Find the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board). Express your answer in terms of some or all of the variables s. m₂, m₂, g, and L. Do not include f in your answer.
Find the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board). Express your answer in terms of some or all of the variables s. m₂, m₂, g, and L. Do not include f in your answer.
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 small box of mass \( m_1 \) is sitting on a board of mass \( m_2 \) and length \( L \) (Figure 1). The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is \( \mu_s \). The coefficient of kinetic friction between the board and the box is \( \mu_k \), as is usual, less than \( \mu_s \).
Throughout the problem, use \( g \) for the magnitude of the free-fall acceleration. In the hints, use \( f \) for the magnitude of the friction force between the board and the box.
**Task:**
Find \( F_{\text{min}} \), the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the box (which will then fall off the opposite end of the board).
Express your answer in terms of some or all of the variables \( \mu_s, m_1, m_2, g \), and \( L \). Do not include \( f \) in your answer.
**Input Field:**
\( F_{\text{min}} = \) [Input Box]
**Diagram Explanation (Figure 1):**
- The diagram shows a board of length \( L \) on a frictionless horizontal surface.
- A small box of mass \( m_1 \) is placed on top of the board.
- A horizontal force \( \vec{F} \) is applied to the board in order to slide it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F114d112a-89da-40ea-8ec8-a25f26317aff%2F73e13181-c7fe-4ba0-a895-833905902a74%2Fje0ylaj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A small box of mass \( m_1 \) is sitting on a board of mass \( m_2 \) and length \( L \) (Figure 1). The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is \( \mu_s \). The coefficient of kinetic friction between the board and the box is \( \mu_k \), as is usual, less than \( \mu_s \).
Throughout the problem, use \( g \) for the magnitude of the free-fall acceleration. In the hints, use \( f \) for the magnitude of the friction force between the board and the box.
**Task:**
Find \( F_{\text{min}} \), the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the box (which will then fall off the opposite end of the board).
Express your answer in terms of some or all of the variables \( \mu_s, m_1, m_2, g \), and \( L \). Do not include \( f \) in your answer.
**Input Field:**
\( F_{\text{min}} = \) [Input Box]
**Diagram Explanation (Figure 1):**
- The diagram shows a board of length \( L \) on a frictionless horizontal surface.
- A small box of mass \( m_1 \) is placed on top of the board.
- A horizontal force \( \vec{F} \) is applied to the board in order to slide it.
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