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Someone goes to lift a crate that is resting on the bottom of the pool filled with water (density of water is 1000 kg/m^3). While

still submerged, only 310 N is required to lift the crate. The crate is shaped like a cube with sides of 0.25 m. What is the density of
the cube? Numerical answer is assumed to be in units of kg/m^3

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Answer:

the density of the cube is approximately 2016.07 kg/m^3.

Step-by-step explanation:

The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Let's first calculate the weight of the crate:

mass of crate = density * volume = density * (side length)^3 = density * 0.25^3 = 0.015625 * density

weight of crate = mass of crate * gravity = 0.015625 * density * 9.81 = 0.1530875 * density

where gravity is the acceleration due to gravity, which is approximately 9.81 m/s^2.

Since the crate is submerged in water, the buoyant force acting on it is:

buoyant force = weight of water displaced = density of water * volume of water displaced * gravity

The volume of water displaced is equal to the volume of the cube, which is 0.25^3 = 0.015625 m^3. Therefore, the buoyant force is:

buoyant force = 1000 kg/m^3 * 0.015625 m^3 * 9.81 m/s^2 = 1.534453125 N

According to the problem, it takes 310 N to lift the crate while it is still submerged. This means that the net force acting on the crate is:

net force = lifting force - buoyant force = 310 N - 1.534453125 N = 308.465546875 N

This net force is equal to the weight of the crate:

net force = weight of crate = 0.1530875 * density

Therefore, we can solve for the density of the crate:

density = net force / 0.1530875 = 308.465546875 / 0.1530875 = 2016.06666667 kg/m^3

Rounding to the nearest hundredth, we get:

density ≈ 2016.07 kg/m^3

Therefore, the density of the cube is approximately 2016.07 kg/m^3

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