/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 32 A block of birch wood floats in ... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 32

A block of birch wood floats in oil with \(90.0 \%\) of its volume submerged. What is the density of the oil? The density of the birch is $0.67 \mathrm{g} / \mathrm{cm}^{3} .$

Short Answer

Expert verified
Answer: The density of the oil is 0.603 g/cm鲁.

Step by step solution

01

Understand the principle of buoyancy

According to Archimedes' principle of buoyancy, the buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. In this case, it must be equal to the weight of the block of wood.
02

Set up equation relating submerged volume, densities of wood, and oil

Let's denote the density of oil as \(\rho_o\), the density of the birch as \(\rho_b\), and the submerged volume ratio as \(r\). We have: \(r \times \rho_b = \rho_o\) We are given that the density of the birch, \(\rho_b = 0.67 \mathrm{g} / \mathrm{cm}^{3}\), and that \(90 \%\) of its volume is submerged, so \(r = 0.90\).
03

Solve for the density of oil

Plug the given values into the equation \(r \times \rho_b = \rho_o\): \((0.90) \times (0.67 \mathrm{g} / \mathrm{cm}^{3}) = \rho_o\) Now, calculate the density of oil: \(\rho_o = 0.603 \mathrm{g} / \mathrm{cm}^{3}\) So, the density of the oil is \(0.603 \mathrm{g} / \mathrm{cm}^{3}\).

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Most popular questions from this chapter

While vacationing at the Outer Banks of North Carolina, you find an old coin that looks like it is made of gold. You know there were many shipwrecks here, so you take the coin home to check the possibility of it being gold. You suspend the coin from a spring scale and find that it has a weight in air of 1.75 oz (mass \(=49.7 \mathrm{g}\) ). You then let the coin hang submerged in a glass of water and find that the scale reads \(1.66 \mathrm{oz}\) (mass $=47.1 \mathrm{g}$ ). Should you get excited about the possibility that this coin might really be gold?
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