### Exercise: Forces on a Diving Board#### Part ACalculate the force that the support A exerts on the diving board. Ignore the weight of the board.**Instructions:**- Express your answer to two significant figures and include the appropriate units.- Enter a positive value if the force is upward and a negative value if the force is downward.**Answer Box:**- \( F_A = \) [Value] [Units][Submit] [Request Answer]---#### Part BCalculate the force that the support B exerts on the diving board. Ignore the weight of the board.**Instructions:**- Express your answer to two significant figures and include the appropriate units.- Enter a positive value if the force is upward and a negative value if the force is downward.**Answer Box:**- \( F_B = \) [Value] [Units][Submit] [Request Answer]---#### Part CCalculate the force that the support A exerts on the diving board. Take into account the board's mass of 27 kg. Assume the board's center of gravity (CG) is at its center.**Instructions:**- Express your answer to two significant figures and include the appropriate units.- Enter a positive value if the force is upward and a negative value if the force is downward.**Answer Box:**- \( F_{A2} = \) [Value] [Units][Submit] [Request Answer]---#### Part DCalculate the force that the support B exerts on the diving board. Take into account the board's mass of 27 kg. Assume the board's center of gravity (CG) is at its center.**Instructions:**- Express your answer to two significant figures and include the appropriate units.- Enter a positive value if the force is upward and a negative value if the force is downward.**Answer Box:**- \( F_{B2} = \) [Value] [Units][Submit] [Request Answer]---**Note:** For each part, ensure that calculations consider the relevant physics principles such as equilibrium of forces and moments. **Title: Calculating Forces on a Diving Board****Problem Statement:**Calculate the forces that the supports A and B exert on the diving board shown in Figure 1 when a 53-kg person stands at its tip.**Figure Description:**The diagram illustrates a diving board supported by two points labeled A and B. The board is positioned over water with a person standing at the end. Point A is located 1.0 meters from the edge of the diving board, and point B is located 3.0 meters from point A, at the tip of the board. The person is standing at the end of the diving board furthest from the supports.

Given that: Mass of diver: m= 53 kg r1= 1 mr2= 3 mApplying equilibrium along y direction: NA+NB=mg ....(1) Applying rotational equilibrium about point A: NA×0+(NB×r1)-mg(r1+r2)=0(NB×r1)=mg(r1+r2)NB=mg(r1+r2)r1NB=53×9.81(1+3)1=2079.72 N From equation (1) NA+NB=mg NA=mg-NBNA=(53×9.81)-2079.72NA=-1559.79 N Answer of Part A: FA =-1559.79 N Answer for Part B: FB =2079.72 N Now the mass of board is comes into the calculation. Mass of board: mB= 27 kg Equilibrium of forces along vertical direction:NA+NB=mg+mBg ....(2)Equilibrium of torque about point A:NB×1= mBg×2 + mg×4NB=27×9.81×2 + 53×9.81×4NB=2609.46 NFrom (2)NA+NB=mg+mBg NA=mg+mBg -NBNA=(27×9.81)+(53×9.81) -2609.46NA=-1824.66 NAnswer for part C: FA2 = -1824.66 N Answer for part D: FB2 = 2609.46 N

Answered: Calculate the forces that the supports…

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Physics

Calculate the forces that the supports A and B exert on the diving board shown in (Figure 1) when a 53-kg person stands at its tip.

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.

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### Exercise: Forces on a Diving Board

#### Part A
Calculate the force that the support A exerts on the diving board. Ignore the weight of the board.

**Instructions:**
- Express your answer to two significant figures and include the appropriate units.
- Enter a positive value if the force is upward and a negative value if the force is downward.

**Answer Box:**
- \( F_A = \) [Value] [Units]

[Submit] [Request Answer]

---

#### Part B
Calculate the force that the support B exerts on the diving board. Ignore the weight of the board.

**Instructions:**
- Express your answer to two significant figures and include the appropriate units.
- Enter a positive value if the force is upward and a negative value if the force is downward.

**Answer Box:**
- \( F_B = \) [Value] [Units]

[Submit] [Request Answer]

---

#### Part C
Calculate the force that the support A exerts on the diving board. Take into account the board's mass of 27 kg. Assume the board's center of gravity (CG) is at its center.

**Instructions:**
- Express your answer to two significant figures and include the appropriate units.
- Enter a positive value if the force is upward and a negative value if the force is downward.

**Answer Box:**
- \( F_{A2} = \) [Value] [Units]

[Submit] [Request Answer]

---

#### Part D
Calculate the force that the support B exerts on the diving board. Take into account the board's mass of 27 kg. Assume the board's center of gravity (CG) is at its center.

**Instructions:**
- Express your answer to two significant figures and include the appropriate units.
- Enter a positive value if the force is upward and a negative value if the force is downward.

**Answer Box:**
- \( F_{B2} = \) [Value] [Units]

[Submit] [Request Answer]

---

**Note:** For each part, ensure that calculations consider the relevant physics principles such as equilibrium of forces and moments.

**Title: Calculating Forces on a Diving Board**

**Problem Statement:**

Calculate the forces that the supports A and B exert on the diving board shown in Figure 1 when a 53-kg person stands at its tip.

**Figure Description:**

The diagram illustrates a diving board supported by two points labeled A and B. The board is positioned over water with a person standing at the end. Point A is located 1.0 meters from the edge of the diving board, and point B is located 3.0 meters from point A, at the tip of the board. The person is standing at the end of the diving board furthest from the supports.

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