A cube of wood with a density of 0.780 g/cm3 is 10.0 cm on each side. When the cube is placed in water, what buoyant force acts on the wood? (ρw = 1.00 g/cm3)

a. 5.00 N
b. 6.40 N
c. 7.65 N
d. 7.65 x 10^3 N

Ben's answer is wrong. He had to cross multiply and then divide but he just straight up multiplied Fg and po

To find the buoyant force acting on the wood cube, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.

Step 1: Calculate the volume of the wood cube.
The volume of a cube is given by the formula side^3. Since the cube has sides measuring 10.0 cm each, the volume would be:
Volume = 10.0 cm * 10.0 cm * 10.0 cm = 1000 cm^3.

Step 2: Calculate the weight of the wood cube.
The weight of an object can be found using the formula weight = mass * gravitational acceleration. We can find the mass of the wood cube using the formula mass = density * volume.
Given that the density of the wood cube is 0.780 g/cm^3 and the volume is 1000 cm^3:
Mass = 0.780 g/cm^3 * 1000 cm^3 = 780 g.

Step 3: Calculate the buoyant force.
The buoyant force is equal to the weight of the fluid displaced by the object, which is equal to the weight of the water that has the same volume as the wood cube.
The volume of the wood cube is 1000 cm^3, and the density of water is 1.00 g/cm^3.
Since the density of water is higher than the density of the wood cube, the wood cube will float. Therefore, the buoyant force will be equal to the weight of the water displaced by the cube.
The weight of water displaced = density of water * volume of water displaced
Weight of water displaced = 1.00 g/cm^3 * 1000 cm^3 = 1000 g.

To convert the weight to Newtons, we can use the conversion factor: 1 N = 1000 g.
Weight of water displaced = 1000 g * (1 N / 1000 g) = 1 N.

So, the buoyant force acting on the wood cube is 1 N, which corresponds to option a. 5.00 N (since there is no option for 1 N).

To calculate the buoyant force acting on the wood cube, we need to use the formula:

Buoyant force = weight of the fluid displaced by the object.

The weight of the fluid displaced by the object is equal to the weight of the water that has the same volume as the cube. The volume of the cube can be calculated by multiplying the length of one side cubed (V = s^3).

First, let's calculate the volume of the cube:
V = (10.0 cm)^3 = 1000 cm^3

Next, we need to calculate the weight of the water displaced. The weight of an object can be calculated using the formula:

Weight = mass x gravity

The mass can be determined using the density formula:

Density = mass/volume

Rearranging the formula, we have:

Mass = Density x Volume

For water, the density (ρw) is given as 1.00 g/cm^3. Therefore, the mass of the water displaced by the cube is:

Mass = (1.00 g/cm^3) x (1000 cm^3) = 1000 g = 1 kg (since 1 kg = 1000 g)

Finally, we can calculate the buoyant force:

Buoyant force = weight of the water = mass x gravity

Assuming the acceleration due to gravity is 9.8 m/s^2, the buoyant force is:

Buoyant force = (1 kg) x (9.8 m/s^2) = 9.8 N

So, the buoyant force acting on the wood cube when placed in water is 9.8 N.

None of the provided answer choices (a, b, c, d) match the calculated value of 9.8 N.

Fg/Fb=p(row)(object)/p(fluid)

9.81/Fb=.78/1

=7.65 N