Archimede e corona del re gerone: problema

[cherry8490]

avete presente il famoso problema in cui bisogna determinare la composizione della corona in oro e argento a partire dal peso in aria e in acqua e dalle densità?
mi dareste un imput? io pensavo di utilizzare la legge di archimede dove si eguagliano la forza peso e la forza di archimede..
voi che dite? grazie a tutti!

[Summerwind78]

Ciao

un aiuto relativo alla tua domanda purtroppo non te lo so dare mi spiace...

però posso dirti che "input" si scrive con la "n"

[cherry8490]

si scusa...errore di distrazione

[chiaraotta1]

"cherry8490":avete presente il famoso problema in cui bisogna determinare la composizione della corona in oro e argento a partire dal peso in aria e in acqua e dalle densità?
mi dareste un imput? io pensavo di utilizzare la legge di archimede dove si eguagliano la forza peso e la forza di archimede..
voi che dite? grazie a tutti!

Trovi discusso questo problema alle pgg 467 e 468 di Fundamentals of Physics [Halliday Resnick Walker].

Eureka!
Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. Legend has it that he solved this problem by weighing the crown first in air and then in water, as shown in Figure 15.12. Suppose the scale read 7.84 N in air and 6.86 N in water. What should Archimedes have told the king?
Solution
When the crown is suspended in air, the scale reads the true weight $T_1 = F_g$ (neglecting the buoyancy of air). When it is immersed in water, the buoyant force $B$ reduces the scale reading to an apparent weight of $T_2 = F_g - B$. Hence, the buoyant force exerted on the crown is the difference between its weight in air and its weight in water:
$B = F_g - T_2 = 7.84 text( N) - 6.86 text( N) = 0.98 text( N)$
Because this buoyant force is equal in magnitude to the weight of the displaced water, we have $rho_w g V_w = 0.98 text( N)$, where $V_w$ is the volume of the displaced water and $rho_w$ is its density.
Also, the volume of the crown $V_c$ is equal to the volume of the displaced water because the crown is completely submerged. Therefore,
$V_c = V_w = (0.98 text ( N))/(g rho_w) = (0.98 text ( N))/((9.8 text ( m/s)^2)(1000 text( kg/m)^3))= 1.0 * 10^(-4) text ( m)^3$.
Finally, the density of the crown is
$rho_c = m_c/V_c = (m_c g)/(V_c g) = (7.84 text( N))/((1 * 10^(-4) text ( m)^3)(9.8 text ( m/s)^2)) = 8.0 * 10^3 text( kg/m)^3$.
From Table 15.1 we see that the density of gold is $19.3 * 10^3 text( kg/m)^3$. Thus, Archimedes should have told the king that he had been cheated. Either the crown was hollow, or it was not made of pure gold.

Puoi scaricare il libro completo in formato pdf da qua:
http://www.mediafire.com/?fmb5k771c10eanv
oppure qua:
http://download281.mediafire.com/vya8td ... hysics.pdf

[cherry8490]

"chiaraotta":
Trovi discusso questo problema alle pgg 467 e 468 di Fundamentals of Physics [Halliday Resnick Walker].

Eureka!
Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. Legend has it that he solved this problem by weighing the crown first in air and then in water, as shown in Figure 15.12. Suppose the scale read 7.84 N in air and 6.86 N in water. What should Archimedes have told the king?
Solution
When the crown is suspended in air, the scale reads the true weight $T_1 = F_g$ (neglecting the buoyancy of air). When it is immersed in water, the buoyant force $B$ reduces the scale reading to an apparent weight of $T_2 = F_g - B$. Hence, the buoyant force exerted on the crown is the difference between its weight in air and its weight in water:
$B = F_g - T_2 = 7.84 text( N) - 6.86 text( N) = 0.98 text( N)$
Because this buoyant force is equal in magnitude to the weight of the displaced water, we have $rho_w g V_w = 0.98 text( N)$, where $V_w$ is the volume of the displaced water and $rho_w$ is its density.
Also, the volume of the crown $V_c$ is equal to the volume of the displaced water because the crown is completely submerged. Therefore,
$V_c = V_w = (0.98 text ( N))/(g rho_w) = (0.98 text ( N))/((9.8 text ( m/s)^2)(1000 text( kg/m)^3))= 1.0 * 10^(-4) text ( m)^3$.
Finally, the density of the crown is
$rho_c = m_c/V_c = (m_c g)/(V_c g) = (7.84 text( N))/((1 * 10^(-4) text ( m)^3)(9.8 text ( m/s)^2)) = 8.0 * 10^3 text( kg/m)^3$.
From Table 15.1 we see that the density of gold is $19.3 * 10^3 text( kg/m)^3$. Thus, Archimedes should have told the king that he had been cheated. Either the crown was hollow, or it was not made of pure gold.

Puoi scaricare il libro completo in formato pdf da qua:
http://www.mediafire.com/?fmb5k771c10eanv
oppure qua:
http://download281.mediafire.com/vya8td ... hysics.pdf

ieri sera alla fine sono riuscita a risolverlo...in ogni caso grazie mille per questi utilissimi link grazie davvero!

[mircoFN1]

"chiaraotta":

Puoi scaricare il libro completo in formato pdf da qua:
http://www.mediafire.com/?fmb5k771c10eanv
oppure qua:
http://download281.mediafire.com/vya8td ... hysics.pdf

ma questo è legale?