/*! 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 27 Estimate the mass of your head. ... [FREE SOLUTION] | 91影视

91影视

Log out

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/m鲁, 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 m鲁

The volume calculated above is in cubic centimeters. Since the density given is in kg/m鲁, 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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Find the magnitude and direction of \(-7 \vec{B}+3 \vec{A}\), where \(\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)\)

A position vector has a length of \(40.0 \mathrm{~m}\) and is at an angle of \(57.0^{\circ}\) above the \(x\) -axis. Find the vector's components.

One cubic centimeter of water has a mass of 1 gram. A milliliter is equal to a cubic centimeter. What is the mass, in kilograms, of a liter of water? A metric ton is a thousand kilograms. How many cubic centimeters of water are in a metric ton of water? If a metric ton of water were held in a thin-walled cubical tank, how long (in meters) would each side of the tank be?

What angle does \(\vec{A}=\left(A_{x}, A_{y}\right)=(30.0 \mathrm{~m},-50.0 \mathrm{~m})\) make with the positive \(x\) -axis? What angle does it make with the negative \(y\) -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

Solid State Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Magnetism

Read Explanation

Torque and Rotational Motion

Read Explanation

Waves Physics

Read Explanation

Nuclear 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.