A system in which only one particle can move has the potential energy shown in (Figure 1). Suppose U₁ = 80 J. Figure U (J) U₁ 0 0 1 2 3 4 5 y (m) 1 of 1 Part A What is the y-component of the force on the particle at y = 0.5 m ? Express your answer with the appropriate units. F₁ = Submit Part B Fy = Submit μÀ Value Request Answer What is the y-component of the force on the particle at y = 4 m? Express your answer with the appropriate units. Provide Feedback μА Value Units Request Answer ? Units ?

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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### Educational Content on Potential Energy and Force

#### Introduction:
A system in which only one particle can move has a potential energy graph as depicted in Figure 1. Suppose the potential energy at \( U_1 = 80 \, \text{J} \).

#### Figure Description:
The graph in Figure 1 shows the potential energy \( U(y) \) in Joules (J) plotted against the position \( y \) in meters (m). The graph is a triangle with the following key points:

- At \( y = 0 \, \text{m} \), \( U = 0 \, \text{J} \).
- The line rises linearly to a peak at \( y = 2 \, \text{m} \) with \( U = U_1 = 80 \, \text{J} \).
- It then descends linearly to \( y = 5 \, \text{m} \) where \( U = 0 \, \text{J} \).

#### Problem Solving:

##### Part A:
- **Question:** What is the \( y \)-component of the force on the particle at \( y = 0.5 \, \text{m} \)?
- **Instructions:** Express your answer with the appropriate units.

\[ F_y = \text{Value} \, \text{Units} \]

##### Part B:
- **Question:** What is the \( y \)-component of the force on the particle at \( y = 4 \, \text{m} \)?
- **Instructions:** Express your answer with the appropriate units.

\[ F_y = \text{Value} \, \text{Units} \]

#### Feedback:
If you have any questions or need further assistance, please provide feedback using the 'Request Answer' option.

---

### Concepts:
- **Potential Energy (U):** Represents energy stored due to a particle's position.
- **Force (F):** Can be determined by the negative gradient of potential energy, \( F = -\frac{dU}{dy} \).

#### Note:
Understanding how changes in potential energy relate to force will help solve problems related to motion and energy conservation in physical systems.
Transcribed Image Text:### Educational Content on Potential Energy and Force #### Introduction: A system in which only one particle can move has a potential energy graph as depicted in Figure 1. Suppose the potential energy at \( U_1 = 80 \, \text{J} \). #### Figure Description: The graph in Figure 1 shows the potential energy \( U(y) \) in Joules (J) plotted against the position \( y \) in meters (m). The graph is a triangle with the following key points: - At \( y = 0 \, \text{m} \), \( U = 0 \, \text{J} \). - The line rises linearly to a peak at \( y = 2 \, \text{m} \) with \( U = U_1 = 80 \, \text{J} \). - It then descends linearly to \( y = 5 \, \text{m} \) where \( U = 0 \, \text{J} \). #### Problem Solving: ##### Part A: - **Question:** What is the \( y \)-component of the force on the particle at \( y = 0.5 \, \text{m} \)? - **Instructions:** Express your answer with the appropriate units. \[ F_y = \text{Value} \, \text{Units} \] ##### Part B: - **Question:** What is the \( y \)-component of the force on the particle at \( y = 4 \, \text{m} \)? - **Instructions:** Express your answer with the appropriate units. \[ F_y = \text{Value} \, \text{Units} \] #### Feedback: If you have any questions or need further assistance, please provide feedback using the 'Request Answer' option. --- ### Concepts: - **Potential Energy (U):** Represents energy stored due to a particle's position. - **Force (F):** Can be determined by the negative gradient of potential energy, \( F = -\frac{dU}{dy} \). #### Note: Understanding how changes in potential energy relate to force will help solve problems related to motion and energy conservation in physical systems.
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