Answered: A block is pushed across a horizontal…

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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A block is pushed across a horizontal surface by the force shown. If the coefficient of kinetic friction between the block and the surface is 0.2, F = 29 N, theta = 32°, and M = 3 kg, what is the magnitude of the acceleration of the block?

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Step 1 :Introduction

The free body diagram of the system is given below:

The horizontal forces acting on the block are horizontal component of applied force , which is , $F_{x} = F \cos (θ)$ acting in the positive x-direction and the frictional force , which is , $f_{k} = μ_{k} M g$ acting in the negative x-direction , where $F = 29 N$ is the applied force , $θ = 32 °$ is the angle , $μ_{k} = 0.2$ is the coefficient of kinetic friction , $M = 3 k g$ is the mass of the block and $g = 9.8 m / s^{2}$ is the acceleration due to gravity .

According to Newton's second law of motion , the horizontal acceleration is calculated by using the formula $a_{x} = \frac{F \cos (θ) - f_{k}}{M}$ .

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