A 201 kg crate hangs from a single cable. A rope pulls with 221 N of force to the right. Find the angle the cable makes relative to the vertical.
A 201 kg crate hangs from a single cable. A rope pulls with 221 N of force to the right. Find the angle the cable makes relative to the vertical.
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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![**Physics Problem: Tension and Angles**
**Problem Statement:**
A 201 kg crate hangs from a single cable. A rope pulls with 221 N of force to the right. Find the angle the cable makes relative to the vertical.
**Your Answer:**
*Leave space here for students to input or calculate their answer.*
---
**Explanation:**
To solve this problem, use the principles of equilibrium and trigonometry. The weight of the crate creates a force due to gravity acting downwards, while the rope creates a horizontal force. By analyzing these forces, one can determine the angle at which the cable is inclined with respect to the vertical.
1. **Calculate the gravitational force:**
\[
F_{\text{gravity}} = m \cdot g = 201 \, \text{kg} \times 9.81 \, \text{m/s}^2
\]
2. **Use trigonometry to find the angle:**
With the horizontal force \( F_{\text{horizontal}} = 221 \, \text{N} \) and the vertical force \( F_{\text{gravity}} \), the tangent function relates these forces to the angle \(\theta\):
\[
\tan(\theta) = \frac{F_{\text{horizontal}}}{F_{\text{gravity}}}
\]
\[
\theta = \tan^{-1}\left(\frac{F_{\text{horizontal}}}{F_{\text{gravity}}}\right)
\]
This calculation will give you the angle of the cable relative to the vertical.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1d700aa-072a-4ff7-be1d-cdca0f10aa9d%2F562e41cd-c6b7-4117-b9cb-e8276d7aaba4%2Febna93g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Tension and Angles**
**Problem Statement:**
A 201 kg crate hangs from a single cable. A rope pulls with 221 N of force to the right. Find the angle the cable makes relative to the vertical.
**Your Answer:**
*Leave space here for students to input or calculate their answer.*
---
**Explanation:**
To solve this problem, use the principles of equilibrium and trigonometry. The weight of the crate creates a force due to gravity acting downwards, while the rope creates a horizontal force. By analyzing these forces, one can determine the angle at which the cable is inclined with respect to the vertical.
1. **Calculate the gravitational force:**
\[
F_{\text{gravity}} = m \cdot g = 201 \, \text{kg} \times 9.81 \, \text{m/s}^2
\]
2. **Use trigonometry to find the angle:**
With the horizontal force \( F_{\text{horizontal}} = 221 \, \text{N} \) and the vertical force \( F_{\text{gravity}} \), the tangent function relates these forces to the angle \(\theta\):
\[
\tan(\theta) = \frac{F_{\text{horizontal}}}{F_{\text{gravity}}}
\]
\[
\theta = \tan^{-1}\left(\frac{F_{\text{horizontal}}}{F_{\text{gravity}}}\right)
\]
This calculation will give you the angle of the cable relative to the vertical.
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