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3 years ago

If feathers have a density of 0.500 lbs/ft^3, what volume in ft^3 will 8.0 lbs of feathers occupy?

Physics

1 answer:

OleMash [197]3 years ago

3 0

Answer:

The volume of the feathers in ft³ = 16 ft³

Explanation:

Density: This can be defined as the ratio of mass of a body to the corresponding volume of that body. The S.I unit of Density is kg/m³

Mathematically it can be expressed as,

D = m/v ................................... Equation 1

making v the subject of the equation above,

v = m/D ............................. Equation 2

Where D = Density of the feathers, m = mass of the feathers, v = volume of the feathers.

Given: D = 0.50 lbs/ft³, m = 8.0 lbs.

Substituting into equation 2

v = 8/0.5

v = 16 ft³

Thus the volume of the feathers in ft³ = 16 ft³

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Explanation:

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$\begin{array}{l}{\mathrm{H}_{0}=\text { height of the object }} \\ {\mathrm{H}_{\mathrm{i}}=\text { height of the image }} \\ {\mathrm{D}_{0}=\text { distance of the object }} \\ {\mathrm{D}_{\mathrm{i}}=\text { distance of the image }}\end{array}$

As per given question,

$\begin{array}{l}{\mathrm{H}_{1}=\text { height of the image }=\text { height of the image of the tree on screen }=16 \mathrm{cm}} \\ {\mathrm{D}_{0}=\text { distance of the object }=\text { distance of the tree from the pinhole }=6 \mathrm{cm}} \\ {D_{1}=\text { distance of the image }=\text { distance of the image from the pinhole }=10 \mathrm{cm}} \\ {\mathrm{H}_{0}=\text { height of the object }=\text { height of the tree }}\end{array}$

Substitute the values in the above formula,

$\begin{array}{l}{\left(\frac{H_{i}}{H_{o}}\right)=\left(\frac{D_{i}}{D_{o}}\right)} \\ {\left(\frac{16}{H_{o}}\right)=\left(\frac{10}{6}\right)} \\ {\mathrm{H}_{\mathrm{o}}=\left(\frac{16 \times 6}{10}\right)} \\ {\mathrm{H}_{\mathrm{o}}=9.6 \mathrm{cm}}\end{array}$

Height of the tree is 9.6 cm.

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3 years ago