So the total energy of our system at any moment will be the kinetic energy of the puck (KE = mv² where m is the puck's mass and v is the velocity of the puck) plus the gravitational potential energy of the puck due to the Earth's attraction ( PE, = mgh where his the vertical height of the center of the puck, g is 9.8 m/s2). For simplicity, let's assume that y=0 when the puck is on the level surface before going up the hill. So which of these statements would summarize how we might analyze this situation? The total energy of the system is largest when the puck is sliding along the bottom, because that is when there is the most movement in the system. When the puck reaches its highest point and momentarily stops, the system has no energy. The total energy of the system remains the same at all times. When the puck is siding at the bottom the energy of the system is all kinetic energy and when it reaches its highest point and momentarily stops, all the energy is gravitational potential energy. The kinetic energy of the system is always the same. The potential energy of the system is largest when the puck reaches its maximum height.

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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### Energy Analysis of a Moving Puck

In this analysis, we explore the total energy of a system, specifically focusing on the kinetic energy and gravitational potential energy of a puck:

- **Kinetic Energy (KE)** is calculated using the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) represents the mass of the puck, and \( v \) is its velocity.
  
- **Gravitational Potential Energy (PE\_g)** is determined using \( PE_g = mgh \), where \( h \) is the vertical height of the puck's center, and \( g = 9.8 \, \text{m/s}^2 \) represents the acceleration due to Earth's gravity.

For simplification, assume \( y = 0 \) when the puck is on the level surface before ascending a hill. 

### Select the Correct Analysis Statement

We are tasked with selecting the statement that accurately reflects the energy behavior of the puck system:

1. **Incorrect Statement (Circle Option):** The total energy is largest when the puck is sliding along the bottom, with no energy at the highest point.
  
2. **Correct Statement:** The total energy remains constant. At the bottom, the system's energy is entirely kinetic. At the highest point, all energy is gravitational potential. (Second Option)

3. **Incorrect Statement (Highlighted Option):** The kinetic energy is always constant, and the potential energy is largest at maximum height.

In this situation, the correct understanding is that while individual kinetic and potential energies change as the puck moves, the total energy remains constant due to energy conservation principles.
Transcribed Image Text:### Energy Analysis of a Moving Puck In this analysis, we explore the total energy of a system, specifically focusing on the kinetic energy and gravitational potential energy of a puck: - **Kinetic Energy (KE)** is calculated using the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) represents the mass of the puck, and \( v \) is its velocity. - **Gravitational Potential Energy (PE\_g)** is determined using \( PE_g = mgh \), where \( h \) is the vertical height of the puck's center, and \( g = 9.8 \, \text{m/s}^2 \) represents the acceleration due to Earth's gravity. For simplification, assume \( y = 0 \) when the puck is on the level surface before ascending a hill. ### Select the Correct Analysis Statement We are tasked with selecting the statement that accurately reflects the energy behavior of the puck system: 1. **Incorrect Statement (Circle Option):** The total energy is largest when the puck is sliding along the bottom, with no energy at the highest point. 2. **Correct Statement:** The total energy remains constant. At the bottom, the system's energy is entirely kinetic. At the highest point, all energy is gravitational potential. (Second Option) 3. **Incorrect Statement (Highlighted Option):** The kinetic energy is always constant, and the potential energy is largest at maximum height. In this situation, the correct understanding is that while individual kinetic and potential energies change as the puck moves, the total energy remains constant due to energy conservation principles.
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