Archimedes principle and wooden block

[tandoorichicken]

A wooden block 20 * 20 *10 cm^3 has a density of .6 g/ cm^3
(a) How much iron (density = 7.86 g/cm^3) can be placed on to p of the block if the top of the block is to be level with the water around it?
(b) If iron were attached to the bottom of the block instead, what mass of iron would it take to bring the top of the wooden block down to the level of the water?

 

[ShawnD]

Originally posted by tandoorichicken
A wooden block 20 * 20 *10 cm^3 has a density of .6 g/ cm^3
(a) How much iron (density = 7.86 g/cm^3) can be placed on to p of the block if the top of the block is to be level with the water around it?
(b) If iron were attached to the bottom of the block instead, what mass of iron would it take to bring the top of the wooden block down to the level of the water?

A).

find the mass of the wood block. iirc, density is P or something like that.
m = pv
m = (0.6)(20)(20)(10)
m = 2400g

find mass of the water if it were the same size
m = pv
m = (1)(20)(20)(10)
m = 4000g

difference of mass:
4000 - 2400 = 1600g

volume of iron:
v = m/p
v = (1600)/(7.86)
v = 203.56 cm^3




B). This is a neat question.

Just as before, the difference between the wood and the water is 1600g but now we have to take into account the boyant force on the iron. To do that, we have to make a new equation to represent the weight (or mass) of the iron.

Gravity is a constant on every term so I can just leave it out. The mass in the equation represents the mass of iron which has an effective downward force. In both terms, the v is the same but the p is different.
m = pv (iron) - pv (water)
1600 = (7.86)v - 1v
1600 = 6.86v
v = 233.236 cm^3

 

[M98Ranger]

(a) According to Archimedes principle, the buoyant force acting on an object is equal to the weight of the displaced fluid. In this case, the wooden block has a density of 0.6 g/cm^3, which means it will float in water. The weight of the wooden block is equal to its mass (0.6 g/cm^3) multiplied by its volume (20 * 20 * 10 cm^3), which is 2400 g. To make the top of the block level with the water, the buoyant force needs to be equal to 2400 g. Since the density of iron is 7.86 g/cm^3, the mass of iron needed can be calculated by dividing 2400 g by 7.86 g/cm^3, which is approximately 305 g. Therefore, 305 g of iron can be placed on top of the wooden block without sinking it.

(b) If iron were attached to the bottom of the block, the buoyant force acting on the block would increase, causing it to sink lower in the water. To bring the top of the wooden block down to the level of the water, the buoyant force needs to be equal to the weight of the block and the attached iron. Since the weight of the block is 2400 g, the buoyant force needs to be increased by 2400 g to bring it down to the water level. This would require an additional mass of 2400 g of iron, which is approximately 306 cm^3. Therefore, attaching 306 cm^3 of iron to the bottom of the wooden block would bring the top of the block down to the level of the water.