hold good by theory also, should satisfy certain conditions. One of the conditions is that the paper must be of uniform thickness, in addition, mass distribution in unit area must be also uniform. Moreover that, both the two mentioned quantities must be within the obtained uncertainty limit.
Therefore, the result of part (d) holds theoretically only if the density and thickness of paper is uniform in the limits of experimental uncertainty.
(f)
Explain the physical significance of slope.
(f)
Answer to Problem 51P
Slope gives the areal density of paper.
Explanation of Solution
In the graph, the mass is plotted along vertical axis and area is plotted long horizontal axis. So the slope actually tells about the mass distribution of paper. In other words, it is called as areal density.
Therefore, the slope of gives the areal density of paper.
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Chapter 1 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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