### Physics Problem: Shelf with Supports and Weight Distribution---#### Problem Statement:You build a shelf by putting a 0.90 m board across two supports. One support is at the left end of the board and the other is 0.10 m from the right end. The board has a mass of 1.25 kg and you place a potted plant with a mass of 3.40 kg, 0.65 m from the left end of the board.#### Diagram Explanation:The diagram shows a horizontal board positioned across two vertical supports. Specific measurements and masses are marked on the diagram as follows:- **Board Length:** 0.90 m- **Left Support Position:** At the left end of the board (0 m mark)- **Right Support Position:** 0.10 m from the right end of the board- **Mass of the Board (m):** 1.25 kg centered along its length- **Mass of the Potted Plant (m):** 3.40 kg located 0.65 m from the left end of the boardThe board and potted plant are shown with arrows indicating the positions and distances from the left end of the board.#### Tasks:a. Draw a free-body diagram labeling all the forces and distances. Also, choose and mark a pivot point for your shelf on the drawing.b. Find the force exerted by both supports.---### Physics Concepts Involved:- **Torque and Equilibrium:** Utilize principles of torque and static equilibrium to solve for the forces at the supports.- **Free-Body Diagram (FBD):** A graphical illustration used to visualize the applied forces, moments, and reactions on a body.To solve the problem:1. **Determine the Pivot Point:** - Typically, one support or the center of mass of the system can be used as a pivot.2. **Calculate Forces:** - Apply the equilibrium condition for both forces and torques: - ΣF = 0 (sum of vertical forces must be zero) - Στ = 0 (sum of torques around any point must be zero)3. **Equations:** - For instance, if taking the left support as the pivot, - Consider the torque due to the board’s weight and the plant’s weight about the left support. - Calculate individual contributions to the net torque to find the unknown forces.Use these principles

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You build a shelf by putting a 0.90 m board across two supports. One support is at the left end of the board and the other is 0.10 m from the right end. The board has a mass of 1.25 kg and you place a potted plant with a mass of 3.40 kg, 0.65 m from the left end of the board.

You build a shelf by putting a 0.90 m board across two supports. One support is at the left end of the board and the other is 0.10 m from the right end. The board has a mass of 1.25 kg and you place a potted plant with a mass of 3.40 kg, 0.65 m from the left end of the board.

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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