Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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?