Question
Question 1 A)Ball A was carried to the top of a hill in a straight line, while ball B was carried in a longer, zigzag path. At the top of the hill, both balls were left at rest. A student draws a graph that depicts each ball's final potential energy. Which statement describes the final potential energy of the balls?(1 point) Responses Both balls have equal potential energy. Both balls have equal potential energy. Ball B has more potential energy. Ball B has more potential energy. Neither ball has any potential energy. Neither ball has any potential energy. Ball A has more potential energy. Ball A has more potential energy. Question 2 A)A swimmer jumps from a diving board into a pool. What would a graph of the swimmer's potential energy and total mechanical energy look like?(1 point) Responses Potential energy would remain constant, while total mechanical energy would decrease. Potential energy would remain constant, while total mechanical energy would decrease. Potential energy would remain constant, while total mechanical energy would increase. Potential energy would remain constant, while total mechanical energy would increase. Potential energy would increase, while total mechanical energy would remain constant. Potential energy would increase, while total mechanical energy would remain constant. Potential energy would decrease, while total mechanical energy would remain constant. Potential energy would decrease, while total mechanical energy would remain constant. Question 3 A)A student wants to design an experiment to study the transformation of mechanical energy. Which object can be used to investigate how gravitational potential energy transforms into kinetic energy?(1 point) Responses a slide a slide a spring a spring a flat race car track a flat race car track a rug a rug Question 4 A)A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point) Responses The displacement of the ball is insignificant compared with Earth's size. The displacement of the ball is insignificant compared with Earth's size. Mass is eliminated when equating elastic potential energy with kinetic energy. Mass is eliminated when equating elastic potential energy with kinetic energy. The mass of the ball is insignificant compared with the mass of Earth. The mass of the ball is insignificant compared with the mass of Earth. Mass is eliminated when equating gravitational potential energy with kinetic energy. Mass is eliminated when equating gravitational potential energy with kinetic energy. Question 5 A)A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system? (1 point) Responses mgh=12kx2mgh=12kx2mg h is equal to 1 half k x squared 12mv2=kx212mv2=kx21 half m v squared is equal to k x squared mgh=kx2mgh=kx2mg h is equal to k x squared 12mv2=12kx212mv2=12kx21 half m v squared is equal to 1 half k x squared
Answers
GPT-4o mini
Here are the answers to your questions based on the concepts of potential energy, kinetic energy, and the conservation of mechanical energy:
**Question 1:**
A) **Both balls have equal potential energy.**
- The potential energy of an object at a certain height depends only on its height and mass, not on the path taken to reach that height. Therefore, both balls have the same potential energy when they are at the top of the hill.
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**Question 2:**
A) **Potential energy would decrease, while total mechanical energy would remain constant.**
- As the swimmer jumps from the diving board into the pool, their potential energy decreases as they fall, while their total mechanical energy (which is the sum of potential and kinetic energy) remains constant assuming no energy is lost to friction or air resistance.
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**Question 3:**
A) **a slide**
- A slide is a good example to investigate how gravitational potential energy transforms into kinetic energy, as it involves an object moving down a slope under the influence of gravity.
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**Question 4:**
A) **Mass is eliminated when equating gravitational potential energy with kinetic energy.**
- The conservation of mechanical energy states that the total mechanical energy (potential + kinetic) remains constant. When considering the equations \(PE = mgh\) and \(KE = \frac{1}{2}mv^2\), the mass \(m\) can be factored out, showing that the relationship is independent of mass.
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**Question 5:**
A) **mgh = ½ kx²**
- This equation represents the conservation of mechanical energy for a marble attached to a compressed spring. When the marble is released, the gravitational potential energy (mgh) at the height will convert into the elastic potential energy in the spring (½ kx²) as the spring releases its stored energy.
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If you have more questions or need further clarification, feel free to ask!
**Question 1:**
A) **Both balls have equal potential energy.**
- The potential energy of an object at a certain height depends only on its height and mass, not on the path taken to reach that height. Therefore, both balls have the same potential energy when they are at the top of the hill.
---
**Question 2:**
A) **Potential energy would decrease, while total mechanical energy would remain constant.**
- As the swimmer jumps from the diving board into the pool, their potential energy decreases as they fall, while their total mechanical energy (which is the sum of potential and kinetic energy) remains constant assuming no energy is lost to friction or air resistance.
---
**Question 3:**
A) **a slide**
- A slide is a good example to investigate how gravitational potential energy transforms into kinetic energy, as it involves an object moving down a slope under the influence of gravity.
---
**Question 4:**
A) **Mass is eliminated when equating gravitational potential energy with kinetic energy.**
- The conservation of mechanical energy states that the total mechanical energy (potential + kinetic) remains constant. When considering the equations \(PE = mgh\) and \(KE = \frac{1}{2}mv^2\), the mass \(m\) can be factored out, showing that the relationship is independent of mass.
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**Question 5:**
A) **mgh = ½ kx²**
- This equation represents the conservation of mechanical energy for a marble attached to a compressed spring. When the marble is released, the gravitational potential energy (mgh) at the height will convert into the elastic potential energy in the spring (½ kx²) as the spring releases its stored energy.
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If you have more questions or need further clarification, feel free to ask!