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Two packing crates of masses m, = 10.0 kg and m,- 3.00 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 3.00 kg crate lies on a smooth incline of angle 42.0°. Find the acceleration of the 3.00 kg crate. m/s2 (up the incline) Find the tension in the string.

Two packing crates of masses m, = 10.0 kg and m,- 3.00 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The 3.00 kg crate lies on a smooth incline of angle 42.0°. Find the acceleration of the 3.00 kg crate. m/s2 (up the incline) Find the tension in the string.

College Physics
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)...
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**Problem Description:** Two packing crates of masses \( m_1 = 10.0 \, \text{kg} \) and \( m_2 = 3.00 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley as shown in the figure. The 3.00 kg crate lies on a smooth incline of angle \( 42.0^\circ \). - **Tasks:** 1. Find the acceleration of the 3.00 kg crate. \(\boxed{\rule{1cm}{0.15mm}} \, \text{m/s}^2\) (up the incline) 2. Find the tension in the string. \(\boxed{\rule{1cm}{0.15mm}} \, \text{N}\) **Diagram Explanation:** - The diagram shows two crates connected by a string over a pulley. - \( m_1 \) hangs vertically, while \( m_2 \) rests on an inclined plane. - The incline makes an angle of \( 42.0^\circ \) with the horizontal. - The system is designed to illustrate the physics of inclined planes and pulley mechanics, focusing on tension and acceleration. **Notes:** - Consider gravitational force acting on both crates. - Account for the force components acting along and perpendicular to the incline for the \( m_2 \) crate. - The system assumes no friction on the inclined plane and an ideal pulley with no rotational inertia.
Transcribed Image Text:**Problem Description:** Two packing crates of masses \( m_1 = 10.0 \, \text{kg} \) and \( m_2 = 3.00 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley as shown in the figure. The 3.00 kg crate lies on a smooth incline of angle \( 42.0^\circ \). - **Tasks:** 1. Find the acceleration of the 3.00 kg crate. \(\boxed{\rule{1cm}{0.15mm}} \, \text{m/s}^2\) (up the incline) 2. Find the tension in the string. \(\boxed{\rule{1cm}{0.15mm}} \, \text{N}\) **Diagram Explanation:** - The diagram shows two crates connected by a string over a pulley. - \( m_1 \) hangs vertically, while \( m_2 \) rests on an inclined plane. - The incline makes an angle of \( 42.0^\circ \) with the horizontal. - The system is designed to illustrate the physics of inclined planes and pulley mechanics, focusing on tension and acceleration. **Notes:** - Consider gravitational force acting on both crates. - Account for the force components acting along and perpendicular to the incline for the \( m_2 \) crate. - The system assumes no friction on the inclined plane and an ideal pulley with no rotational inertia.
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