To calculate the buoyant force experienced by the cube, first, we need to determine the volume of water displaced by the submerged part of the cube.
Given that the volume of the cube is \( 10 , \text{cm}^3 \), and it is submerged halfway, the volume of water displaced will be:
\[ \text{Volume of water displaced} = \frac{1}{2} \times \text{Volume of the cube} = \frac{1}{2} \times 10 , \text{cm}^3 = 5 , \text{cm}^3 \]
Next, we need to find the weight of the water that is displaced. To do this, we can use the density of water, which is approximately \( 1 , \text{g/cm}^3 \). Therefore, the mass of the displaced water is:
\[ \text{Mass of displaced water} = \text{Volume of water displaced} \times \text{Density of water} = 5 , \text{cm}^3 \times 1 , \text{g/cm}^3 = 5 , \text{g} \]
To find the weight of the displaced water (which is equal to the buoyant force), we can convert the mass into weight using the relation \( \text{Weight} = \text{Mass} \times g \), where \( g \) (acceleration due to gravity) is approximately \( 9.81 , \text{m/s}^2 \).
However, for practicality in this context, we can calculate the weight directly in grams, and since \( 1 , \text{g} \) of mass experiences a weight of \( 0.00981 , \text{N} \) (in terms of newtons):
\[ \text{Buoyant Force} = \text{Weight of displaced water} = 5 , \text{g} \times 0.00981 , \text{N/g} \approx 0.04905 , \text{N} \]
Thus, the buoyant force experienced by the cube is approximately \( 0.049 , \text{N} \).
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