Log out Go to App
Go to App

Learning Materials

Features

Discover

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/cm³.

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 \(0.603 \mathrm{g} / \mathrm{cm}^{3}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The pressure in a water pipe in the basement of an apartment house is $4.10 \times 10^{5} \mathrm{Pa},\( but on the seventh floor it is only \)1.85 \times 10^{5} \mathrm{Pa} .$ What is the height between the basement and the seventh floor? Assume the water is not flowing; no faucets are opened.
An IV is connected to a patient's vein. The blood pressure in the vein has a gauge pressure of \(12 \mathrm{mm}\) Hg. At least how far above the vein must the IV bag be hung in order for fluid to flow into the vein? Assume the fluid in the IV has the same density as blood.
A hypodermic syringe is attached to a needle that has an internal radius of \(0.300 \mathrm{mm}\) and a length of \(3.00 \mathrm{cm} .\) The needle is filled with a solution of viscosity $2.00 \times 10^{-3} \mathrm{Pa} \cdot \mathrm{s} ;\( it is injected into a vein at a gauge pressure of \)16.0 \mathrm{mm}$ Hg. Ignore the extra pressure required to accelerate the fluid from the syringe into the entrance of the needle. (a) What must the pressure of the fluid in the syringe be in order to inject the solution at a rate of $0.250 \mathrm{mL} / \mathrm{s} ?$ (b) What force must be applied to the plunger, which has an area of \(1.00 \mathrm{cm}^{2} ?\)
A dinoflagellate takes 5.0 s to travel 1.0 mm. Approximate a dinoflagellate as a sphere of radius \(35.0 \mu \mathrm{m}\) (ignoring the flagellum). (a) What is the drag force on the dinoflagellate in seawater of viscosity $0.0010 \mathrm{Pa} \cdot \mathrm{s} ?$ (b) What is the power output of the flagellate?
A sphere of radius \(1.0 \mathrm{cm}\) is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is \(12.0 \mathrm{g}\) and the density of the liquid is \(1200 \mathrm{kg} / \mathrm{m}^{3} .\) The sphere reaches a terminal speed of \(0.15 \mathrm{m} / \mathrm{s} .\) What is the viscosity of the liquid?
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Electromagnetism

Read Explanation

Force

Read Explanation

Atoms and Radioactivity

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Quantum Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free