A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density 350 kg/m³.The board is floating partially submerged in water of density 1000 kg/m³.What fraction of the volume of the board is above the surface of the water? A)0.350 B)0.650 C)zero D)0.200 E)The answer depends on which edge of the board is vertical.

Question

Quizplus · Accepted Answer

To solve the problem, we need to compare the weight of the board to the weight of the water it displaces. The weight of the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of the board, density is its density, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of the board can be found using the formula: 
volume = width x thickness x length 
Plugging in the given values, we get: 
volume = 20.0 cm x 5.00 cm x 3.00 m = 3000 cm^3 = 0.003 m^3

The weight of the board is then: 
weight = 0.003 m^3 x 350 kg/m^3 x 9.81 m/s^2 = 10.3 N

The weight of the water displaced by the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of water displaced by the board, density is the density of water, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of water displaced by the board is equal to the volume of the submerged part of the board. Let h be the height of the submerged part of the board. Then: 
volume of water = width x h x length 
Plugging in the given values, we get: 
volume of water = 20.0 cm x h x 3.00 m = 0.6 h m^3

The weight of the water displaced by the board is then: 
weight of water = 0.6 h m^3 x 1000 kg/m^3 x 9.81 m/s^2 = 5886 h N

Since the board is floating partially submerged, the weight of the board is equal to the weight of the water displaced by the submerged part of the board. Thus, we have: 
10.3 N = 5886 h N 
Solving for h, we get: 
h = 0.00175 m

Therefore, the fraction of the volume of the board above the surface of the water is: 
fraction = (width x thickness x length - width x h x length) / (width x thickness x length) 
Plugging in the given values, we get: 
fraction = (20.0 cm x 5.00 cm x 3.00 m - 20.0 cm x 0.00175 m x 3.00 m) / (20.0 cm x 5.00 cm x 3.00 m) = 0.65

So, the answer is (B) 0.650.

A Board That Is 20