An 11.4 kg block of metal is suspended from a scale and immersed in water, as in the figure below. The dimensions of the block are 12.0 cm multiplied by 11.1 cm multiplied by 11.1 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water.

(a) What are the forces exerted by the water on the top and bottom of the block? Take P0 = 1.0130 105 N/m2.

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To find the forces exerted by the water on the top and bottom of the block, we need to consider the concept of buoyancy and the pressure exerted by the water.

First, let's calculate the volume of the block:
Volume = length x width x height
Volume = 0.12 m x 0.111 m x 0.111 m (converting cm to m)
Volume = 0.00148 m^3

Since the block is submerged in water, it displaces an equal volume of water. This displacement creates an upward force on the block known as the buoyant force.

Next, we need to calculate the weight of the block:
Weight = mass x gravity
Weight = 11.4 kg x 9.8 m/s^2
Weight = 111.72 N

According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid. Therefore, the buoyant force on the block is also 111.72 N.

Now, let's calculate the pressure exerted by the water:
Pressure = density x gravity x height
Density of water = 1000 kg/m^3
Pressure = 1000 kg/m^3 x 9.8 m/s^2 x 0.05 m (converting cm to m)
Pressure = 490 Pa

Since the block is submerged in water, the water exerts pressure on all sides, including the top and bottom surfaces. The force exerted by pressure is given by the formula: Force = Pressure x Area

To calculate the forces on the top and bottom of the block, we need to calculate the area of these surfaces.

Area of the top surface = length x width
Area of the top surface = 0.12 m x 0.111 m
Area of the top surface = 0.01332 m^2

Area of the bottom surface is the same as the top surface.

Now, let's calculate the force on the top and bottom surfaces:
Force = Pressure x Area
Force = 490 Pa x 0.01332 m^2
Force ≈ 6.5 N

Therefore, the forces exerted by the water on the top and bottom of the block are approximately 6.5 N each.