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

  • Thread starter Thread starter AznBoi
  • Start date Start date
  • Tags Tags
    Confused Energy
Click For Summary
SUMMARY

The maximum energy for a child on a pogo stick is determined by the spring constant (k=2.5 x 10^4 N/m) and the mass of the child and pogo stick (25 kg). The total energy of the system is calculated using the formula for spring potential energy and gravitational potential energy. The correct total energy at maximum spring compression is 101J, which aligns with the textbook answer. The maximum kinetic energy occurs when the potential energy is minimized, specifically at the point where the pogo stick is fully decompressed.

PREREQUISITES
  • Understanding of spring potential energy (U(spring) = 1/2 kx^2)
  • Knowledge of gravitational potential energy (U(gravity) = mgh)
  • Familiarity with the conservation of energy principle
  • Basic calculus concepts for determining maxima and minima
NEXT STEPS
  • Study the conservation of energy in mechanical systems
  • Learn how to differentiate functions to find maxima and minima
  • Explore the dynamics of oscillatory motion in springs
  • Investigate the effects of mass and spring constant on energy transfer
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for practical examples of energy transfer in spring systems.

  • #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
 
Physics news on Phys.org
  • #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.
 

Similar threads

What is the stiffness of the spring in a child's pogo stick?
  • · Replies 11 ·
Replies
11
Views
3K
Calculating Energy Components in a Pogo Stick Jump
  • · Replies 8 ·
Replies
8
Views
4K
How Does Spring Compression Relate to Energy Changes?
  • · Replies 4 ·
Replies
4
Views
834
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Maximum angle made by rotating hinge with energy and gravity
  • · Replies 12 ·
Replies
12
Views
2K
Pan suspended by a spring (Energy + SHM)
  • · Replies 20 ·
Replies
20
Views
4K
How Does a Pogo Stick Utilize Spring Mechanics for Maximum Jump Height?
  • · Replies 3 ·
Replies
3
Views
3K
Time period of SHM & Energy conservation in pulley-spring-block system
  • · Replies 24 ·
Replies
24
Views
4K
Child bouncing on pogo stick-harmonic motion
  • · Replies 10 ·
Replies
10
Views
7K
A rocket on a spring, related to potential/kinetic energy
  • · Replies 3 ·
Replies
3
Views
2K