Mechanical properties of matter problem,

[StudentPhys]

Mechanical properties of matter problem, urgent!

Homework Statement

When a beaker partially filled with water is placed on an accurate scale, the scale reads 22g . If a piece of metal with density 3800 kg/m^3 and volume 2,4 cm^3 is suspended by a thin string so that the metal is submerged in the water but does not rest at the bottom of the beaker, what does the scale read?

Homework Equations

Fnet=0
Fb= mg-Fs
N(y) + Fs(Y)+mg(-y)+(22*g)(-y)=0

The Attempt at a Solution

V=2,4cm^3=2.4*10^-6 m^3 density= 3800 kg/m^3
mass metal= 0,00912 [kg]
System Metall: Fs+ Fb+ mg= 0
Fb= mg-Fs
System: Beaker + Metall+ H20
System : Beaker + metall + h20
N(y) + Fs(Y)+mg(-y)+(22*g)(-y)=0
N= 22*g+ Fb
solving for N= 9.8 / 24.4*10^-3)

Is this the right way of solving the problem? Are there other methods-easier? In that case please let me know, asap i have a crucial-grade determining -test in 2 days!

Btw , another question, how come in the equation for the Bigger system , one disregards the buoyancy force but then is allowed to plug it in ?
Thanks in advance

 

[jbsteele]

! Yes, your solution is correct. You have correctly used the equations of equilibrium and calculated the net force on the system.The buoyancy force is not included in the equation for the bigger system because it does not act on the whole system. The buoyancy force only acts on the metal, so it is included in the equation for the metal.