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

Answer:

$\mathbf{G_m = 2.25}$

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;

$G_m = \dfrac{W_{mw}}{v \delta_w} --- (2)$

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

$v \delta_w = \dfrac{W_{ma}}{G_m}$

Now, equation (1) can be rewritten as:

$W_{mw} = W_{ma} - \dfrac{W_{ma}}{G_m}$

$G_m = \dfrac{W_{ma}}{W_{ma} - W_{mw}}$

Replacing the values;

$G_m = \dfrac{1173.5}{1173.5 -652.5}$

$G_m = \dfrac{1173.5}{521}$

$\mathbf{G_m = 2.25}$