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

`5.000 (g)/(cm^3)`

Step-by-step 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

`(1 \ kg)/(1   \ kg ) = (1000  \ g)/( 1 \ kg)`

`1 = (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

`( 1 \ m^3 )/( 10^6 \ cm^3 ) = 1`

Obtaining the density

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

`5000 (kg)/(m^3) * ( 1 \ m^3 )/( 10^6 \ cm^3 ) *  (1000  \ g)/( 1 \ kg) =5 (g)/(cm^3)`

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