Final answer:
The mass of the wooden block is determined through the principle of buoyancy. Since the block initially floats with half its volume underwater, and submerges fully when 20g is added, the total mass of the wooden block is 40 g assuming the missing half balances the given 20g.
Step-by-step explanation:
The mass of the wooden block can be determined using the principle of buoyancy. Initially, the block floats with half of its volume underwater, which means the buoyant force balances the weight of the block. When 20 g of mass is added, the block just submerges, indicating that the weight of the added mass plus the block equals the weight of the volume of water displaced. Since the density of water is 1 g/cm3, the volume of the block is equal to the mass of water displaced, which is the weight of the block plus 20 g.
Let M be the mass of the wooden block. Initially, the block displaces an amount of water equivalent to half its volume. The buoyancy force (the weight of the displaced water) is equivalent to the weight of the block:
weight of displaced water = weight of block
0.5Mg = Mg
0.5M = M (assuming g=1 since we are using weight)
However, this equation seems incomplete as we no additional data to compare. There is a typo or missing information because normally we would find that 0.5M (half the block's volume) corresponds to a specific mass of water. Given that 20 g is required to submerge it fully, this extra mass is likely meant to be equated to the other half of the block's volume (since it was previously floating with half volume submerged). If that's the case, the block’s mass plus the mass of the added weights should equal the total volume of the block:
M + 20g = total volume of the block in grams (since the density of water is 1 g/cm3)
If the block was initially floating with half of its volume below the waterline, then M = 2 x 20g, thus
M = 40 g.