Two forces act on an 5 kg object: F1 = 60N applied at the origin in the direction of positive x- axis, and F2 = 40N, also applied at the origin but in the direction of positive y- axis. Calculate the magnitude of object's acceleration
Two forces act on an 5 kg object: F1 = 60N applied at the origin in the direction of positive x- axis, and F2 = 40N, also applied at the origin but in the direction of positive y- axis. Calculate the magnitude of object's acceleration
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)...
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![Two forces act on a 5 kg object: \( F_1 = 60 \, \text{N} \) applied at the origin in the direction of the positive x-axis, and \( F_2 = 40 \, \text{N} \), also applied at the origin but in the direction of the positive y-axis.
Calculate the magnitude of the object's acceleration.
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### Explanation:
In this scenario, the forces are applied perpendicularly. To calculate the resultant force (\( F_{\text{resultant}} \)), use the Pythagorean theorem:
\[ F_{\text{resultant}} = \sqrt{(F_1)^2 + (F_2)^2} \]
Once the resultant force is found, use Newton's second law, \( F = ma \), to find the acceleration (\( a \)). The formula rearranges to:
\[ a = \frac{F_{\text{resultant}}}{m} \]
Where:
- \( m \) is the mass of the object (5 kg).
Substitute the values to determine the magnitude of the acceleration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ca4b84d-c518-47ce-bd33-9b129e18b52b%2Fc9ae05f8-5d04-4062-bec6-9b64a4f67588%2F4hcosgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Two forces act on a 5 kg object: \( F_1 = 60 \, \text{N} \) applied at the origin in the direction of the positive x-axis, and \( F_2 = 40 \, \text{N} \), also applied at the origin but in the direction of the positive y-axis.
Calculate the magnitude of the object's acceleration.
---
### Explanation:
In this scenario, the forces are applied perpendicularly. To calculate the resultant force (\( F_{\text{resultant}} \)), use the Pythagorean theorem:
\[ F_{\text{resultant}} = \sqrt{(F_1)^2 + (F_2)^2} \]
Once the resultant force is found, use Newton's second law, \( F = ma \), to find the acceleration (\( a \)). The formula rearranges to:
\[ a = \frac{F_{\text{resultant}}}{m} \]
Where:
- \( m \) is the mass of the object (5 kg).
Substitute the values to determine the magnitude of the acceleration.
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