A cube of wood of density 0.780 g/cm³ is 11.2 cm on a side.When placed in water,what height of the block will float above the surface? (water density = 1.00 g/cm³) A)8.74 cm B)11.2 cm C)2.46 cm D)3.46 cm E)1.46 cm

Question

Quizplus · Accepted Answer

First, we need to determine whether the wood will float or sink in water. If the wood is less dense than water, it will float. If it's more dense, it will sink. We can use the densities given in the problem to determine this:

Density of wood (d1) = 0.780 g/cm³
Density of water (d2) = 1.00 g/cm³

Since the density of wood (0.780 g/cm³) is less than the density of water (1.00 g/cm³), the wood will float in water.

Now, we need to determine how much of the wood will be above the surface of the water. To do this, we can use Archimedes' principle:

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

In other words, the weight of the wood that is submerged in water will be equal to the weight of the water that the wood displaces. We can set up an equation to solve for the height of the wood that will be above the surface of the water:

Volume of wood (V) = (11.2 cm)³ = 1400.4 cm³
Weight of wood (W1) = Volume x Density = 1400.4 cm³ x 0.780 g/cm³ = 1093.312 g

Weight of displaced water (W2) = Volume x Density = 1400.4 cm³ x 1.00 g/cm³ = 1400.4 g

Buoyant force (B) = Weight of displaced water = 1400.4 g

Since the buoyant force is equal to the weight of the submerged wood, we can set the two weights equal to each other and solve for the height of the wood that is above the surface of the water:

Weight of submerged wood = Weight of displaced water
1093.312 g = (11.2 cm - h)³ x 1.00 g/cm³

Solving for h, we get:
h = 2.46 cm

Therefore, the height of the wood that will float above the surface of the water is 2.46 cm, so the answer is (C) 2.46 cm.

A Cube of Wood of Density 0