A 183 block is launched by compressing a spring of constant 200 a distance of 15

Question

A 183 block is launched by compressing a spring of constant 200 a distance of 15 . The spring is mounted horizontally, and the surface directly under it is frictionless. But beyond the equilibrium position of the spring end, the surface has coefficient of friction . This frictional surface extends 85 , followed by a frictionless curved rise, as shown in the figure. After launch, where does the block finally come to rest? Measure from the left end of the frictional zone.


http://session.masteringphysics.com/problemAsset/1256165/1/RW-07-57.jpg

Explanation / Answer

the amount of energy lost to non-conservative work during each pass through the frictional zone. In passing through the zone, friction does an amount of work on the block given by

Now for the block to stop, all of the energy imparted by the spring must be dissipated by friction, so the total amount of work necessary is

So the number of passes must be given by the total amount of work done divided by the amount of work done on one pass, or

Now we can find the position by remembering that on the first trip, the block is traveling to the right, on the second to the left, right on the third, etc. So the block should end up 0.467 of the way from the right hand edge, or

Wnc,1 = Ff d = mN d = mm g d = (0.27) (0.183  kg) (9.8 m/s2) (0.85 m) Wnc,1 = 0.4115 J

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