Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 27

Estimate the mass of your head. Assume that its density is that of water, \(1000 \mathrm{~kg} / \mathrm{m}^{3}\)

Short Answer

Expert verified
Based on the assumption that the density of a human head is the same as water, 1000 kg/m³, and the average adult head dimensions, the estimated mass of a human head is approximately 2.64 kg. Keep in mind that this estimation is based on an ellipsoid model and may vary for each individual.

Step by step solution

01

Approximate the volume of your head

To make this estimation, you can use the average adult head dimensions found in various studies. The human head can be roughly modeled as an ellipsoid. The general formula for the volume of an ellipsoid is given by: \(V = \frac{4}{3}\pi abc\) Where \(a\), \(b\), and \(c\) are the semi-axes lengths of the ellipsoid. You can find reference measurements for an average head and use those as the semi-axis lengths. For example, using the measurements: \(a = 9.5\mathrm{~cm}\), \(b = 8\mathrm{~cm}\), and \(c = 11.5\mathrm{~cm}\) Based on these approximations, let us calculate the volume.
02

Calculate the volume using the ellipsoid formula

Plugging the dimensions into the ellipsoid formula, you get: \(V = \frac{4}{3}\pi (9.5\mathrm{~cm})(8\mathrm{~cm})(11.5\mathrm{~cm})\) Now, calculate the volume: \(V \approx 2636.1 \mathrm{~cm}^3\)
03

Convert volume to m³

The volume calculated above is in cubic centimeters. Since the density given is in kg/m³, we will need to convert the volume to cubic meters, as follows: \(V \approx \frac{2,636.1\mathrm{~cm^3}}{100^3}\mathrm{~m^3}\) \(V \approx 2.6361 \times 10^{-5}\mathrm{~m^3}\)
04

Compute the mass using the density formula

The mass of your head can be computed using the formula for density, which is given by: \(\rho = \frac{m}{V}\) Rearranging the formula to solve for mass, we get: \(m =\rho \times V \) Now, plug in the density of water and the calculated volume of your head: \(m =(1000\mathrm{~kg/m^3})(2.6361\times 10^{-5} \mathrm{~m^3})\) Calculate the mass: \(m\approx 2.6361\mathrm{~kg}\) So, the estimated mass of your head is approximately 2.64 kg. Remember, this is just an estimation based on assumptions and the actual mass may be different for every individual.

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

In Europe, cars' gas consumption is measured in liters per 100 kilometers. In the United States, the unit used is miles per gallon. a) How are these units related? b) How many miles per gallon does your car get if it consumes 12.2 liters per 100 kilometers? c) What is your car's gas consumption in liters per 100 kilometers if it gets 27.4 miles per gallon? d) Can you draw a curve plotting miles per gallon versus liters per 100 kilometers? If yes, draw the curve.

The distance from the center of the Moon to the center of the Earth ranges from approximately \(356,000 \mathrm{~km}\) to \(407,000 \mathrm{~km}\). What are these distances in miles? Be certain to round your answers to the appropriate number of significant figures.

Is it possible to add three equal-length vectors and obtain a vector sum of zero? If so, sketch the arrangement of the three vectors. If not, explain why not.

A position vector has components \(x=34.6 \mathrm{~m}\) and \(y=-53.5 \mathrm{~m} .\) Find the vector's length and angle with the \(x\) -axis.

The radius of Earth is \(6378 . \mathrm{km}\). What is its circumference to three significant figures?
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Engineering Physics

Read Explanation

Astrophysics

Read Explanation

Energy Physics

Read Explanation

Work Energy and Power

Read Explanation

Kinematics 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