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 = 410 N/m; the other end of the spring is fixed in place. The cookie has a kinetic energy of 19.0 J as it passes through the spring's equilibrium position. As the cookie slides, a frictional force of magnitude 9.00 N acts on it. (a) How far will the cookie slide from the equilibrium position before coming momentarily to rest? (b) What will be the kinetic energy of the cookie as it slides back through the equilibrium position?

Explanation / Answer

Using conservation of energy
0.5mv^2 = 0.5k d^2 + Fd where F is the frictional force

19 = 205 d^2 + 9 d
d = -0.32 m
and
d = 0.28 m

Since the direction of motion and the direction of displacement are the same, we take the positive value of the distance as d = 0.28 m
======================================...
When the speed is zero the spring has the maxium p.e given by
0.5 k d^2 = 205 d^2 =(19 - 9d) = 16.48 J

When the mass returns
16.48 = k.e + Fd
k.e = 16.48-(9*0.28) = 13.96 J

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