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3 years ago

Which of the following states Bernoulli’s principle?

1 answer:

8 0

The correct answer is <span>B. As speed of a fluid increases, the pressure within decreases.
Using formulas, Bernoulli's principle can be written as
</span> $p+ \frac{1}{2}\rho v^2 + \rho g h=cost.$
where p is the pressure of the fluid, $\rho$ its density, v its speed, and h its elevation above a reference level.
Assuming h does not change, we can see that if the speed v increases, the pressure p must decrease in order to keep constant the sum of the three terms.

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the density of ice is 917.what fraction of the volume of a piece of ice will be above the liquid when floating in fresh water

yulyashka [42]

Answer:

$8.3\,\%$ of that piece of ice would be above the freshwater. Assumptions:

the density of the ice is $\rho(\text{ice}) = 917\; \rm kg \cdot m^{-3}$ , and
the density of freshwater is $\rho(\text{water}) = 1.00 \times 10^3\; \rm kg \cdot m^{-3}$ .

Explanation:

The volume of that chunk of ice can be split into two halves: volume above water $V(\text{above})$ , and volume under water $V(\text{under})$ . The mass of the whole chunk of ice would be:

$m(\text{ice}) = \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under}))$ .

Let $g$ be the acceleration due to gravity. The gravity on the entire chunk of ice would be

$\begin{aligned}&W(\text{ice}) \\ &= m({\text{ice}}) \cdot g \\ &= \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under})) \cdot g\end{aligned}$ .

On the other hand, the size of buoyant force on an object is equal to the weight of the liquid that it displaces. That is: $F(\text{bouyancy}) = W(\text{water displaced})$ .

Recall that $V(\text{above})$ is the volume of the ice above the water, and $V(\text{under})$ is the volume of the ice under the water.

The mass of water displaced would be equal to:

$\begin{aligned}& m(\text{water displaced}) \\ &= \rho(\text{water}) \cdot V(\text{water displaced}) \\ &= \rho(\text{water}) \cdot V(\text{under})\end{aligned}$ .

The weight of that much water would be

$\begin{aligned} &W(\text{water displaced}) \\ &= m(\text{water displaced}) \cdot g \\ &= \rho(\text{water}) \cdot V(\text{under}) \cdot g \end{aligned}$ .

Apply the equation $F(\text{bouyancy}) = W(\text{water displaced})$ . The bouyant force on this chunk of ice would be equal to $\begin{aligned} &W(\text{water displaced}) = \rho(\text{water}) \cdot V(\text{under}) \cdot g \end{aligned}$ .

Since the ice is floating, the forces on it need to be balanced. In other words, $\begin{aligned}W(\text{ice}) &= F(\text{bouyancy}) \\ &= \rho(\text{water}) \cdot V(\text{under}) \cdot g\end{aligned}$ .

On the other hand, recall that

$\begin{aligned}&W(\text{ice}) = \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under})) \cdot g\end{aligned}$ .

Combine the two halves to obtain:

$\begin{aligned}& \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under})) \cdot g \\ &= W(\text{ice}) = \rho(\text{water}) \cdot V(\text{under}) \cdot g\end{aligned}$ .

$\begin{aligned}& \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under})) \cdot g = \rho(\text{water}) \cdot V(\text{under}) \cdot g\end{aligned}$ .

Divide both sides by $g$ (assume that $g \ne 0$ ) to obtain:

$\begin{aligned}& \rho(\text{ice}) \cdot (V(\text{above}) + V(\text{under})) = \rho(\text{water}) \cdot V(\text{under})\end{aligned}$ .

Rearrange to obtain:

$\begin{aligned}& \frac{V(\text{under})}{V(\text{above}) + V(\text{under})} = \frac{\rho(\text{water})}{\rho(\text{ice})}\end{aligned}$ .

However, the question is asking for $\displaystyle \frac{V(\text{above})}{V(\text{above}) + V(\text{under})}$ , the fraction of the volume above water. Note that

$\begin{aligned}& \frac{V(\text{under})}{V(\text{above}) + V(\text{under})} + \frac{V(\text{above})}{V(\text{above}) + V(\text{under})} = 1\end{aligned}$ .

Therefore,

$\begin{aligned} &\frac{V(\text{above})}{V(\text{above}) + V(\text{under})} \\ &= 1 - \frac{V(\text{under})}{V(\text{above}) + V(\text{under})} \\ &= 1 - \frac{\rho(\text{water})}{\rho(\text{ice})} = 1 - \frac{917}{10^3} = 0.083\end{aligned}$ .

That's equivalent to $8.3\,\%$ .

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3 years ago

The speed of light in vinegar is 2.30 x 10^8 m/s. Determine the index of refraction. (2

pantera1 [17]

Answer:

$n _{v} = \frac{c}{v} \\ = \frac{3 \times {10}^{8} }{2.30 \times {10}^{8} } \\ = 1.30$

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3 years ago

a 2 kilogram wooden block raised on an inclined plane making angle 30 degree frictional force will be equal to

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Answer:

fvSvfbikufdclknfmfl us

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3 years ago

Is KBr a covalent or ionic compound

raketka [301]

Answer:

Ionic Compound

Explanation:

To identify the type of chemical bond in a molecule, look at the atoms that make up the compound. If there are two nonmetals, it is a covalent bond. If the two atoms are metals, it is a metallic bond. If one atom is a metal and the other is a nonmetal, it is an ionic bond. Ionic compounds are also known as salts. You can identify KBr as an ionic compound because potassium is a metal and a salt.

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