A block of wood, with density 828 kg/m3 , has a cubic shape with sides 0.340 m long. A rope of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water. What is the mass of the lead? [Hint: Don't forget to consider the buoyant force on both the wood and the lead.]

Question

A block of wood, with density 828 kg/m3 , has a cubic shape with sides 0.340 m long. A rope of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water. What is the mass of the lead? [Hint: Don't forget to consider the buoyant force on both the wood and the lead.]

Kg?

Since d=m/v do i multiply 0.340m or 0.340m^3 because its a cube by 828?

Answer 1

To solve this question, we need to consider the buoyant force acting on both the wood and the lead.

First, let's find the volume of the wooden block. Since it has a cubic shape with sides 0.340 m long, the volume can be calculated as V = side^3 = 0.340 m × 0.340 m × 0.340 m.

Next, we can find the mass of the wooden block using the density formula, d = m/v. Rearranging this formula, we get m = d × v, where d is the density and v is the volume. Plug in the values of density and volume to find the mass of the wooden block.

Now, when the block is submerged in water, there will be a buoyant force acting on it. The magnitude of this buoyant force is equal to the weight of the water displaced by the block. Since the block is completely covered with water, the buoyant force acting on it will be equal to the weight of the block itself.

Now let's consider the lead tied to the bottom of the wooden block. The buoyant force acting on the lead will be equal to the weight of the water displaced by the lead. Since the lead is also completely covered with water, the buoyant force acting on the lead is equal to its weight.

Therefore, to find the mass of the lead, we need to equate the buoyant forces acting on the wooden block and the lead. Since the buoyant force is dependent on the density, volume, and acceleration due to gravity, we can equate the densities, volumes, and acceleration due to gravity to find the mass of the lead.

To summarize, you need to:
1. Calculate the volume of the wooden block using the side length.
2. Use the density formula, d = m/v, to find the mass of the wooden block.
3. Equate the buoyant forces on the wooden block and the lead by comparing their densities, volumes, and the acceleration due to gravity.
4. Solve the equation to find the mass of the lead.