### 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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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

### 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 board

The 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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