in the buoyancy lab, you suspended various metal objects from a force sensor and compared their weight when…

in the buoyancy lab, you suspended various metal objects from a force sensor and compared their weight when suspended in the air and under water. suppose you have a cube of iron, and you hang it from your force sensor, and it reads 22.4 n when the iron is not submerged. if the density of iron is 7,874 kg/m³, what would the force sensor read (in newtons) if the iron was weighed underwater?

in the buoyancy lab, you suspended various metal objects from a force sensor and compared their weight when suspended in the air and under water. suppose you have a cube of iron, and you hang it from your force sensor, and it reads 22.4 n when the iron is not submerged. if the density of iron is 7,874 kg/m³, what would the force sensor read (in newtons) if the iron was weighed underwater?

Answer

Explanation:

Step1: Calculate the volume of the iron cube

We know that weight $W = mg$ and density $\rho=\frac{m}{V}$, so $m = \rho V$. Given $W = 22.4\ N$, and $W=mg$, then $m=\frac{W}{g}=\frac{22.4\ N}{9.8\ m/s^{2}}$. Also, since $\rho = 7874\ kg/m^{3}$ and $\rho=\frac{m}{V}$, we can find $V$. First, $m=\frac{22.4}{9.8}\ kg$. Then $V=\frac{m}{\rho}=\frac{22.4/9.8}{7874}\ m^{3}$. $V=\frac{22.4}{9.8\times7874}\ m^{3}\approx2.92\times 10^{-4}\ m^{3}$

Step2: Calculate the buoyant force

The buoyant force $F_b=\rho_{water}gV$. The density of water $\rho_{water} = 1000\ kg/m^{3}$, $g = 9.8\ m/s^{2}$ and $V$ is the volume we just calculated. $F_b=1000\ kg/m^{3}\times9.8\ m/s^{2}\times2.92\times 10^{-4}\ m^{3}=2.86\ N$

Step3: Calculate the force sensor reading underwater

The force sensor reading underwater $F$ is given by $F = W - F_b$. We know $W = 22.4\ N$ and $F_b=2.86\ N$. $F=22.4 - 2.86=19.54\ N$

Answer:

$19.54$