Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 47

Full-circle rotation is common in mechanical systems, but less evident in biology. Yet many single-celled organisms are propelled by spinning, tail-like flagella. The Flagellum of the bacterium \(E\) coli spins at some 600 rad/s, propelling the bacterium at speeds around \(25 \mu \mathrm{m} / \mathrm{s}\). How many revolutions does \(E .\) coli's flagellum make as the bacterium crosses a microscope's \(150-\mu \mathrm{m}-\) wide field of view?

Short Answer

Expert verified
The flagellum of E. coli makes approximately 573 revolutions as the bacterium crosses a microscope's 150-micrometer-wide field of view.

Step by step solution

01

Calculate time taken to cross the field of view

First, find out how long it takes for E. coli to cross the field of view. This can be done by dividing the distance across the field of view (150µm) by the speed of E. coli (25µm/s): \( \frac{150\mu m}{25\mu m/s} = 6s \)
02

Determine the number of rotations

Next, calculate the number of rotations made by the flagellum during this time. As the flagellum spins at 600 rad/s and for one full circle the angle in radian is \(2\pi\), the rotations per second is \( \frac{600rad/s}{2 \pi} \). The total number of rotations in 6 seconds is \( \frac{600rad/s}{2 \pi} * 6s = 573 \) rotations approximately.

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 shaft connecting a power plant's turbine and electric generator is a solid cylinder of mass \(6.8 \mathrm{Mg}\) and diameter \(85 \mathrm{cm} .\) Find its rotational inertia.

A \(320-\mathrm{N}\) frictional force acts on the rim of a 1.0 -m-diameter wheel to oppose its rotational motion. Find the torque about the wheel's central axis.

A car tune-up manual calls for tightening the spark plugs to a torque of \(35.0 \mathrm{N} \cdot \mathrm{m} .\) To achieve this torque, with what force must you pull on the end of a 24.0 -cm-long wrench if you pull (a) at a right angle to the wrench shaft and (b) at \(110^{\circ}\) to the wrench shaft?

If a centrifuge's radius and mass are both doubled without other. wise changing the design, its rotational inertia will a. double. b. quadruple. c. increase by a factor of \(8 .\) d. increase by a factor of 16

A disk of radius \(R\) and thickness \(w\) has a mass density that increases from the center outward, given by \(\rho=\rho_{0} r / R,\) where \(r\) is the distance from the disk axis. Calculate (a) the disk's total mass \(M\) and (b) its rotational inertia about its axis in terms of \(M\) and \(R\). Compare with the results for a solid disk of uniform density and for a ring.
See all solutions

Recommended explanations on Physics Textbooks

Dynamics

Read Explanation

Space Physics

Read Explanation

Magnetism

Read Explanation

Physics of Motion

Read Explanation

Oscillations

Read Explanation

Force

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