Physics, 29.02.2020 02:58 Dajuan2x

A wooden block of dimensions of 6 cm ⨯ 6 cm ⨯ 15 cm floats with the long axis oriented horizontally and the of the square faces are oriented so that they point up vertically, straight up out of the water like a diamond shape. If the wooden block is submerged to a depth 7.96 cm (the bottom point to the water level), then: (a) What is the submerged volume of the block?(b) What is the mass of the block
(c) What is the density of the block?

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Answer from: kitttimothy55

Explanation:

(a) Formula to calculate volume of the submerged wooden block is as follows.

$V_{sub} = l \times w \times d$

It is given data of the wooden block is as follows.

depth = 7.96 cm, length (l) = 6 cm

width (w) = 4 cm,

So, we will calculate the volume of the submerged wooden block as follows.

$V_{sub} = l \times w \times d$

= $6 \times 6 \times 7.96$

= 286.56 $cm^{3}$

Hence, the submerged volume of the block is 286.56 $cm^{3}$ .

(b) Expression for the buoyant force acting on the wooden block is as follows.

$F_{B} = \rho_{w} g V_{sub}$

And, expression for the force of gravity of the wooden block is as follows.

$F_{g} = m_{b}g$

As the wooden block is floating on the water hence, buoyant force is balanced by the weight of the block.

$F_{g} = F_{B}$

Hence, mass of the wooden block will be calculated as follows.

$F_{g} = F_{B}$

$m_{b}g = \rho_{w}gV_{sub}$

$m_{b} = \rho_{w}V_{sub}$

= $997 kg/m^{3} \times 286.56 cm^{3}$

= $997 kg/m^{3} \times 286.56 \times 10^{-6} m^{3}$

= 0.02857 kg

Therefore, mass of the given block is 0.02857 kg

$\rho_{b} = \frac{m_{b}}{V_{b}}$

Now, expression for the total volume of the wooden block is as follows.

$V_{b} = l \times w \times h$

Hence, density of the given block is as follows.

$\rho_{b} = \frac{m_{b}}{V_{b}}$

= $\frac{m_{b}}{lwh}$

= $\frac{0.02857 kg}{4 \times 4 \times 15}$

= $1.19 \times 10^{-4} kg/cm^{3}$

Therefore, density of the given block is $1.19 \times 10^{-4} kg/cm^{3}$ .

Answer from: Quest

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Answer from: Quest

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A wooden block of dimensions of 6 cm ⨯ 6 cm ⨯ 15 cm floats with the long axis oriented horizontally...

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