Calculating Spring Compression for Desired Block Speed

[MJC8719]

In Figure 8-34, a 1.2 kg block is held at rest against a spring with a force constant k = 670 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless, except for a rough patch of width 5.0 cm that has a coefficient of kinetic friction µk = 0.44. Find d such that the block's speed after crossing the rough patch is 1.6 m/s.



onservation of energy:

energy stored in spring = final kinetic energy + energy taken by friction (work)

(1/2) k d2 = (1/2) m v2 - u m g d


or (1/2) * 670 * d2 = (1/2) * 1.2 * 1.62 - 0.44 * 1.2 * 9.8 * 0.05

335 * d2 = 1.536 - 0.259 = 1.277

d2 = 1.277/335 = 0.003812 so d = 0.0617 meters or 6.17 cm

Cannot figure out what I am missing here...

 

[Doc Al]

energy stored in spring = final kinetic energy + energy taken by friction (work)

Correct.

(1/2) k d2 = (1/2) m v2 - u m g d

Incorrect.

 

[MJC8719]

A simple sign error lol...Thansk so much...would have hated to lose points after doing all the real work correctly lol