Homework Help is Here – Start Your Trial Now!
Science
Physics
Find the magnitude and direction of the resultant of the five concurrent forces acting on a bolt.

Find the magnitude and direction of the resultant of the five concurrent forces acting on a bolt.

Principles of Physics: A Calculus-Based Text
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
Chapter5: More Applications Of Newton’s Laws
Section: Chapter Questions
Problem 1CQ: A car is moving forward slowly and is speeding up. A student claims that the car exerts a force on...
See similar textbooks
icon
Related questions
Question
### Finding the Magnitude and Direction of the Resultant of Five Concurrent Forces #### Problem Statement Find the magnitude and direction of the resultant of the five concurrent forces acting on a bolt. #### Diagram Analysis ![Five concurrent forces acting on a bolt](Fig. P2-54) In the diagram (Fig. P2-54), five forces act on a bolt at various angles. The forces and their respective angles from the horizontal axis are as follows: - **Force F1:** - Magnitude: 80 N - Angle: 27° below the negative x-axis - **Force F2:** - Magnitude: 400 N - Angle: 22° below the negative x-axis - **Force F3:** - Magnitude: 150 N - Angle: 46° above the negative y-axis - **Force F4:** - Magnitude: 300 N - Angle: 45° above the positive x-axis - **Force F5:** - Magnitude: 250 N - Angle: 18° below the positive x-axis These forces create various directional components that need to be resolved into x and y components to find the resultant force. ### Method to Find Resultant Force 1. **Resolve all forces into x and y components:** - For each force \( F_i \): - \( F_{ix} = F_i \cos(\theta_i) \) - \( F_{iy} = F_i \sin(\theta_i) \) where \( \theta_i \) is the angle the force makes with the horizontal axis. 2. **Summing Components:** - Sum all the x-components to get the total x-component \( F_{Rx} \): \[ F_{Rx} = \sum (F_{ix}) \] - Sum all the y-components to get the total y-component \( F_{Ry} \): \[ F_{Ry} = \sum (F_{iy}) \] 3. **Calculate Magnitude of Resultant Force:** \[ F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} \] 4. **Find Direction of Resultant Force:** - The angle \( \theta_R \) can be found using: \[
Transcribed Image Text:### Finding the Magnitude and Direction of the Resultant of Five Concurrent Forces #### Problem Statement Find the magnitude and direction of the resultant of the five concurrent forces acting on a bolt. #### Diagram Analysis ![Five concurrent forces acting on a bolt](Fig. P2-54) In the diagram (Fig. P2-54), five forces act on a bolt at various angles. The forces and their respective angles from the horizontal axis are as follows: - **Force F1:** - Magnitude: 80 N - Angle: 27° below the negative x-axis - **Force F2:** - Magnitude: 400 N - Angle: 22° below the negative x-axis - **Force F3:** - Magnitude: 150 N - Angle: 46° above the negative y-axis - **Force F4:** - Magnitude: 300 N - Angle: 45° above the positive x-axis - **Force F5:** - Magnitude: 250 N - Angle: 18° below the positive x-axis These forces create various directional components that need to be resolved into x and y components to find the resultant force. ### Method to Find Resultant Force 1. **Resolve all forces into x and y components:** - For each force \( F_i \): - \( F_{ix} = F_i \cos(\theta_i) \) - \( F_{iy} = F_i \sin(\theta_i) \) where \( \theta_i \) is the angle the force makes with the horizontal axis. 2. **Summing Components:** - Sum all the x-components to get the total x-component \( F_{Rx} \): \[ F_{Rx} = \sum (F_{ix}) \] - Sum all the y-components to get the total y-component \( F_{Ry} \): \[ F_{Ry} = \sum (F_{iy}) \] 3. **Calculate Magnitude of Resultant Force:** \[ F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} \] 4. **Find Direction of Resultant Force:** - The angle \( \theta_R \) can be found using: \[
Expert Solution
steps

Step by step

Solved in 9 steps with 113 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Third law of motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS