Question

Some dragonflies splash down on the surface of a lake and then fly upward, spinning rapidly to spray the water off their bodies. When the dragonflies spin, they tuck themselves into a "ball." They spin with a linear speed of $2.3 \mathrm{~m} / \mathrm{s}$ and produce a centripetal acceleration of $250 \mathrm{~m} / \mathrm{s}^{2}$. What is the radius of the ball they form?

Name: Problem 108, Chapter 9: Pearson Physics
Uploaded: 2023-02-22T21:04:22-08:00
Duration: 1 min 33 s
Channel: James Kiss
Description: Some dragonflies splash down on the surface of a lake and then fly upward, spinning rapidly to spray the water off their bodies. When the dragonflies spin, they tuck themselves into a "ball." They spin with a linear speed of 2.3 m / s and produce a centripetal acceleration of 250 m / s^2. What is the radius of the ball they form?

   Some dragonflies splash down on the surface of a lake and then fly upward, spinning rapidly to spray the water off their bodies. When the dragonflies spin, they tuck themselves into a "ball."
They spin with a linear speed of $2.3 \mathrm{~m} / \mathrm{s}$ and produce a centripetal acceleration of $250 \mathrm{~m} / \mathrm{s}^{2}$. What is the radius of the ball they form?

Pearson Physics

James S. Walker 1st Edition

Chapter 9, Problem 108

Instant Answer

Solved by Expert James Kiss

02/22/2023

Step 1

The formula for centripetal acceleration is given by: \[a = \frac{v^2}{r}\] where: - $a$ is the centripetal acceleration, - $v$ is the linear speed, and - $r$ is the radius of the circular path. Show more…

Show all steps

Thanks for your feedback!

Some dragonflies splash down on the surface of a lake and then fly upward, spinning rapidly to spray the water off their bodies. When the dragonflies spin, they tuck themselves into a "ball." They spin with a linear speed of $2.3 \mathrm{~m} / \mathrm{s}$ and produce a centripetal acceleration of $250 \mathrm{~m} / \mathrm{s}^{2}$. What is the radius of the ball they form?

Play audio

Feedback

James Kiss and 79 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Centripetal Acceleration

Centripetal acceleration is the acceleration that acts toward the center of a circle, which is necessary to keep an object moving in circular motion. It is given by the formula a = v² / r, where v is the constant linear speed and r is the radius of the circular path. This concept is central to understanding how objects maintain their curved trajectory.

Linear Speed in Circular Motion

In the context of circular motion, linear speed refers to the constant rate at which an object moves along the circular path. This speed, combined with the requirement of centripetal acceleration, determines the radius of the curvature through the relationship r = v² / a. Understanding this relationship is key to analyzing motions that involve spinning or circular trajectories.

Please give Ace some feedback