Download Density, Mass and Surface Area

Density, Mass and Surface Area
To understand the various parametric relationships that describe stars, it is
important that the Astronomy student understand basic physical relationships. Common
terms like size and weight are not precise enough for scientific understanding; it is
better to use diameter and mass to describe some of the physical attributes of stars.
Size (volume) can be scaled by diameter, the largest distance through a sphere, and
weight depends on mass (and what planet you are on). But are size and mass the same
thing?
Before you are the following pieces of equipment:
Object
Diameter
Styrofoam Sphere
100mm
Steel Sphere 1
25mm
Wooden Sphere
25mm
Steel Sphere 2
20mm
…and a triple beam balance scale.
Mass
Density, Mass and Surface Area
Put each sphere one at a time on the scale and get its mass. The scale is just like your
doctor’s scale: add up the readings on each beam to get total mass. Enter these masses in
the appropriate box in the table above.
1) Compare the two steel spheres. Which one is heavier? Which one has more mass?
Considering ONLY these two spheres, would you conclude that bigger objects are
always heavier? Support your answer.
2) A quantity called surface area is important when discussing the luminosity of stars. You
can think of the paint required to cover something as related to surface area. Still
considering only the two steel spheres; if you were to paint each sphere, which would
require more paint? Can you conclude that large spheres always require more paint to
cover their surface?
3) Now compare the Styrofoam sphere and the smaller Steel Sphere 2. Which is heavier?
Which has more mass? Is your earlier conclusion about size and weight still correct?
Support your answer.
4) Still considering the Styrofoam and steel spheres: if you were to paint each sphere,
which would require more paint? Is your earlier conclusion about the size of spheres and
the paint needed to cover their surfaces still correct?
Density, Mass and Surface Area
5) Compare the wooden sphere and the Steel Sphere 1. Which is heavier? Which has
more mass? Can you conclude that objects about the same size always weigh the
same? Support your answer.
6) Still considering the wooden and steel spheres: if you were to paint each sphere, which if
either would require more paint? Can you conclude that spheres of the same size
always require the same paint to cover their surface?
7) Pretend that a special paint emits light. Which painted sphere would be brighter, the
wooden sphere or the Styrofoam sphere? Why?
8) If Star A has twice the diameter of Star B, all else being equal, which star would be
brighter?
Density, Mass and Surface Area
The relationship between diameter and mass yields a third important parameter:
density. The old ‘trick question” goes: which weighs more, a pound of feathers or a
pound of bricks? The clever student will respond: neither, they both weigh a pound, that
is, they have the same mass. But suppose you were asked simply which weighs more,
feathers or bricks? What you really mean is that bricks are more dense.
Density is how much stuff you can squeeze into a certain space. Feathers take
up a lot of room; the same mass of bricks takes up much less room. So you can begin
to see a relationship between density, mass, and diameter.
More mass, same diameter = more density
Bigger diameter, same mass = less density
When talking about stars we say that some stars are massive, but we don’t
necessarily mean huge: we actually mean a lot of mass. Some stars are enormous, with
huge diameters, but are no more massive than the Sun. On the other hand, some stars
aren’t much bigger than the Earth but have more mass than the Sun.
9) Steel Sphere 1 and Steel Sphere 2 both have the same density because they are both
steel. Can you say that if one sphere has more weight of the other it must also have a
bigger diameter? Explain.
10) A linear relationship means that if, for instance, one number is doubled then another
number that is related to it also doubles. Consider the two steel spheres again: if you
doubled the diameter of the smaller sphere (Steel Sphere 2) to 40mm, how much do you
think it would weigh?
Density, Mass and Surface Area
11) Look at your table of spheres: compare the increase in both diameter and mass from
smaller to larger steel sphere. Do you want to change your answer to the previous
question?
12) Star B has twice the diameter of Star A; both are the same density. About how many
times more massive is Star B than Star A?
13) Suppose you take the Sun and squeeze it down to the size of the Earth without ejecting
any mass; what would happen to the density?
14) Suppose instead you take the Sun and puff it up to 20 times its present diameter without
adding any mass; what would happen to its density?