A large fake cookie sliding on a horizontal surface is attached to one end of a

Question

A large fake cookie sliding on a horizontal surface is attached to one end of a horizontal spring with spring constant k = 425 N/m; the other end of the spring is fixed in place. The cookie has a kinetic energy of 22.0 J as it passes through the position where the spring is unstretched. As the cookie slides, a frictional force of magnitude 10.0 N acts on it.
(a) How far will the cookie slide from the position where the spring is unstretched before coming momentarily to rest?
(b) What will be the kinetic energy of the cookie as it slides back through the position where the spring is unstretched?

PLEASE HELP ASAP! I don't understand!

Explanation / Answer

Conservation of energy

22.00 = Force friction x d + 1/2 kd^2 = 10d + 1/2 (425) d^2. Solve for d.
22 = 10d + 212.5d^2
iT IS A QUADRATIC EQUATION AND WE TAKE ONLY THE POSITIVE VALUE
d = 0.299 m

b) As it slides back, 1/2 k d^2 = Force friction x d + KE
1/2 (425)(0.299)^2 = 10* 0.299 +KE
solve for KE = 16.0077J16 J

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