Answer to Question #133245 in Mechanics | Relativity for Megan Corby

Question

A scale reads 300 N when a piece of nickel is hanging from it. What does it read (in N) when it is lowered so that the nickel is submerged in water?

_______N

Answer 1

Finding the mass of Nickel:

$W=mg$

W=300N when in the air $m$ is the mass of the piece of nickel and $g=9.8m/s^2$ (acceleration due to gravity).

Therefore;

$m=\frac{W}{g}=\frac{300N}{9.8m/s^2}=30.6kg$

Finding volume of piece of Nickel;

$\rho=\frac{m}{V}$

$\rho$$=8553kg/m^3$ is the density of Nickel and $V$ is the volume of piece of Nickel.

$V=\frac{m}{\rho}=\frac{30.6kg}{8553kg/m^3}=3.58\times10^{-3}m^3$

assuming the upwards to be positive direction and the apparent weight of the piece of Nickel in water directed downward, the force of gravity that acts on the piece of Nickel (or weight) directed downward and the buoyant force directed upward

$-W_{App}=F_B-W$

$W_{App}=W-F_B$

$-W_{App}$ is the apparent weight of the piece of Nickel submerged in water.

$F_B=\rho_wV_wg=\rho_wVg$ is the buoyant force acting on the piece of Nickel; $\rho=1000kg/m^3$ is the density of the water.$V_w$ is the volume the water displaced by the piece of Nickel.

Finding the scale readings of the Piece of Nickel submerged in water.

$W_App=W-\rho_wVg$

$W_{App}=300N-1000kg/m^3\times3.58\times10^{-3}\times9.8m/s^2$

=264N