One Last Problem, also related to energy

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In summary: Therefore, x = -0.140 m is the value for which the kinetic energy of the system is a maximum. In summary, the conversation is about a physics question regarding a child's pogo stick and its energy. The question asks for the value of x for which the kinetic energy of the system is a maximum. The answer is that the kinetic energy is maximized when the spring is compressed the most, which is at position A (xA = -0.140 m). This is due to the conversion of elastic potential energy into kinetic energy.
  • #1
Antepolleo
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Ok, this is the last time I'll bug you for a while, I promise. Actually I have two questions here.

I cannot for the life of me figure out why these answers are wrong. Here's the first question:

A child's pogo stick stores energy in a spring with a force constant of 2.40 104 N/m. At position A (xA = -0.140 m), the spring compression is a maximum and the child is momentarily at rest. At position B (xB = 0), the spring is relaxed and the child is moving upward. At position C , the child is again momentarily at rest at the top of the jump.

This problem has 5 parts, and I've managed to successfully obtain the answer to four of those parts. Here's the trouble:

(d) Determine the value of x for which the kinetic energy of the system is a maximum.

Now some information is imparted in an eariler question here:

(a) Calculate the total energy of the child-stick-Earth system if both gravitational and elastic potential energies are zero for x = 0.

I got the answer to that just fine. I noted that all associated potential energies are 0 for x = 0. Since this problem never mentions nonconservative forces, wouldn't it be safe to assume, due to the concept of conservation of energy, that the kinetic energy of the system is at a maximum when x = 0? I tried that and it did not work.
 
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  • #2
The answer to your question is that the kinetic energy of the system is maximized when the spring is compressed the most, which is at position A (xA = -0.140 m). This is because the spring stores elastic potential energy which is converted into kinetic energy as the pogo stick compresses the spring and the child moves upwards. Since the spring is compressed the most at position A, this is where the kinetic energy is at its maximum.
 
  • #3


It's understandable that you're frustrated with this problem, but let's take a closer look at the information given and see if we can figure out why your answer for part (d) may be incorrect.

First, let's review the concept of conservation of energy. This principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this problem, we are dealing with potential and kinetic energy, which are both forms of mechanical energy. So, when the child is at position A, all of the energy in the system is in the form of potential energy (elastic potential energy in the spring and gravitational potential energy due to the child's height above the ground). As the child jumps, this potential energy is converted into kinetic energy, reaching a maximum at position C when the child is at the top of the jump.

Now, let's look at the information given for part (d). We are asked to find the value of x for which the kinetic energy of the system is a maximum. This means that we need to find the position at which the kinetic energy is at its highest point. This may not necessarily be at position A (x = -0.140 m), as you suggested. Remember, the child is moving upward at this point, so the kinetic energy is increasing, but it is not yet at its maximum. The kinetic energy will continue to increase until the child reaches the top of the jump at position C, and then it will start to decrease as the child begins to descend.

So, to answer part (d), we need to find the position at which the child has the highest velocity, since kinetic energy is directly proportional to velocity. This position will be at the top of the jump, when the child is momentarily at rest (velocity = 0) and about to start descending. This is why the correct answer for part (d) is x = 0, not x = -0.140 m.

I hope this explanation helps you understand why your previous approach may not have worked. Keep in mind that when dealing with energy problems, it's important to consider all forms of energy in the system and how they are changing as the system moves. Keep practicing and you'll get the hang of it. Good luck!
 

What is the concept of "One Last Problem" in terms of energy?

The concept of "One Last Problem" refers to the idea that there is one final major challenge that needs to be addressed in the field of energy in order to create a sustainable and efficient energy system for the future.

What are the main sources of energy that contribute to this "One Last Problem"?

The main sources of energy that contribute to this "One Last Problem" include fossil fuels such as coal, oil, and natural gas, as well as nuclear energy. These sources are non-renewable and have a negative impact on the environment.

What are some potential solutions to the "One Last Problem" related to energy?

Some potential solutions to the "One Last Problem" include transitioning to renewable energy sources such as solar, wind, and hydro power, as well as implementing energy efficiency measures and promoting energy conservation.

How does the "One Last Problem" impact our environment?

The "One Last Problem" has a significant impact on our environment, as the use of non-renewable energy sources contributes to air and water pollution, deforestation, and climate change. It also leads to the depletion of natural resources and loss of biodiversity.

What role do individuals and governments play in addressing the "One Last Problem"?

Individuals can make a difference by adopting sustainable energy practices and advocating for renewable energy policies. Governments also play a crucial role in implementing regulations and incentives to promote the use of renewable energy and reduce our reliance on non-renewable sources.

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