Chapter 14: Q. 17 (page 384)

A $2.0 c m \times 2.0 c m \times 6.0 c m$ block floats in water with its long axis vertical. The length of the block above water is $2.0 c m$ . What is the block’s mass density?

Short Answer

Expert verified

The block's mass density is $ρ_{b} = 667 k g / m^{3}$

Step by step solution

Mass density.

The mass density of a substance, material, or item could be a measure of what quantity mass (or what number particles) it's in regard to the number of space it takes up.

Derive the mass formula.

Because the block is afloat That's, the burden performing on it's capable to the buoyant force, and it's not moving, neither up nor down. That is,

$m_{b} g = ρ_{w} g V_{w} \Rightarrow m_{b} = ρ_{w} V_{w}$

where $b$ stands for block and $w$ for water.

Find the mass density.

We can calculate the mass of a body by multiplying its density by its mass, $m_{b} = ρ_{b} V_{b}$ .

$ρ_{b} V_{b} = ρ_{w} V_{w} \Rightarrow ρ_{b} = \frac{ρ_{w} V_{w}}{V_{b}} = ρ_{w} \frac{a \times b \times (2 / 3) c}{a \times b \times c} = \frac{2}{3} ρ_{w}$

We can calculate the density of a block using the density of water.

$ρ_{b} = \frac{2}{3} 1000 = 667 kg / m^{3}$

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A $2.0 c m \times 2.0 c m \times 6.0 c m$ block floats in water with its long axis vertical. The length of the block above water is $2.0 c m$ . What is the block’s mass density?

Short Answer

Step by step solution

Mass density.

Derive the mass formula.

Find the mass density.

One App. One Place for Learning.

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A 2.0cm×2.0cm×6.0cmblock floats in water with its long axis vertical. The length of the block above water is 2.0cm. What is the block’s mass density?

Short Answer

Step by step solution

Mass density.

Derive the mass formula.

Find the mass density.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Solid State Physics

Atoms and Radioactivity

Radiation

Astrophysics

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

A $2.0 c m \times 2.0 c m \times 6.0 c m$ block floats in water with its long axis vertical. The length of the block above water is $2.0 c m$ . What is the block’s mass density?