If you want to design a set of five density rods (made of aluminum, iron, copper, brass, and lead), determine the ratios of the lengths of each rod to the length of the lead rod, the densest material in the group. The specific gravities of the elements are approximately SG alum = 2.7, SG iron = 7.8, SG copper = 8.9, SG brass = 8.5, SG lead = 11.3.


Lalum
Llead
=

Liron
Llead
=

Lcopper
Llead
=

Lbrass
Llead
=

I don't know what the objective is. Is it to have the rods the same mass?

IF so, then the length is inversely proportional to density, to keekp mass constant.
Mass=volume*density=L*area*density

A set of density rods is designed to illustrate the concept of density. The idea is to create cylinders of equal diameters and masses, but varying lengths, to show which have the largest and smallest densities. How do I do it?

Ok, then the mass is the same, so length is inversly prop to density.

take the brass/lead combo.

if the lead say is some length L, then the length of the brass (to have the same mass of lead)
masslead=massbrass
PI r^2 Llead*densitylead=PI r^2 Lbrass*Dbrass

or Lbrass=Llead*densitylead/densitybrass

with all having the same diameter.

How do I do that to answer my question?

Ok, decide on the length of lead rod first. Then use the formula for the other rods like this (for the brass first)

Lbrass=Llead*densitylead/densitybrass

Density of lead is 11.36g/cm3 and density of brass is 8.553g/cm3 but I was not given the lenghts of anything. The info above was the only thing given to me.

you have to specify a length for the standard (lead) if you want a number length. Otherwise, you have to just cite a fraction of Length lead.

They also said Derive a formula that will predict the ratio of the length of one rod to the length of another rod. Assume the radius and mass of each cylinder is the same and express your answer in terms of the specific gravity of each rod. (Use the following as necessary: SG1, SG2.)

L1
L2
I need help on how to do that.

To determine the ratios of the lengths of each rod to the length of the lead rod, we need to compare their densities or specific gravities.

The ratio of the lengths can be determined by considering the densities or specific gravities of the materials. The specific gravity is the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is water, which has a specific gravity of 1.

To find the ratios of the lengths, we can use the formula:
Ratio = Specific Gravity of Material / Specific Gravity of Lead

Let's calculate the ratios for each material:

For aluminum:
Ratio = SG aluminum / SG lead
= 2.7 / 11.3
≈ 0.239

For iron:
Ratio = SG iron / SG lead
= 7.8 / 11.3
≈ 0.690

For copper:
Ratio = SG copper / SG lead
= 8.9 / 11.3
≈ 0.788

For brass:
Ratio = SG brass / SG lead
= 8.5 / 11.3
≈ 0.753

Therefore, the ratios of the lengths of each rod to the length of the lead rod are approximately:
Lalum/Llead ≈ 0.239
Liron/Llead ≈ 0.690
Lcopper/Llead ≈ 0.788
Lbrass/Llead ≈ 0.753