3. A uniform disk of mass M and radius R compressed a spring (with spring constant k) a distance of xo from equilibrium. The spring is released and the disk begins to roll smoothly (there is no friction between the spring and the disk) up a ramp, as seen in (I) of the figure below. (1) +7 M, R (II) Max Height, H ++ k ¦¦M,R H }/ (a) What is the speed of the disk after it is released from the spring? (b) What is the maximum height, H, reached by the disk? Imagine now, as seen in (II), that the disk is reset to its initial position and the ramp is replaced with one that abruptly ends after a vertical height of H/2, where H is what you found in (b), and guides any rolling on it straight up. (c) The disk is once again released from the spring. What is the new maximum height it reaches (in mid-air)?

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)...
icon
Related questions
Question
### Question 3: Dynamics of a Uniform Disk and Spring System

#### Problem Statement:
A uniform disk of mass \( M \) and radius \( R \) compresses a spring (with spring constant \( k \)) a distance of \( x_0 \) from equilibrium. Upon release, the disk begins to roll smoothly up a ramp, as depicted in diagram (I) below. There is no friction between the spring and the disk.

**Diagrams Explanation:**

**Diagram (I):**
- A spring is compressed by a uniform disk.
- The compressed distance is \( x_0 \).
- Upon release, the disk rolls up a ramp reaching a maximum height \( H \).

**Diagram (II):**
- The same initial setup, but the ramp now ends at a vertical height of \( H/2 \).
- Beyond this, the disk is guided vertically upward.

**Questions:**

**(a)** What is the speed of the disk after it is released from the spring?

**(b)** What is the maximum height \( H \) reached by the disk?

Imagine now, as seen in (II), that the disk is reset to its initial position and the ramp is replaced with one that abruptly ends after a vertical height of \( H/2 \), where \( H \) is what you found in (b), and guides any rolling on it straight up.

**(c)** The disk is once again released from the spring. What is the new maximum height it reaches (in mid-air)?

---
### Figures:

**Diagram (I):**
- Depicts the initial compression \( x_0 \) and the trajectory of the disk up the ramp.
- The disk rolls up, reaching a maximum height \( H \).

**Diagram (II):**
- Depicts the same initial conditions but with the ramp terminating at height \( H/2 \).
- Beyond \( H/2 \), the disk follows a vertical path.

--- 

Calculating the specifics of the disk's motion involves understanding energy conservation, rotational motion, and potentially projectile dynamics for part (c).
Transcribed Image Text:### Question 3: Dynamics of a Uniform Disk and Spring System #### Problem Statement: A uniform disk of mass \( M \) and radius \( R \) compresses a spring (with spring constant \( k \)) a distance of \( x_0 \) from equilibrium. Upon release, the disk begins to roll smoothly up a ramp, as depicted in diagram (I) below. There is no friction between the spring and the disk. **Diagrams Explanation:** **Diagram (I):** - A spring is compressed by a uniform disk. - The compressed distance is \( x_0 \). - Upon release, the disk rolls up a ramp reaching a maximum height \( H \). **Diagram (II):** - The same initial setup, but the ramp now ends at a vertical height of \( H/2 \). - Beyond this, the disk is guided vertically upward. **Questions:** **(a)** What is the speed of the disk after it is released from the spring? **(b)** What is the maximum height \( H \) reached by the disk? Imagine now, as seen in (II), that the disk is reset to its initial position and the ramp is replaced with one that abruptly ends after a vertical height of \( H/2 \), where \( H \) is what you found in (b), and guides any rolling on it straight up. **(c)** The disk is once again released from the spring. What is the new maximum height it reaches (in mid-air)? --- ### Figures: **Diagram (I):** - Depicts the initial compression \( x_0 \) and the trajectory of the disk up the ramp. - The disk rolls up, reaching a maximum height \( H \). **Diagram (II):** - Depicts the same initial conditions but with the ramp terminating at height \( H/2 \). - Beyond \( H/2 \), the disk follows a vertical path. --- Calculating the specifics of the disk's motion involves understanding energy conservation, rotational motion, and potentially projectile dynamics for part (c).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Rotational Kinetic energy
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.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON