Respuesta :
Answer:
a) the density of the object is 1.9302 g/mL
b) The procedure used to determine the density of a solid, is the principle of Archimeides
c) In order to use this procedure we had to assume a total volume of the fluid mixture and a percentage of the solid submerged in this
Explanation:
- assuming the volume of the mixture is: vAB = 1000 mL
⇒ vA = 413.7 mL ∧ vB = 586.3 mL
mix (A+B) density = mass AB / volume AB
∴ mAB = mA + mB
⇒ mA = vA * dA = 413.7 mL * 2.0514 g/mL = 848.664 g A
⇒ mB = vB * dB = 586.3 mL * 2.6678 g/mL = 1564.13 g B
⇒ mAB = 2412.795 g AB
⇒ mix density = 2412.795 g / 1000 mL = 2.4127 g/mL AB
Starting from the principle of Archimides to find the density of a solid suspended in a liquid, we have:
- E = dAB * g * Vs ........ (1)
∴ Vs : submerged solid volume;
∴ E : fluid weight displaced by the solid
∴ dAB : mix density
∴ g : gravity
in the sum of forces: ∑F = 0
⇒ E - Wsolid = 0
⇒ E = Wsolid
∴ Wsolid = msolid * g........... (2)
(1) = (2)
⇒ msolid * g = dAB * g * Vs
⇒ msolid = dsolid * Vs......(3)
∴ msolid = dsolid * Vsolid
- assuming that 80% of the solid is submerged in the mixture, we have:
⇒ Vs = 0.8 * Vsolid.....(4)
(4) in (3):
⇒ dsolid * Vsolid = dAB * 0.8 * Vsolid
⇒ dsolid = dAB * o.8
⇒ dsolid = 2.4127 g/mL * 0.8 = 1.9302 g/mL
