Using Conservation of Energy to Analyze a Potential Energy Graph

In summary, the conversation discusses a problem involving relating time to a potential energy graph. The equation F = -dU/dx is mentioned, along with attempts to use F = ma and the conservation of energy to solve the problem. The conversation also mentions considering the velocity and position at a turning point to determine the type of motion expected.
  • #1
chuuke
3
1

Homework Statement


I'm trying to figure out how to do D) and relate time to this potential energy graph.
Screenshot (27).png


Homework Equations


All I really know is that F = -dU/dx

The Attempt at a Solution


I tried to do something with F = ma
and a = d2x/ dt2
and then set the - derivative of U(x) equal to the above equation
but I can't really get an answer, and am quite frustrated cause I don't know how to go about answering this.
 

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  • #2
You need to use the conservation of energy. When released from B, what is going to be the velocity at any point? How is that related to position?

Also, what position do you have as the turning point? Based on that, what kind of motion do you expect?
 

1. What is a potential energy graph?

A potential energy graph is a visual representation of the potential energy of a system as a function of its position or configuration. It shows how the potential energy of the system changes as the system moves or changes.

2. How is potential energy shown on a potential energy graph?

Potential energy is represented on a potential energy graph by the height of the curve at a given point. The higher the curve, the higher the potential energy at that point.

3. What can a potential energy graph tell us about a system?

A potential energy graph can tell us about the stability and equilibrium of a system. The minimum points on the graph represent the most stable positions of the system, while the maximum points represent the least stable positions.

4. How does the shape of a potential energy graph change with different types of forces?

The shape of a potential energy graph can vary depending on the type of forces acting on the system. For example, a system with conservative forces will have a smooth, continuous curve, while a system with non-conservative forces will have a more jagged curve.

5. Can potential energy be negative on a potential energy graph?

Yes, potential energy can be negative on a potential energy graph. This indicates that the system has a lower potential energy at that point compared to a reference point. It does not mean that the potential energy is "less" than zero, but rather it is a relative measure.

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