On the axes below, make sketches of the kinetic energy (K), gravitational potential energy (Ugrav), and elastic potential energy (Uel) of the system on the y-axis as a function of the height of m2 on the x-axis, where the location y=0 is defined as the point where mass m2 collides with the spring. Note that the start of the x-axis is height h, and the end of the x-axis is height -d.

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Chapter1: Units, Trigonometry. And Vectors
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**Topic: Energy in Oscillating Systems**

**Text Transcription:**

On the axes below, make sketches of the kinetic energy (\(K\)), gravitational potential energy (\(U_{\text{grav}}\)), and elastic potential energy (\(U_{\text{el}}\)) of the system on the \(y\)-axis as a function of the height of \(m_2\) on the \(x\)-axis, where the location \(y=0\) is defined as the point where mass \(m_2\) collides with the spring. Note that the start of the \(x\)-axis is height \(h\), and the end of the \(x\)-axis is height \(-d\).

**Graphs Description:**

1. **Kinetic Energy (\(K\)) Graph:**
   - The vertical axis represents kinetic energy (\(K\)).
   - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\).
   - The graph should show how kinetic energy varies as mass \(m_2\) moves from height \(h\) toward the spring.

2. **Gravitational Potential Energy (\(U_{\text{grav}}\)) Graph:**
   - The vertical axis represents gravitational potential energy (\(U_{\text{grav}}\)).
   - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\).
   - The graph should depict changes in gravitational potential energy as \(m_2\) approaches the spring.

3. **Elastic Potential Energy (\(U_{\text{el}}\)) Graph:**
   - The vertical axis represents elastic potential energy (\(U_{\text{el}}\)).
   - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\).
   - The graph should illustrate how elastic potential energy develops as \(m_2\) compresses the spring.

**Purpose:**
These sketches help visualize the transformation of energy types as \(m_2\) moves, collides, and interacts with the spring, providing insight into the principles of energy conservation in mechanical systems.
Transcribed Image Text:**Topic: Energy in Oscillating Systems** **Text Transcription:** On the axes below, make sketches of the kinetic energy (\(K\)), gravitational potential energy (\(U_{\text{grav}}\)), and elastic potential energy (\(U_{\text{el}}\)) of the system on the \(y\)-axis as a function of the height of \(m_2\) on the \(x\)-axis, where the location \(y=0\) is defined as the point where mass \(m_2\) collides with the spring. Note that the start of the \(x\)-axis is height \(h\), and the end of the \(x\)-axis is height \(-d\). **Graphs Description:** 1. **Kinetic Energy (\(K\)) Graph:** - The vertical axis represents kinetic energy (\(K\)). - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\). - The graph should show how kinetic energy varies as mass \(m_2\) moves from height \(h\) toward the spring. 2. **Gravitational Potential Energy (\(U_{\text{grav}}\)) Graph:** - The vertical axis represents gravitational potential energy (\(U_{\text{grav}}\)). - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\). - The graph should depict changes in gravitational potential energy as \(m_2\) approaches the spring. 3. **Elastic Potential Energy (\(U_{\text{el}}\)) Graph:** - The vertical axis represents elastic potential energy (\(U_{\text{el}}\)). - The horizontal axis is labeled "height of mass \(m_2\) above the spring," ranging from \(h\) to \(-d\). - The graph should illustrate how elastic potential energy develops as \(m_2\) compresses the spring. **Purpose:** These sketches help visualize the transformation of energy types as \(m_2\) moves, collides, and interacts with the spring, providing insight into the principles of energy conservation in mechanical systems.
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