Answer to Question #185537 in Physics for Ali

Question

A 16.0 kg block of metal measuring 12.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and immersed in water as shown in the figure below. The 12.0 cm dimension is vertical, and the top of the block is 5.55 cm below the surface of the water.

(a) What are the magnitudes of the forces (in N) acting on the top and on the bottom of the block due to the surrounding water? (Use P₀ = 1.0130  10⁵ N/m². Enter your answers accurate to at least four significant figures.)

(b) What is the reading of the spring scale (in N)?

(c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block

Answer 1

a)

$$F_T = (P_0 + h_1\rho g) A\\F_T = (1.013\cdot10^5 +(0.0555)(1000)(9.8))(0.01)\\=1018\ N$$

$$F_B = (P_0 + h_2\rho g) A\\F_T = (1.013\cdot10^5 +(0.1755)(1000)(9.8))(0.01)\\=1030\ N$$

b)

$$F=16(9.8)-1030+1018=145\ N$$

c)

$$\rho gV=(0.1)(0.1)(0.12)(9.8)(1000)=12\ N\\1030-1018=12\ N$$