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?
To find the mass of the lead, we need to consider the buoyant force acting on both the wood and the lead.
First, let's find the volume of the wood. Since it is a cubic shape with each side measuring 0.340 m, we can calculate the volume using the formula V = s^3, where s is the length of one side:
V = (0.340 m)^3 = 0.039 m^3
Now, we can find the mass of the wood using the formula m = d * V, where d is the density of the wood:
m_wood = 828 kg/m^3 * 0.039 m^3
Next, we need to consider the buoyant force on the wood, which is equal to the weight of the water displaced by the wood. Since the wood is completely covered with water, the buoyant force on the wood will be equal to its weight. We can calculate the weight of the wood using the formula:
weight_wood = m_wood * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
But the buoyant force on the wood is equal to the weight of the lead, so we can write this as:
weight_lead = weight_wood
Now, we have a relationship between the weight of the lead and the mass of the wood. We can rearrange our equation to solve for the mass of the lead:
m_lead = weight_lead / g
To calculate the weight of the lead, we need to subtract the weight of the wood from the buoyant force acting on it:
weight_lead = (m_wood * g) - (buoyant force on wood)
To find the buoyant force on the wood, we need to calculate the weight of the water displaced by the wood. Since the wood is completely covered by water, the volume of water displaced by it will be equal to the volume of the wood:
V_water_displaced = V_wood = 0.039 m^3
The weight of the water displaced by the wood can be calculated using the formula:
weight_water_displaced = density_water * V_water_displaced * g
The density of water is approximately 1000 kg/m^3, so we can calculate the weight of the water displaced:
weight_water_displaced = 1000 kg/m^3 * 0.039 m^3 * g
Now we can substitute this expression for the weight of the water displaced into our earlier equation:
weight_lead = (m_wood * g) - (weight_water_displaced)
Finally, we can substitute this expression into the formula to calculate the mass of the lead:
m_lead = (m_wood * g - weight_water_displaced) / g
Simplifying the equation, we get:
m_lead = m_wood - (weight_water_displaced / g)
Substituting the values we know, we can now calculate the mass of the lead:
m_lead = (828 kg/m^3 * 0.039 m^3) - (1000 kg/m^3 * 0.039 m^3 * g)
Simplifying this equation will give you the mass of the lead in kilograms.