a piece of wood 50 cm long , 20 cm wide, 40 cm thick. its density is 0.6 g cm^3. this is connected to a string with negligible mass attached to a piece of lead. what is the mass of the lead and what volume underneath is needed to sink the wood in calm water so that its top is just even with the water level.

VOLUME OF WOOD: .2*.5*.4 M^3=.04 M^3

MASS OF WOOD: .04*6e6 GRAMG=.024e6G=24000grams

now, to sink that block, you need a total mass of .04m^3*1Eg/m^3=40,000 grams, so the mass of lead then is 40-24 kg of lead

check my thinking

To find the mass of the lead and the volume of water displaced by the wood, we need to calculate the volume of the wood and compare it with the volume of water displaced.

First, let's find the volume of the wood:
The wood has dimensions of 50 cm (length) x 20 cm (width) x 40 cm (thickness).
The volume of the wood is given by the formula: volume = length x width x thickness.
Therefore, the volume of the wood = 50 cm x 20 cm x 40 cm.

Now, let's calculate the mass of the wood:
We are given that the density of the wood is 0.6 g/cm^3. This means that for each cubic centimeter (cm^3) of wood, it has a mass of 0.6 grams.
To find the mass of the wood, we need to multiply the volume of the wood by its density.
Mass of the wood = volume of the wood x density of wood.

Now, to determine the mass of the lead, we need to consider the equilibrium of forces:
When the wood is floating in calm water, the weight of the wood and the weight of the lead attached to it are balanced by the buoyant force exerted upwards by the water.
The weight of an object is given by the formula: weight = mass x acceleration due to gravity (g).
Since the wood is floating, its weight is balanced by the buoyant force, so the weight of the wood is equal to the weight of the lead.
Therefore, the mass of the lead is equal to the mass of the wood.

Finally, to find the volume of water displaced, we need to know the density of water.
The density of water is approximately 1 g/cm^3.

Let's calculate the values now:
1. Volume of the wood = 50 cm x 20 cm x 40 cm
2. Mass of the wood = volume of the wood x density of wood
3. Mass of the lead = mass of the wood
4. Volume of water displaced = mass of the lead / density of water

Plug in the values into the equations above and perform the calculations to find the desired answers.