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1 Two student, Lee and Melanie, each hold a solid object. Lee has solid object A and Melanie has solid object B. The students make the following observations:

Larry: "My object has three times the mass of object B and since density is directly proportional to mass, my object has 3 times the density of object B."

Melanie: "My object takes up 1/3 of the volume of object A, and since density is inversely proportional to mass, my object is 3 times as dense as object A."

a) which student, if either, is correct?

b) If the statements about the mass and the volumes of each object are correct, how do the densities of each object compare?

2007-07-23 12:59:18 · 4 answers · asked by sunshinegirl93534 2 in Science & Mathematics Physics

4 answers

No one is corret, because mass and volume TOGETHER result in density, so you have to consider both in order to draw conclusions.

if A is 3 times heavier than B and also three times bigger than B, their densities are the same. It goes the same for B: If B is 3 times lighter and also 3 times smaller than A, their densities are the same.

density A = m / V
density B = (m / 3) / (V / 3) = m / V

conclusion:
density A = density B

2007-07-23 13:55:04 · answer #1 · answered by Anonymous · 0 0

I think you meant to say "density is inversely proportional to volume" in Melanie's statement. Correct me if I'm wrong, but aren't Lee and Larry the same person?

Consider the following fact: The density of an object is its mass divided by its volume.

So, if an object has twice the mass of another, but also twice the volume, then it has the same density as the other object. In fact, neither of the students' answers is correct. Only by knowing the relative masses AND relative volumes of the two objects can the relative density be calculated.

If Lee/Larry's object has mass m and volume V, it has density d.

According to the statements, Melanie's object has 1/3 the mass of Lee/Larry's object, and also 1/3 the volume. Since the mass and volume change by the same proportion, the density of each object is actually the same.

2007-07-23 20:11:15 · answer #2 · answered by lithiumdeuteride 7 · 1 0

a) Both are wrong.
Larry is less wrong: It is at least true that density is proportional to mass. However, without addressing the volume, one cannot make any conclusion about the density.

Melanie is completely wrong: Density is NOT inversely proportional to mass.

b) If it is true that M-a = 3*M-b
and V-b = V-a/3

then
Density-a = M-a/V-a = (3*M-b)/(3*V-b) = M-b/V-b = Density-b

So the densities are identical.

2007-07-23 20:10:49 · answer #3 · answered by ? 6 · 0 0

a) neither.
b) densities are equal

density of A = Da; density of B = Db
mass of A = Ma; mass of B = Mb
volume of A = Va; volume of B= Vb

Da = Ma/Va; Db = Mb/Vb

from the statements: Ma = 3Mb; Vb=(1/3)Va or Va = 3Vb
Da = Ma/Va = 3Mb/3Vb = Mb/Vb = Db

2007-07-23 20:14:25 · answer #4 · answered by gowings! 1 · 0 0

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