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4.29 ** A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.0° below the hori- zontal, and the chair slides along the floor. (a) Draw a clearly la- beled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.

4.29 ** A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.0° below the hori- zontal, and the chair slides along the floor. (a) Draw a clearly la- beled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.

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 4.29** A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force \( F = 40.0 \, \text{N} \) that is directed at an angle of \( 37.0^\circ \) below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair. --- **Explanation:** The problem involves analyzing the forces acting on a chair with a mass of 12.0 kg as it is pushed along the floor. The push applied is 40.0 N at a \(37.0^\circ\) angle below the horizontal direction, and the surface is not frictionless. **Solution Approach:** 1. **Free-Body Diagram**: - Show the forces acting on the chair. - Include the gravitational force (weight) acting downward. - The normal force perpendicular to the floor. - The applied force split into horizontal and vertical components. 2. **Calculating Forces**: - Determine the horizontal and vertical components of the applied force using trigonometric functions. - \( F_x = 40.0 \, \text{N} \cdot \cos(37.0^\circ) \) - \( F_y = 40.0 \, \text{N} \cdot \sin(37.0^\circ) \) 3. **Normal Force Calculation**: - The normal force is affected by the vertical component of the applied force and the chair's weight. - Use Newton’s second law in the vertical direction to solve for the normal force.
Transcribed Image Text:**Problem 4.29** A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force \( F = 40.0 \, \text{N} \) that is directed at an angle of \( 37.0^\circ \) below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair. --- **Explanation:** The problem involves analyzing the forces acting on a chair with a mass of 12.0 kg as it is pushed along the floor. The push applied is 40.0 N at a \(37.0^\circ\) angle below the horizontal direction, and the surface is not frictionless. **Solution Approach:** 1. **Free-Body Diagram**: - Show the forces acting on the chair. - Include the gravitational force (weight) acting downward. - The normal force perpendicular to the floor. - The applied force split into horizontal and vertical components. 2. **Calculating Forces**: - Determine the horizontal and vertical components of the applied force using trigonometric functions. - \( F_x = 40.0 \, \text{N} \cdot \cos(37.0^\circ) \) - \( F_y = 40.0 \, \text{N} \cdot \sin(37.0^\circ) \) 3. **Normal Force Calculation**: - The normal force is affected by the vertical component of the applied force and the chair's weight. - Use Newton’s second law in the vertical direction to solve for the normal force.
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