Answered: The sum of the x components (question…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 50P: Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component...

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The sum of the x components (question #1), is 19.45 N.

Question 2) what is the sum of the Y components of all 3 forces depicted?

Question 3) what is the magnitude for the resultant force?

Question 4) what is the angle (magnitude only) of the resultant force?

Expert Solution

Step 1 :Introduction

The force diagram of the system is given below:

The sum of the horizontal force acting on the system is calculated by using the formula $F_{x} = F_{1} \cos (30 °) - (F_{2} + F_{3} \sin (20 °))$ , where $F_{1} = 65 N, F_{2} = 30 N$ and $F_{3} = 20 N$ .The sum of the vertical force acting on the system is calculated by using the formula $F_{y} = F_{1} \sin (30 °) - (F_{3} \cos (20 °))$

The magnitude of the resultant force is calculated by using the formula $F = \sqrt{{(F_{x})}^{2} + {(F_{y})}^{2}}$ and the direction is calculated by using the formula $θ = \tan^{- 1} (\frac{F_{y}}{F_{x}})$ .

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