Forces of 9 Ibs and 13 lbs act at a 38° angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.

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)...
icon
Related questions
Question

Answer in writing on paper, please. Thank you.

**Topic: Resultant Forces**

Forces of 9 lbs and 13 lbs act at a 38° angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force.

**Understanding the Problem:**

- To solve for the resultant force when two forces are acting at an angle, use the formula for the magnitude of the resultant force (R):

  \[
  R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos(\theta)}
  \]

  where \( F_1 \) and \( F_2 \) are the magnitudes of the two forces, and \( \theta \) is the angle between them.

- To find the angle between the resultant force and one of the given forces (\( F_1 \) in this case), you can use the formula:

  \[
  \tan(\alpha) = \frac{F_2 \sin(\theta)}{F_1 + F_2 \cos(\theta)}
  \]

  where \( \alpha \) is the angle between the resultant force and \( F_1 \).

**Steps to Solve:**

1. Substitute the values \( F_1 = 9 \, \text{lbs} \), \( F_2 = 13 \, \text{lbs} \), and \( \theta = 38^\circ \) into the formula for \( R \).

2. Calculate the angle \( \alpha \) using the tangent formula. 

This process will give the magnitude of the resultant force and the angles with the original forces.
Transcribed Image Text:**Topic: Resultant Forces** Forces of 9 lbs and 13 lbs act at a 38° angle to each other. Find the magnitude of the resultant force and the angle that the resultant makes with each force. **Understanding the Problem:** - To solve for the resultant force when two forces are acting at an angle, use the formula for the magnitude of the resultant force (R): \[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos(\theta)} \] where \( F_1 \) and \( F_2 \) are the magnitudes of the two forces, and \( \theta \) is the angle between them. - To find the angle between the resultant force and one of the given forces (\( F_1 \) in this case), you can use the formula: \[ \tan(\alpha) = \frac{F_2 \sin(\theta)}{F_1 + F_2 \cos(\theta)} \] where \( \alpha \) is the angle between the resultant force and \( F_1 \). **Steps to Solve:** 1. Substitute the values \( F_1 = 9 \, \text{lbs} \), \( F_2 = 13 \, \text{lbs} \), and \( \theta = 38^\circ \) into the formula for \( R \). 2. Calculate the angle \( \alpha \) using the tangent formula. This process will give the magnitude of the resultant force and the angles with the original forces.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Relative velocity
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
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON