Question

The density of an alloy is 5000 kg/m3. What is the density in g/cm 0.005 @ 0.500 5.000 50.000

Answer 1

Answer:

$5.000 \frac{g}{cm^3}$

Explanation:

We can obtain our answer using conversion factors.

kg to g

We know that 1 kilogram is 1000 grams, this is

$1 \ kg = 1000 \ g$

Now, we can divide both sides by 1 kg

$\frac{1 \ kg}{1   \ kg } = \frac{1000  \ g}{ 1 \ kg}$

$1 = \frac{1000  \ g}{ 1 \ kg}$

The left side of the equations is 1, this means that our conversion factor is dimensionless, and can be multiplied in any equation, without changing the physical meaning of it.

m^3 to cm^3

same as before, we know that 1 m equals 100 cm

$1 \ m = 100 \ cm$

Now, lets take the cube on both side of the equation

$(1 \ m)^3 = (100 \ cm)^3$

$1^3 \ m^3 = 100^3 \ cm^3$

$1 \ m^3 = (10^2)^3 \ cm^3$

$1 \ m^3 = 10^{(2*3)} \ cm^3$

$1 \ m^3 = 10^6 \ cm^3$

Now, we can  divide both sides by 10^6 \ cm^3 to obtain

$\frac{ 1 \ m^3 }{ 10^6 \ cm^3 } = 1$

Obtaining the density

Now, we can simply multiply the density for our conversion factors

$5000 \frac{kg}{m^3} * \frac{ 1 \ m^3 }{ 10^6 \ cm^3 } *  \frac{1000  \ g}{ 1 \ kg} =5 \frac{g}{cm^3}$

We are allowed to do this, as our conversion factors are dimensionless and equal to one.