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How far have you pulled the block and cylinder when everything stops?

How far have you pulled the block and cylinder when everything stops?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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How far have you pulled the block and cylinder when everything stops?

**Problem Description:** You apply a horizontal force with magnitude \( F_{yb} = 59 \, \text{N} \) to a system on an inclined plane. The system consists of a block with mass \( m_b = 6.3 \, \text{kg} \) and a solid cylinder with mass \( m_c = 5.9 \, \text{kg} \) and radius \( r = 0.4 \, \text{m} \). The cylinder is connected to a spring with a spring constant \( k = 145 \, \text{N/m} \). The inclined plane has an angle \( \theta = 28 \) degrees and features both static friction (\( \mu_s = 0.63 \)) and kinetic friction (\( \mu_k = 0.36 \)). Initially, everything is at rest, and the spring is unstretched. As the block slides and the cylinder rolls down the plane, the spring stretches. **Diagram Explanation:** The diagram illustrates a block labeled "b" and a cylinder labeled "c" on an inclined plane. The block is being pulled horizontally by a force \( \vec{F}_{yb} \). A spring with a constant \( k \) is attached to the cylinder, and the angle of the incline is shown as \( \theta \). **Question:** Determine the speed of the block and the cylinder after being pulled 96 cm down the plane. **Solution:** The calculated speed of the block and cylinder is \( v = 1.92 \, \text{m/s} \).
Transcribed Image Text:**Problem Description:** You apply a horizontal force with magnitude \( F_{yb} = 59 \, \text{N} \) to a system on an inclined plane. The system consists of a block with mass \( m_b = 6.3 \, \text{kg} \) and a solid cylinder with mass \( m_c = 5.9 \, \text{kg} \) and radius \( r = 0.4 \, \text{m} \). The cylinder is connected to a spring with a spring constant \( k = 145 \, \text{N/m} \). The inclined plane has an angle \( \theta = 28 \) degrees and features both static friction (\( \mu_s = 0.63 \)) and kinetic friction (\( \mu_k = 0.36 \)). Initially, everything is at rest, and the spring is unstretched. As the block slides and the cylinder rolls down the plane, the spring stretches. **Diagram Explanation:** The diagram illustrates a block labeled "b" and a cylinder labeled "c" on an inclined plane. The block is being pulled horizontally by a force \( \vec{F}_{yb} \). A spring with a constant \( k \) is attached to the cylinder, and the angle of the incline is shown as \( \theta \). **Question:** Determine the speed of the block and the cylinder after being pulled 96 cm down the plane. **Solution:** The calculated speed of the block and cylinder is \( v = 1.92 \, \text{m/s} \).
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