Question

archimedes principal A cylindrical body of diameter d heigh h and mass m is completely immersed in fluid of density pf

Archimedes Principle Pre-Lab Completely READ the entire lab before coming to lab class. You may be given a laboratory quiz based on information contained in this lab. The pre-lab must be submitted to the lab instructor at the beginning of lab. Write your answer(s) on the opposite side of this sheet of paper and submit this page to the instructor at the beginning of laboratory. A cylindrical body of diameter d, height h, and mass m is completely immersed in a fluid of density pr 1) Write an for m's density in terms of m, d, and h. 2) write an expression for the buoyant force acting on m in terms py, g, d, and h by a of 3) Derive an expression for the apparent weight Wrof m as by a scale if is attached light string to the scale and is completely immersed in the fluid. Your answer should be in 4) terms of p, m, g, d, and h terms of wi m. and Given an apparent weight of Wa write an expression for m's buoyancy in 5) g only. expression density in terms of w py, g, d. Given an apparent weight of Wa write an for m 's and h only

Answer 1

1) Density of the body is given by :

4m 7m

2) Bouyant force acting on m is given by :

gpfT

3) Apparent weight of the body = Actual weight of the body - Weight of liquid displaced

$\therefore W_f = mg - \rho_f V_f g = mg - \frac{\rho_f \pi d^2 hg}{4}$

4) Bouyancy or bouyant force is given by :

$F= (\rho_f-\rho) V_fg =\rho_fV_fg - mg =-W_f$

5)

Density of body Density of fluid Weight of body Weight of fluid

or, $\frac{\rho}{\rho_f} = \frac{mg}{mg - W_f} \\\Rightarrow \boxed{\rho = \frac{mg\rho_f}{mg - W_f}}$