College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**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.](https://content.bartleby.com/qna-images/question/33693f5b-e996-45d6-9361-e39b55dcab94/6aba6208-5c8a-48c9-9d72-8d5d78f12aba/mp1uq95_processed.png)
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.
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