Need help with this equation

[megadeth95]

Hi guys, I need help with the following problems:

1. Find an equation for the mass of the moon in terms of the mass of the cheese sample, the volume of the cheese sample, and the volume of the moon (V=4/3*pi*r^³)

*mass of the cheese sample

weight: 454 grams
mass = 46.3 grams/m/s²

*Volume of the cheese sample

radius = 4.8 cm

v=4/3 * (3.14) * (4.8)³
v=463 cm³

*Volume of the moon

radius= 1.738 * 10⁸ cm?? (please confirm this, thank you)

v=4/3 * (3.14) * (1.738 * 10⁸cm)³
v=2.2 * 10²⁵ cm³

This is the equation I have so far

Mass(moon) = Mass (cheese) (Volume(cheese)/Volume(moon))

Is this right???


Thanks!

 

[mmm4444bot]

*mass of the cheese sample

weight: 454 grams
mass = 46.3 grams/m/s²

Is this result the mass of the cheese ball on the moon, with the same cheese ball having a 454-g mass on the earth? (I do not understand why the unit is g/m/s^2.)

*Volume of the moon

radius= 1.738 * 10⁸ cm?? (please confirm this, thank you)

The mean volume of the moon is generally reported as 1738.1 km, so you're safe to use 1.7381*10^8 cm.

Are you rounding-off intermediate results?

This is the equation I have so far

Mass(moon) = Mass (cheese) (Volume(cheese)/Volume(moon))

I'm thinking that ratio may be (Volume(moon)/Volume(cheese)).

Did you start with the following proportion and then solve for Mass(moon)?

Mass(moon)/Volume(moon) = Mass(cheese)/Volume(cheese)

It may help tutors here, if you post the exact wording of the given exercise.

Cheers :cool:

 

[Fanguy67]

Mass does not change

Megadeth95, I think you're getting your mass and weight mixed up. The cheese has the same MASS, regardless of where it is located, on the moon, on the Earth, or on Neptune. If the mass was given as 454 g, then that is the mass.

However, the question was posted as find an equation to determine the mass of the moon based on the mass of the cheese and the volume of the moon and the cheese sample. The actual radius figures do not initially relate to finding the equation.

You are on the right track with your equation but have mixed up some terms. Once you get the equation sorted out, you can substitute the volume equations and also eliminate like terms. You should find that the equation should take the form mass(cheese) x radius^3 / radius ^3

The actual radius values should not interfere with your creation of the equation.

Good luck!

Is this result the mass of the cheese ball on the moon, with the same cheese ball having a 454-g mass on the earth? (I do not understand why the unit is g/m/s^2.)




The mean volume of the moon is generally reported as 1738.1 km, so you're safe to use 1.7381*10^8 cm.

Are you rounding-off intermediate results?




I'm thinking that ratio may be (Volume(moon)/Volume(cheese)).

Did you start with the following proportion and then solve for Mass(moon)?

Mass(moon)/Volume(moon) = Mass(cheese)/Volume(cheese)

It may help tutors here, if you post the exact wording of the given exercise.

Cheers :cool:

 

[HallsofIvy]

I think we are misunderstanding the problem. It does NOT ask for the mass of the moon assuming there is a given mass of a sample of cheese ON the moon because, as fanguy67 said, the mass does not change, the weight, which we are not given, does.

Rather, the problem is asking 'what is the mass of the moon assuming it is made of cheese'! (Green cheese, of course).

The density of the cheese (and so the moon) is (mass/volume)_cheese and that must be multiplied by the volume of the moon. "density= density" gives "\(\displaystyle \frac{mass_{moon}}{volume_{moon}}= \frac{mass_cheese}{volume_chees}\)", NOT, as megadeth95 has it "\(\displaystyle (mass_{moon})(volume_moon)= (mass_{cheese})(volume_{cheese})\)".