2. Box 1 (m₁ = 1.8 kg) sits on a frictionless surface that is inclined at an angle from horizontal. It is connected to box 2 (m₂ = 2.4 kg) using a lightweight flexible cord that passes over a lightweight frictionless pulley (see figure). When a vertical force F of magnitude 5.0 N pushes up on box 2, the box has a downward acceleration of 4.5 m/s². Find a. the tension in the connecting cord, and b. the angle of the inclined surface. 7221 mq

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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**Problem Description:**

Box 1 (\(m_1 = 1.8 \, \text{kg}\)) sits on a frictionless surface that is inclined at an angle \(\beta\) from the horizontal. It is connected to box 2 (\(m_2 = 2.4 \, \text{kg}\)) using a lightweight flexible cord that passes over a lightweight frictionless pulley. When a vertical force \(F\) of magnitude \(5.0 \, \text{N}\) pushes up on box 2, the box has a downward acceleration of \(4.5 \, \text{m/s}^2\).

Find:

a. the tension in the connecting cord, and  
b. the angle \(\beta\) of the inclined surface.

**Diagram Explanation:**

The diagram shows:

- Box 1 (\(m_1\)) positioned on an inclined plane with angle \(\beta\) from the horizontal.
- Box 2 (\(m_2\)) hanging vertically and connected to box 1 via a cord that runs over a pulley.
- The force \(F\) acting upward on box 2.
- An arrow illustrating the angle \(\beta\) at the base of the inclined plane.

This setup demonstrates two boxes connected by a cord over a pulley with external forces and accelerations included.
Transcribed Image Text:**Problem Description:** Box 1 (\(m_1 = 1.8 \, \text{kg}\)) sits on a frictionless surface that is inclined at an angle \(\beta\) from the horizontal. It is connected to box 2 (\(m_2 = 2.4 \, \text{kg}\)) using a lightweight flexible cord that passes over a lightweight frictionless pulley. When a vertical force \(F\) of magnitude \(5.0 \, \text{N}\) pushes up on box 2, the box has a downward acceleration of \(4.5 \, \text{m/s}^2\). Find: a. the tension in the connecting cord, and b. the angle \(\beta\) of the inclined surface. **Diagram Explanation:** The diagram shows: - Box 1 (\(m_1\)) positioned on an inclined plane with angle \(\beta\) from the horizontal. - Box 2 (\(m_2\)) hanging vertically and connected to box 1 via a cord that runs over a pulley. - The force \(F\) acting upward on box 2. - An arrow illustrating the angle \(\beta\) at the base of the inclined plane. This setup demonstrates two boxes connected by a cord over a pulley with external forces and accelerations included.
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