A wooden block of mass 2,52 kg and density 500 kg m–3 floats on water. What minimum mass (in kg) of lead, density, 11,3 × 103 kg m–3 , hung from it by a light string, will cause it to sink? The density of water is 1,00 × 103 kg m–3 .

To make the wooden block sink, a minimum mass of lead of 5 kg must be hung from it. This calculation accounts for the weight of the wooden block itself, ensuring that the combined weight of the block and lead exceeds the buoyant force acting on the block when fully submerged in water.

Explanation:

To find the minimum mass of lead required to make the wooden block sink, we need to consider the principle of buoyancy. When an object floats, the buoyant force on the object equals its weight. When an object sinks, the weight of the object must be greater than the buoyant force.

Given:

Mass of the wooden block (m_wood) = 2.52 kg
Density of wood (ρ_wood) = 500 kg/m³
Density of lead (ρ_lead) = 11,300 kg/m³
Density of water (ρ_water) = 1,000 kg/m³

First, calculate the volume of the wooden block using its mass and density:

Volume of wood (V_wood) = m_wood / ρ_wood = 2.52 kg / 500 kg/m³ = 0.00504 m³

Next, calculate the weight of the wooden block:

Weight of wood (W_wood) = m_wood * g, where g is the acceleration due to gravity (approximately 9.81 m/s²)

W_wood = 2.52 kg * 9.81 m/s² = 24.6952 N

Now, calculate the buoyant force acting on the wooden block when it is fully submerged in water:

Buoyant force (F_buoyant) = V_wood * ρ_water * g

F_buoyant = 0.00504 m³ * 1,000 kg/m³ * 9.81 m/s² = 49.1784 N

For the wooden block to sink, the weight of the lead (m_lead * g) hanging from it must exceed the buoyant force. Therefore, the minimum mass of lead (m_lead) required can be found by:

m_lead * g > F_buoyant

m_lead > F_buoyant / g

m_lead > 49.1784 N / 9.81 m/s²

m_lead > 5 kg

So, to make the wooden block sink, a minimum mass of lead of 5 kg must be hung from it. This takes into account the weight of the wooden block itself.

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