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

[AznBoi]

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

 

[AznBoi]

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...

 

[Doc Al]

Sorry for the delayed response... I forgot to follow up on this thread.

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.

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.