Answer to Question #272770 in Classical Mechanics for joseph

Question

1. A 200-kg granite rock (p = 2700 kg/m³) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

2. The hull of a boat has a volume of 180 m³, and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking (a) in a lake and (b) in seawater with a specific gravity of 1.03.

3. It is estimated that 90 percent of an iceberg’s volume is below the surface, while only 10 percent is visible above the surface. For seawater with a density of 1025 kg/m³, estimate the density of the iceberg.

4. The weight of a body is usually measured by disregarding buoyancy force applied by the air. Consider a 20-cm-diameter spherical body of density 7800 kg/m³. What is the percentage error associated with the neglecting of air buoyancy?

Answer 1

1.

$F=mg-\rho_w gV=\frac{\rho-\rho_w}{\rho}mg=1260~N,$ can't,

2.

a)

$m_1=\rho_1V-m=171.4~tn,$

b)

$m_2=\rho_2V-m=176.8~tn,$

3.

$\rho_w g\cdot 0.9V=\rho_i gV,$

$\rho_i=0.9\rho_w=923~\frac{kg}{m^3},$

4.

$n=\frac{F_A}{P}=\frac{\rho_a g V}{\rho g V}=\frac{\rho_a}{\rho}=0.00017=0.017\%.$