Problem 4: A cord is wrapped around each of the two disks A and B with masses of m, and mg respectively. They are currently being held in place. If they are released from rest determine the angula acceleration of each disk and the tension in the cord C. Neglect the mass of the cords. Disk A is attache to cord C via a pin so it can freely rotate. a.) What is the tension in cord C in Newtons? b.) What is the acceleration of disk B in the y direction in m/s² (use + for the upward direction c.) What is the acceleration of B in the y direction in m/s² if mg » MA Hint: you don't necessarily need the answer to c to solve but it can help. d.) What is the acceleration of B in the y direction if ma >> Mg Hint: you don't necessarily need the answer to c to solve but it can help. C
Problem 4: A cord is wrapped around each of the two disks A and B with masses of m, and mg respectively. They are currently being held in place. If they are released from rest determine the angula acceleration of each disk and the tension in the cord C. Neglect the mass of the cords. Disk A is attache to cord C via a pin so it can freely rotate. a.) What is the tension in cord C in Newtons? b.) What is the acceleration of disk B in the y direction in m/s² (use + for the upward direction c.) What is the acceleration of B in the y direction in m/s² if mg » MA Hint: you don't necessarily need the answer to c to solve but it can help. d.) What is the acceleration of B in the y direction if ma >> Mg Hint: you don't necessarily need the answer to c to solve but it can help. C
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Transcribed Image Text:**Problem 4: Analysis of Cord Wrapped Around Disks**
**Problem Statement:**
A cord is wrapped around each of the two disks (A and B) with masses \(m_A\) and \(m_B\) respectively. Currently, they are being held in place. Upon release from rest, determine the following:
1. The angular acceleration of each disk.
2. The tension in the cord (C).
3. The acceleration of disk B in the y-direction under different conditions.
**Assumptions:**
- Neglect the mass of the cords.
- Disk A is attached to cord C via a pin, allowing it to freely rotate.
**Questions:**
a.) What is the tension in cord C in Newtons?
b.) What is the acceleration of disk B in the y-direction in \(m/s^2\) (consider upward direction as positive)?
c.) What is the acceleration of B in the y direction in \(m/s^2\) if \(m_B \gg m_A\)?
- Hint: You don’t necessarily need the answer to (c) to solve it, but it can help.
d.) What is the acceleration of B in the y direction if \(m_A \gg m_B\)?
- Hint: You don’t necessarily need the answer to (c) to solve it, but it can help.
**Diagram Explanation:**
The diagram shows two disks, A and B, each with a radius (r) and different masses. A cord wraps around each disk and is attached at point C for disk A and point D for disk B.
Key variables presented in the diagram:
- \(h_A\) is the vertical distance for disk A = 0.3 m
- \(h_B\) is the vertical distance for disk B = 0.5 m
- \(r_A\) is the radius of disk A = 0.1 m
- \(r_B\) is the radius of disk B = 0.1 m
- \(m_A\) is the mass of disk A = 10 kg
- \(m_B\) is the mass of disk B = 15 kg
**Table of Variables and Values:**
| Variable | Value |
|----------|-------|
| \(m_A\) | 10 kg |
| \(m_B\) | 15 kg |
| \(r_A\) | 0.1 m
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