Conservation of energy I think

In summary, the conversation discusses the problem of a bead on a vertical spring moving along a horizontal wire without friction. It is shown that when the spring is perfectly vertical, the bead experiences a restoring force. Additionally, it is proven that when x is small, the magnitude of the force is proportional to x^3 rather than x^1, using the approximation (1+x)^n = 1+nx for x<<1. The conversation also suggests thinking about the problem as a pendulum with kx as the restoring force and drawing a free body diagram for the bead at some displacement x to analyze the forces acting on it. The equation U + K = E is also mentioned.
  • #1
Benevelli
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Homework Statement


PLEASE HELP: A bead at the end of a vertical spring moves without friction along a horizontal wire. WHen the spring is perfectly vertical , the spring is neither stretched or compressed. Show that the bead experiences a restoring force, and that if x is small, then the magnitude of the force is proportional to x^3 rather x^1. You will want to use the approximation (1+x)^n = 1+nx for x<<1

Homework Equations


U + K = E

The Attempt at a Solution


I tried thinking about this like a pendulum with kx as the restoring force. Other than that, my work has gotten me nowhere.
 
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  • #2
Draw a free body diagram for the bead at some displacement x. What are the forces on it?
 

Related to Conservation of energy I think

1. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. How does the conservation of energy apply to everyday life?

The conservation of energy applies to everyday life in many ways. For example, when you turn on a light switch, electrical energy is transformed into light energy. When you ride a bike, your body converts chemical energy from food into kinetic energy. In all of these examples, energy is neither created nor destroyed, but simply changes form.

3. What are the different forms of energy that can be conserved?

There are many forms of energy that can be conserved, including mechanical energy (kinetic and potential), thermal energy, chemical energy, nuclear energy, electromagnetic energy, and more. All of these forms of energy can be transformed into one another, but the total amount of energy remains constant.

4. How does the conservation of energy relate to the laws of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed. The second law of thermodynamics states that in any energy transformation, some energy will be lost as heat, making the total amount of usable energy decrease over time. These laws work together to explain the conservation of energy in all systems.

5. How can we apply the principle of conservation of energy to help the environment?

By understanding and applying the principle of conservation of energy, we can make more sustainable choices to help the environment. This can include using renewable energy sources, reducing energy consumption, and finding ways to transform and use energy more efficiently. Conserving energy also helps to reduce our carbon footprint and mitigate the effects of climate change.

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