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 = 440 N/m; the other end of the spring is fixed in place. The cookie has a kinetic energy of 20.0 J as it passes through the spring's equilibrium position. As the cookie slides, a frictional force of magnitude 8.00 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

a)

let the cookie slides distance = d

compression of spring = d

k = spring constant = 410

KE = 25 J

f = frictional force = 8 N

Using conservation of energy

Kinetic energy = work done by friction + spring energy

25 = f d + (0.5) k d2

25 = 8 d + (0.5) (410) d2

d = 0.33 m

b)

Using conservation of energy

spring energy = KE + work done by friction

(0.5) k d2 = KE + fd

(0.5) (410) (0.33)2 = KE + 8 (0.33)

KE = 19.685 J

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