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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![**Problem Description:**
A weight with mass \( m_w = 250 \, \text{g} \) is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds.
Assume that the spool can be treated as a uniform solid cylinder of radius \( R = 3.00 \, \text{cm} \) and mass \( M_s = 100 \, \text{g} \). Find the magnitude \( a \) of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.
Use \( g = 9.81 \, \text{m/s}^2 \).
\[ a = \underline{\hspace{3cm}} \, \text{m/s}^2 \]
Find the tension \( T \) in the thread.
**Diagram Explanation:**
The diagram shows a spool (represented as a cylinder) with a radius \( R \) and mass \( M_s \). A thread is wrapped around it, leading down to a weight with mass \( m_w \). The spool is able to rotate freely, and as the weight descends, the thread unwinds from the spool, causing it to rotate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F726ba96a-8f61-467f-b06f-8b424ce252fa%2F9aaa9f96-9244-4221-8b6b-d6189cd1c6a7%2Fu5kjtg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A weight with mass \( m_w = 250 \, \text{g} \) is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds.
Assume that the spool can be treated as a uniform solid cylinder of radius \( R = 3.00 \, \text{cm} \) and mass \( M_s = 100 \, \text{g} \). Find the magnitude \( a \) of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.
Use \( g = 9.81 \, \text{m/s}^2 \).
\[ a = \underline{\hspace{3cm}} \, \text{m/s}^2 \]
Find the tension \( T \) in the thread.
**Diagram Explanation:**
The diagram shows a spool (represented as a cylinder) with a radius \( R \) and mass \( M_s \). A thread is wrapped around it, leading down to a weight with mass \( m_w \). The spool is able to rotate freely, and as the weight descends, the thread unwinds from the spool, causing it to rotate.
![**Problem Statement:**
A cylinder of radius \( R = 3.00 \, \text{cm} \) and mass \( M_s = 100 \, \text{g} \).
**Task:**
1. Find the magnitude \( a \) of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.
Use \( g = 9.81 \, \text{m/s}^2 \).
\[
a = \underline{\hspace{3cm}} \, \text{m/s}^2
\]
2. Find the tension \( T \) in the thread.
\[
T = \underline{\hspace{3cm}} \, \text{N}
\]
**Diagram Description:**
- The image includes a vertical setup with a mass \( m_w \) hanging from a thread that is wrapped around a cylinder.
- The cylinder has the radius and mass as given in the problem.
- The thread is connected to the mass and unwinds as it descends, causing the cylinder to rotate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F726ba96a-8f61-467f-b06f-8b424ce252fa%2F9aaa9f96-9244-4221-8b6b-d6189cd1c6a7%2Fe02ni6n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A cylinder of radius \( R = 3.00 \, \text{cm} \) and mass \( M_s = 100 \, \text{g} \).
**Task:**
1. Find the magnitude \( a \) of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.
Use \( g = 9.81 \, \text{m/s}^2 \).
\[
a = \underline{\hspace{3cm}} \, \text{m/s}^2
\]
2. Find the tension \( T \) in the thread.
\[
T = \underline{\hspace{3cm}} \, \text{N}
\]
**Diagram Description:**
- The image includes a vertical setup with a mass \( m_w \) hanging from a thread that is wrapped around a cylinder.
- The cylinder has the radius and mass as given in the problem.
- The thread is connected to the mass and unwinds as it descends, causing the cylinder to rotate.
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