A box of mass m = 22.0 kg is pulled up a ramp that is inclined at an angle 0 = 23.0° angle with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is u = 0.275, and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of a = 2.89 m/s², calculate the tension Fr in the rope. Use g = 9.81 m/s? for the acceleration due to gravity. He Fr = Enter numeric value

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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**Problem Statement:**

A box of mass \( m = 22.0 \, \text{kg} \) is pulled up a ramp that is inclined at an angle \( \theta = 23.0^\circ \) with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is \( \mu_k = 0.275 \), and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of \( a = 2.89 \, \text{m/s}^2 \), calculate the tension \( F_T \) in the rope. Use \( g = 9.81 \, \text{m/s}^2 \) for the acceleration due to gravity.

**Calculation:**

\[ F_T = \, \boxed{\text{Enter numeric value}} \, \text{N} \]

**Diagram Description:**

The diagram on the right illustrates a box on an inclined ramp. The ramp is colored green and is inclined at an angle \( \theta \) to the horizontal. A rope pulling the box is shown with an arrow labeled \( \vec{a} \), indicating the direction of acceleration parallel to the ramp. The angle \( \theta \) is marked near the ramp's base, and \( \mu_k \) denotes the coefficient of kinetic friction between the box and the surface of the ramp.
Transcribed Image Text:**Problem Statement:** A box of mass \( m = 22.0 \, \text{kg} \) is pulled up a ramp that is inclined at an angle \( \theta = 23.0^\circ \) with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is \( \mu_k = 0.275 \), and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of \( a = 2.89 \, \text{m/s}^2 \), calculate the tension \( F_T \) in the rope. Use \( g = 9.81 \, \text{m/s}^2 \) for the acceleration due to gravity. **Calculation:** \[ F_T = \, \boxed{\text{Enter numeric value}} \, \text{N} \] **Diagram Description:** The diagram on the right illustrates a box on an inclined ramp. The ramp is colored green and is inclined at an angle \( \theta \) to the horizontal. A rope pulling the box is shown with an arrow labeled \( \vec{a} \), indicating the direction of acceleration parallel to the ramp. The angle \( \theta \) is marked near the ramp's base, and \( \mu_k \) denotes the coefficient of kinetic friction between the box and the surface of the ramp.
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