Help understanding a distance problem

• kari82
In summary, a student performed an experiment with various shapes cut from copy paper and created a graph showing a linear relationship between the mass and area of the cutouts. The slope of the line represents the areal density of the paper, and this result is expected due to the uniform thickness and density of the paper.
kari82
This is a review problem, I have the solution but I cannot understand the way my professor solved the problem. Can someone be kind enough to help me understand? Thanks!

A student is supplied with a stack of copy paper, ruler, compass, scissors, and a sensitive balance. He cuts out various shapes in various sizes, calculates their areas, measures their masses, and prepares the graph of Figure I4 (see attachment). Consider the fourth experimental point from the top. How far is it from the best-fit straight line?

(c) Express both of the answers to parts (a) and (b) as a percentage.
(d) Calculate the slope of the line.
(e) State what the graph demonstrates, referring to the shape of the graph and the results of parts (c) and (d).
(f) Describe whether this result should be expected theoretically. Describe the physical meaning of the slope.

(a) We read from the graph a vertical separation of 0.3 spaces = 0.015 g.
(b) Horizontally, 0.6 spaces = 30 cm2.
(c) Because the graph line goes through the origin, the same percentage describes the
vertical and the horizontal scatter: 30 cm2/380 cm2 = 8%.
(d) Choose a grid point on the line far from the origin: slope = 0.31 g/600 cm2 = 0.000 52
g/cm2 = (0.000 52 g/cm2)(10 000 cm2/1 m2) = 5.2 g/m2 .
(e) For any and all shapes cut from this copy paper, the mass of the cutout is proportional
to its area. The proportionality constant is 5.2 g/m2 ± 8%, where the uncertainty is
estimated.
(f) This result should be expected if the paper has thickness and density that are uniform
within the experimental uncertainty. The slope is the areal density of the paper, its mass per unit area.

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This means that the paper has a consistent thickness and density throughout, which is expected in a stack of copy paper. The graph demonstrates a linear relationship between the mass and the area of the cutouts, with a proportionality constant of 5.2 g/m2. This result is expected theoretically because the paper should have a consistent thickness and density throughout, leading to a proportional relationship between mass and area. The slope of the line represents the areal density of the paper, which is an important physical characteristic of the paper.

1. How do I calculate distance?

To calculate distance, you will need to use the formula D = RT, where D is the distance, R is the rate, and T is the time. Plug in the known values and solve for the missing variable.

2. What is the difference between distance and displacement?

Distance is the actual length between two points, while displacement is the shortest distance between the two points, taking into account the direction of movement.

3. How do I convert between different units of distance?

To convert between units of distance, you will need to use conversion factors. For example, to convert from miles to kilometers, you can use the conversion factor 1 mile = 1.60934 kilometers.

4. What is the difference between speed and velocity?

Speed is the rate at which an object is moving, while velocity is the speed and direction of an object's movement.

5. How can I use distance to find the time of travel?

You can use the formula T = D/R to find the time of travel, where T is time, D is distance, and R is the rate. Rearrange the formula to solve for T.

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