**Transcription and Explanation for Educational Website:****Title: Analyzing a Free Body Diagram: Calculating Net Force****Task Description:**Complete the free body diagram in your work and solve for the magnitude and angle of the net force. Use the following assumptions:- The block has a mass of 15 kg.- The spring is stretched 0.5 m and has a spring constant of 150 N/m.- There is a cord attached to the block with a tension of \(T = 200 \text{ N}\).- The cord is connected at an angle of \(\theta = 40^\circ\).**Diagram Explanation:**The diagram shows a horizontal surface with a block attached to a spring on the left side. The spring is in a stretched position, indicating a force opposing the tension. A cord is attached to the block, exerting a tension force at an angle \(\theta\) with the horizontal surface. The angle \(\theta\) is specified as \(40^\circ\).**Forces to Consider:**1. **Spring Force (\(F_{spring}\))**: - Acting in the opposite direction of the tension. - Calculated using Hooke's Law: \(F_{spring} = k \cdot x\), where \(k = 150 \text{ N/m}\) and \(x = 0.5 \text{ m}\).2. **Tension Force (\(T\))**: - Magnitude is 200 N. - Acts at an angle \(\theta = 40^\circ\) from the horizontal.**Objective:**- Complete the free body diagram by adding vectors for the spring force and the components of the tension force.- Solve for the net force's magnitude and direction using vector addition principles.**Solution Approach:**1. Decompose the tension force into its horizontal (\(T_x\)) and vertical (\(T_y\)) components: - \(T_x = T \cdot \cos(\theta)\) - \(T_y = T \cdot \sin(\theta)\)2. Calculate the spring force: - \(F_{spring} = 150 \, \text{N/m} \times 0.5 \, \text{m} = 75 \, \text{N}\)3. Determine the net force by summing up forces considering

The weight of the block "mg"=15 kg x 9.81 m/s2= 147.15 N Spring force= Fs= kx= 150 N/m x 0.5 m= 75…

omplete the below free body diagram in your work and solve for the magnitude and angle of the r orce. Assume the following: the block has a mass of 15 kg, the spring is stretched 0.5 m and has a oring constant of 150 N/m, there is a cord attached to the block with a tension of T = 200 N onnected at an angle of 0 = 40°.

omplete the below free body diagram in your work and solve for the magnitude and angle of the r orce. Assume the following: the block has a mass of 15 kg, the spring is stretched 0.5 m and has a oring constant of 150 N/m, there is a cord attached to the block with a tension of T = 200 N onnected at an angle of 0 = 40°.

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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Question

**Transcription and Explanation for Educational Website:**

**Title: Analyzing a Free Body Diagram: Calculating Net Force**

**Task Description:**

Complete the free body diagram in your work and solve for the magnitude and angle of the net force. Use the following assumptions:

- The block has a mass of 15 kg.
- The spring is stretched 0.5 m and has a spring constant of 150 N/m.
- There is a cord attached to the block with a tension of \(T = 200 \text{ N}\).
- The cord is connected at an angle of \(\theta = 40^\circ\).

**Diagram Explanation:**

The diagram shows a horizontal surface with a block attached to a spring on the left side. The spring is in a stretched position, indicating a force opposing the tension. A cord is attached to the block, exerting a tension force at an angle \(\theta\) with the horizontal surface. The angle \(\theta\) is specified as \(40^\circ\).

**Forces to Consider:**

1. **Spring Force (\(F_{spring}\))**:
- Acting in the opposite direction of the tension.
- Calculated using Hooke's Law: \(F_{spring} = k \cdot x\), where \(k = 150 \text{ N/m}\) and \(x = 0.5 \text{ m}\).

2. **Tension Force (\(T\))**:
- Magnitude is 200 N.
- Acts at an angle \(\theta = 40^\circ\) from the horizontal.

**Objective:**

- Complete the free body diagram by adding vectors for the spring force and the components of the tension force.
- Solve for the net force's magnitude and direction using vector addition principles.

**Solution Approach:**

1. Decompose the tension force into its horizontal (\(T_x\)) and vertical (\(T_y\)) components:
- \(T_x = T \cdot \cos(\theta)\)
- \(T_y = T \cdot \sin(\theta)\)

2. Calculate the spring force:
- \(F_{spring} = 150 \, \text{N/m} \times 0.5 \, \text{m} = 75 \, \text{N}\)

3. Determine the net force by summing up forces considering

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