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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.

Sagot :

ajeigbeibraheem

Answer:

[tex]\mathbf{G_m = 2.25}[/tex]

Explanation:

From the given information:

Let the weight of the mix in the air be = [tex]W_{ma}[/tex]

Let the weight of the mix in water be = [tex]W_{mw}[/tex]; &

the bulk specific gravity be = [tex]G_m[/tex]

SO;

[tex]W_{mw} = W_{ma} - v \delta _{w} --- (1)[/tex]

Also;

[tex]G_m = \dfrac{W_{mw}}{v \delta_w} --- (2)[/tex]

From (2), make[tex]v \delta_w[/tex] the subject:

[tex]v \delta_w = \dfrac{W_{ma}}{G_m}[/tex]

Now, equation (1) can be rewritten as:

[tex]W_{mw} = W_{ma} - \dfrac{W_{ma}}{G_m}[/tex]

[tex]G_m = \dfrac{W_{ma}}{W_{ma} - W_{mw}}[/tex]

Replacing the values;

[tex]G_m = \dfrac{1173.5}{1173.5 -652.5}[/tex]

[tex]G_m = \dfrac{1173.5}{521}[/tex]

[tex]\mathbf{G_m = 2.25}[/tex]

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