Question

An asphalt binder is mixed with aggregate and compacted into a sample. The mass of the dry sample is 1173.5 g, the mass of the sample submerged and then surface-dried with a damp towel is 1175.5 g, and the mass of the sample completely submerged in water is 652.5 g. Find the bulk specific gravity of the compacted sample.

Answer 1

`\mathbf{G_m = 2.25}`

Step-by-step explanation:

From the given information:

Let the weight of the mix in the air be =
`W_(ma)`

Let the weight of the mix in water be =
`W_(mw)`; &

the bulk specific gravity be =
`G_m`

SO;

`W_(mw) = W_(ma) - v \delta _(w) --- (1)`

Also;

`G_m = (W_(mw))/(v \delta_w) --- (2)`

From (2), make
`v \delta_w` the subject:

`v \delta_w = (W_(ma))/(G_m)`

Now, equation (1) can be rewritten as:

`W_(mw) = W_(ma) - (W_(ma))/(G_m)`

`G_m = (W_(ma))/(W_(ma) - W_(mw))`

Replacing the values;

`G_m = (1173.5)/(1173.5 -652.5)`

`G_m = (1173.5)/(521)`

`\mathbf{G_m = 2.25}`