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How do I find the maximum kinetic energy of an object on a spring? (no mass given)?

So brief intro. This problem comes from WebAssign (online homework website) and I can not figure out the last part. I can practice another version and see the correct answers, but I can not view the solution. So my hope is that if I give you the problem and the answer, you can explain the last part of it to me?Then I can go to my actual problem (the same thing but different numbers) then I will be able to get it right. Thanks! ******* THE ANSWERS FOR EACH PART ARE CORRECT! I JUST WANT TO KNOW HOW TO GET THE ANSWER GIVEN FOR PART E!*******

"The block in the figure below lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 50 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 2.9 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops.

Assume that the stopping point is reached."

(The picture given shows a wall on the left with a spring going towards the right with a block attached to the end of the spring. It is at rest and not moving.)

A) What is the position of the block?

W=FDcos(theta)

W=(-1/2)K(Xfinal^2 - Xinitial^2)

skipping some steps...

D = .116m

B) What is the work that has been done on the block by the applied force?

W = F D

W = .336J

C) What is the work that has been done on the block by the spring force?

The same amount of work but in the opposite direction

W = -.336J

DURING THE BLOCKS DISPLACEMENT, FIND THE FOLLOWING VALUES.

D) the block's position when it's kinetic energy is maximum.

Well half way through the displacement would be where it has maximum velocity because that is where the acceleration = 0. And maximum velocity leads to maximum kinetic energy.

The position is 0.058 meters.

THIS IS WHERE I GET LOST!

E) The value of that maximum kinetic energy.

I clicked view answer and it gave me 84.1 mJ (NOTE THE UNITS) as the answer. Please can someone explain how to do this? It gives you a hint for this part and it reads...

"(a) Because the applied force is constant, how is its work related to the block's position? Because the spring force is a variable force, how is its work related to the block's position? The net work done by these two forces is equal to the change in the kinetic energy. What is the kinetic energy at the stopping point? (d) Rewrite all this in terms of a variable kinetic energy instead of a zero final kinetic energy. What do you do to a function to find its maximum value?"

Basically I just need someone to show me ANY way to get the correct answer.

Thank you tons!

-Michael

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