Two packing crates of masses m, = 10.0 kg and m, = 4.90 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 4.90-kg crate lies on a smooth incline of angle 37.0°. Find the following. m2 (a) the acceleration of the 4.90-kg crate m/s? (up the incline) (b) the tension in the string N.

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

Two packing crates of masses \( m_1 = 10.0 \, \text{kg} \) and \( m_2 = 4.90 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley as shown in the figure. The 4.90-kg crate lies on a smooth incline of angle \( 37.0^\circ \). Find the following:

(a) The acceleration of the 4.90-kg crate:
\[ \underline{\phantom{m/s^2}}\; (\text{up the incline}) \]

(b) The tension in the string:
\[ \underline{\phantom{N}} \, N \]

**Diagram Explanation:**

The diagram illustrates two crates connected by a string passing over a frictionless pulley. 
- Crate \( m_1 \) (10.0 kg) is hanging vertically.
- Crate \( m_2 \) (4.90 kg) is on an incline with a smooth surface, with an angle \( \theta = 37.0^\circ \) to the horizontal. 
- The pulley facilitates the motion between the two crates, with the string oriented along the direction of the incline for crate \( m_2 \).

The objective is to determine the acceleration of the crate on the incline moving upwards and the tension in the string connecting the two crates.
Transcribed Image Text:**Problem Statement:** Two packing crates of masses \( m_1 = 10.0 \, \text{kg} \) and \( m_2 = 4.90 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley as shown in the figure. The 4.90-kg crate lies on a smooth incline of angle \( 37.0^\circ \). Find the following: (a) The acceleration of the 4.90-kg crate: \[ \underline{\phantom{m/s^2}}\; (\text{up the incline}) \] (b) The tension in the string: \[ \underline{\phantom{N}} \, N \] **Diagram Explanation:** The diagram illustrates two crates connected by a string passing over a frictionless pulley. - Crate \( m_1 \) (10.0 kg) is hanging vertically. - Crate \( m_2 \) (4.90 kg) is on an incline with a smooth surface, with an angle \( \theta = 37.0^\circ \) to the horizontal. - The pulley facilitates the motion between the two crates, with the string oriented along the direction of the incline for crate \( m_2 \). The objective is to determine the acceleration of the crate on the incline moving upwards and the tension in the string connecting the two crates.
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