Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Three forces with magnitudes 70 pounds, 100 pounds and 20 pounds act on an object at angles 50°, -40°, and 110° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. Draw a diagram of your analysis, and include the resultant force.

Three forces with magnitudes 70 pounds, 100 pounds and 20 pounds act on an object at angles 50°, -40°, and 110° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. Draw a diagram of your analysis, and include the resultant force.

icon
Related questions
Question
**Question 7** Three forces with magnitudes 70 pounds, 100 pounds, and 20 pounds act on an object at angles 50°, -40°, and 110° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. Draw a diagram of your analysis, and include the resultant force. **Analysis:** To solve this problem, we need to determine the components of each force in the x and y directions, sum these components, and then find the magnitude and direction of the resultant force. ### Step-by-Step Solution: 1. **Resolve each force into x and y components using trigonometry:** - **Force \( F_1 \) (70 pounds at 50°):** \( F_{1x} = 70 \cos(50°) \) \( F_{1y} = 70 \sin(50°) \) - **Force \( F_2 \) (100 pounds at -40°):** \( F_{2x} = 100 \cos(-40°) \) \( F_{2y} = 100 \sin(-40°) \) - **Force \( F_3 \) (20 pounds at 110°):** \( F_{3x} = 20 \cos(110°) \) \( F_{3y} = 20 \sin(110°) \) 2. **Calculate the numerical values of the components:** Use a calculator (ensure it is in degree mode): - \( F_{1x} = 70 \cos(50°) \approx 45 \) - \( F_{1y} = 70 \sin(50°) \approx 54 \) - \( F_{2x} = 100 \cos(-40°) \approx 77 \) - \( F_{2y} = 100 \sin(-40°) \approx -64 \) - \( F_{3x} = 20 \cos(110°) \approx -7 \) - \( F_{3y} = 20 \sin(110°) \approx 19 \) 3. **Sum the x and y components:** - \( R_x = F_{1x} + F_{2x} + F_{3x} \) \( R
Transcribed Image Text:**Question 7** Three forces with magnitudes 70 pounds, 100 pounds, and 20 pounds act on an object at angles 50°, -40°, and 110° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. Draw a diagram of your analysis, and include the resultant force. **Analysis:** To solve this problem, we need to determine the components of each force in the x and y directions, sum these components, and then find the magnitude and direction of the resultant force. ### Step-by-Step Solution: 1. **Resolve each force into x and y components using trigonometry:** - **Force \( F_1 \) (70 pounds at 50°):** \( F_{1x} = 70 \cos(50°) \) \( F_{1y} = 70 \sin(50°) \) - **Force \( F_2 \) (100 pounds at -40°):** \( F_{2x} = 100 \cos(-40°) \) \( F_{2y} = 100 \sin(-40°) \) - **Force \( F_3 \) (20 pounds at 110°):** \( F_{3x} = 20 \cos(110°) \) \( F_{3y} = 20 \sin(110°) \) 2. **Calculate the numerical values of the components:** Use a calculator (ensure it is in degree mode): - \( F_{1x} = 70 \cos(50°) \approx 45 \) - \( F_{1y} = 70 \sin(50°) \approx 54 \) - \( F_{2x} = 100 \cos(-40°) \approx 77 \) - \( F_{2y} = 100 \sin(-40°) \approx -64 \) - \( F_{3x} = 20 \cos(110°) \approx -7 \) - \( F_{3y} = 20 \sin(110°) \approx 19 \) 3. **Sum the x and y components:** - \( R_x = F_{1x} + F_{2x} + F_{3x} \) \( R
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer