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

The given values are,

Spring constant k = 410 N/m

kinetic energy = 19.0 J

Frictional force = 9.00 N

F = -k x Where x is distance of cookie from its mean position

Therefore

x = - F/ k

x = - 9 / 410 = - 0.02195 m

(Please Note : Here negative sign for the direction only because distance value never negative.)

i.e. approximately x = 2.19 cm

K.E. = (1/2) mv2

Here m = mass of the cookie and v = velocity

But velocity after collision is same because spring shows elastic behavior.

Therefore ,

Kinetic energy of cookie is when it slides back is same.

i.e. K.E. = 19.0 J

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