Question

In: Physics

A uniform plastic block floats in water with 40.0 % of its volume above the surface...

A uniform plastic block floats in water with 40.0 % of its volume above the surface of the water. The block is placed in a second liquid and floats with 20.0 % of its volume above the surface of the liquid.

What is the density of the second liquid?

Expert Solution

Gravitational acceleration = g

Density of water = ₁ = 1000 kg/m³

Density of the second liquid = ₂

Density of the plastic block =

Volume of the plastic block = V

Weight of the plastic block = W

The plastic block floats with 40% of it's volume above the surface of the water therefore 60% of the volume of the plastic block is submerged in water.

Volume of the plastic block submerged in water = V₁ = 0.6V

Buoyancy force on the plastic block from the water = F_b1

When the block is floating in water the buoyancy force from the water supports the weight of the plastic block.

= 600 kg/m³

The block floats in the second liquid with 20% of its volume above the surface of the liquid therefore 80% of the volume of the block is submerged in this liquid.

Volume of the plastic block submerged in the second liquid = V₂ = 0.8V

Buoyancy force on the plastic block from the second liquid = F_b2

When the block is floating in the second liquid the weight of the block is supported by the buoyancy force on it.

₂ = 750 kg/m³

Density of the second liquid = 750 kg/m³

genius_generous answered 1 year ago

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