What is the Maximum Energy for a Child on a Pogo Stick?

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Homework Help Overview

The discussion revolves around a physics problem involving a child's pogo stick, focusing on energy conservation principles related to spring potential energy and gravitational potential energy. The problem includes calculating total energy, maximum height, speed, and conditions for maximum kinetic energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of total energy using spring potential energy and gravitational potential energy, questioning the correctness of their approaches and the need for different energy forms at various positions.
  • Some participants attempt to clarify the relationship between kinetic energy and potential energy, particularly when one is maximized and the other minimized.
  • Questions arise about how to express potential energy as a function of position and how to apply conservation of energy principles effectively.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and seeking clarification on specific calculations. Some have provided insights into the conservation of energy, while others are still grappling with the concepts and calculations involved.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a noted confusion regarding the treatment of potential energy relative to different reference points.

  • #31
Yay, I found the position by doing what you said lol. I realized that the spring force has distance in it. F(spring)+W=0 --> -kx=mg and x=-9.8x10^-3

However, I was unable to find the velocity of the max KE. Do you just plug x into 1/2kx^2+mgx=K and solve for v? I did that but it doesn't work.. Something is weird here though, the velocity is only .01 m/s greater than x=0.1m
 
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  • #32
What I did to find the velocity of the max KE was:

101J=1/2mv^2+mgx+1/2kx^2

I plugged -.0098m for x and I solved for v I got 2.8591m/s but the answer says 2.85 m/s. I don't know if I did this correctly because I don't think 5 can be rounded down? I never learned about sig figures and I think I've heard something about 5 being rounded down.

Did I solve the velocity of max KE correctly? I considered all of the potential energies because x is not 0...
 
  • #33
Sorry for the delayed response... I forgot to follow up on this thread. :redface:

AznBoi said:
Yay, I found the position by doing what you said lol. I realized that the spring force has distance in it. F(spring)+W=0 --> -kx=mg and x=-9.8x10^-3
Good.

AznBoi said:
What I did to find the velocity of the max KE was:

101J=1/2mv^2+mgx+1/2kx^2

I plugged -.0098m for x and I solved for v I got 2.8591m/s but the answer says 2.85 m/s. I don't know if I did this correctly because I don't think 5 can be rounded down? I never learned about sig figures and I think I've heard something about 5 being rounded down.

Did I solve the velocity of max KE correctly? I considered all of the potential energies because x is not 0...
You solved it correctly. I wouldn't worry about the 3rd sig figure, since the initial data was only given to 2 sig figures anyway.
 

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