Physics, 03.10.2019 01:30 gioc3948

Let ρal represent the density of aluminum and ρfe that of iron. find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rfe on an equal-arm balance. (use any variable or symbol stated above as necessary.)

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Because the balancing arm is equal, therefore the masses of the aluminum and iron spheres are equal.

Define
$r_{A}$ = radius of aluminum sphere
$r_{I}$ = radius of iron sphere
$\rho _{A}$ = density of aluminum
$\rho _{I}$ = density of iron

Therefore
$\frac{4 \pi }{3} r_{A}^{3} \rho _{A} = \frac{4 \pi }{3} r_{I}^{3} \rho _{I} \\\\ r_{A}^{3} = \frac{\rho _{I}}{\rho_{A}} r_{I}^{3} \\\\ r_{A} = r_{I} ( \frac{\rho _{I}}{\rho _{A}})^{1/3}$

$r_{A} = r_{I} ( \frac{\rho _{I}}{\rho _{A}} )^{1/3}$

Answer from: carmen69

The radius of a solid aluminum sphere that balances a solid iron sphere of radius rFe on an equal-arm balance

$r_{Al}~=~r_{Fe}\sqrt[3]{\frac{\rho.Fe}{\rho.Al} } }$

Further explanation

Density is the amount derived from mass and volume

density is the ratio of mass per unit volume

With the same mass, the volume of objects that have a high density will be smaller than objects with a smaller density

The unit of density can be expressed in g / cm³ or kg / m³

Density formula:

$\large{\boxed{\bold{\rho~=~\frac{m}{V} }}}$

ρ = density

m = mass

v = volume

A common example is the density of water 1 gr / cm³

the mass itself can be measured by the balance sheet, the arm balance

Known density of Al (aluminum) and Fe (iron)

Because both are spherical, the volume = $\frac{4}{3} .\pi .r^3$

the mass of the two metals is the same because the scales are equal

mass Al = mass of Fe

ρ. V Al = ρ.V Fe

$\rho.V_{Al}~=~\rho.V_{Fe}$

$\rho_{Al}.\frac{4}{3} \pi.r^3~=~\rho_{Fe}.\frac{4}{3} .r^3$

$r^3_{Al}~=~\frac{\rho_{Fe}.\frac{4}{3}.\pi.r_{Fe}^3 }{\rho_{Al}.\frac{4}{3} \pi }$

$r_{Al}~=~r_{Fe}\sqrt[3]{\frac{\rho.Fe}{\rho.Al} } }$

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Keywords: density, volume, mass, arm balance

Let ρal represent the density of aluminum and ρfe that of iron. find the radius of a solid aluminum

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Let ρal represent the density of aluminum and ρfe that of iron. find the radius of a solid aluminum...