(ex) A ball of mass 2.0 kg is connected by two massless strings, each with length L = 0.25 m, to a vertical rotating rod. The strings are tied to the rod with separation d = 0.40 m, and are taut. The period of rotation is 0.50 seconds. (a) Determine the tangential speed of the ball. (b) Determine the tensions in the upper and lower strings. (c) Suppose the rotation is slowed, so that the lower string just barely goes slack. Then what is the new tangential speed of the ball? LACOS
(ex) A ball of mass 2.0 kg is connected by two massless strings, each with length L = 0.25 m, to a vertical rotating rod. The strings are tied to the rod with separation d = 0.40 m, and are taut. The period of rotation is 0.50 seconds. (a) Determine the tangential speed of the ball. (b) Determine the tensions in the upper and lower strings. (c) Suppose the rotation is slowed, so that the lower string just barely goes slack. Then what is the new tangential speed of the ball? LACOS
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
Please check my work and answer part 3. This is an example question NOT HOMEWORK
![**Example Problem: Circular Motion with Tension**
A ball of mass 2.0 kg is connected by two massless strings, each with length \(L = 0.25 \, \text{m}\), to a vertical rotating rod. The strings are tied to the rod with separation \(d = 0.40 \, \text{m}\), and both are taut. The period of rotation is 0.50 seconds.
1. **Determine the tangential speed of the ball**:
\[
V_{\text{tan}} = 2 \pi r f
\]
The frequency \(f\) is given by:
\[
f = \frac{1}{\text{Period}} = \frac{1}{0.5}
\]
For a triangle formed with the strings:
\[
\cos \theta = \frac{d/2}{L} = \frac{0.2}{0.25} = 0.8 \implies \theta = \cos^{-1}(0.8)
\]
Calculating \(r\):
\[
r^2 + \left(\frac{d}{2}\right)^2 = L^2 \;\Rightarrow\; r^2 = 0.25 - 0.04 = 0.21 \;\Rightarrow\; r = 0.15
\]
Use for \(V_{\text{tan}}\):
\[
V_{\text{tan}} = \frac{2 \pi \times 0.15}{0.5} = 1.88 \, \text{m/s}
\]
2. **Determine the tensions in the upper and lower strings**:
- Equations for forces in x and y directions:
\[
T_u \cos \theta + T_l \cos \theta = \frac{mv^2}{r}
\]
\[
T_u \sin \theta + T_l \sin \theta = mg
\]
- Solving for \(T_u\) and \(T_l\):
\[
T_u = \frac{mv^2}{2 \cos \theta} + \frac{mg}{2 \sin \theta} \Rightarrow T_u = \frac{2(1.88)^2}{2(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d3c3ab0-3648-4520-b7d5-a83f201d4237%2Ff8267eb9-d391-4016-a741-f5fe77eb38b0%2Fuue0z1f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem: Circular Motion with Tension**
A ball of mass 2.0 kg is connected by two massless strings, each with length \(L = 0.25 \, \text{m}\), to a vertical rotating rod. The strings are tied to the rod with separation \(d = 0.40 \, \text{m}\), and both are taut. The period of rotation is 0.50 seconds.
1. **Determine the tangential speed of the ball**:
\[
V_{\text{tan}} = 2 \pi r f
\]
The frequency \(f\) is given by:
\[
f = \frac{1}{\text{Period}} = \frac{1}{0.5}
\]
For a triangle formed with the strings:
\[
\cos \theta = \frac{d/2}{L} = \frac{0.2}{0.25} = 0.8 \implies \theta = \cos^{-1}(0.8)
\]
Calculating \(r\):
\[
r^2 + \left(\frac{d}{2}\right)^2 = L^2 \;\Rightarrow\; r^2 = 0.25 - 0.04 = 0.21 \;\Rightarrow\; r = 0.15
\]
Use for \(V_{\text{tan}}\):
\[
V_{\text{tan}} = \frac{2 \pi \times 0.15}{0.5} = 1.88 \, \text{m/s}
\]
2. **Determine the tensions in the upper and lower strings**:
- Equations for forces in x and y directions:
\[
T_u \cos \theta + T_l \cos \theta = \frac{mv^2}{r}
\]
\[
T_u \sin \theta + T_l \sin \theta = mg
\]
- Solving for \(T_u\) and \(T_l\):
\[
T_u = \frac{mv^2}{2 \cos \theta} + \frac{mg}{2 \sin \theta} \Rightarrow T_u = \frac{2(1.88)^2}{2(
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON