A 2.0kg block in pressed against a spring with spring constant 2000N/m until the

Question

A 2.0kg block in pressed against a spring with spring constant 2000N/m until then spring is compressed a distance of 20 cm. The block is then released.

Part A)

If the mass slides on a frictionless horizontal surface and up a frictionless 30 degree hill, what is the maximum height that the mass will reach ?

Part B)

Now suppose that the block and the hill have a coefficient of kinetic friction of 0.25 (the horizontal surface is still frictionless) To what maximum height does the mass reach now? (Note: sin 30 degree =0.5, so that d=2h)

Explanation / Answer

mass of block m
2.0 kg, force constant K = 2000 N/m, x = 20cm = 0.2 m

elastic potential energy = 1/2 k x^2 = 1/2 *2000*(0.2^2)= 40 J

turns in to kinetic energy = 1/2 mv^2 = 40 J ==> v = sqrt(40*2/2)= 6.32 m/s

maximum height reached (zero friction) is h = 0.5*2*6.32^2 /2*9.8 = 2.04 m

Part B)
   with friction

   k.e = mue k* mg*cos theta*h
         => h= k.e/(mue k* mg*cos theta)
            h = 6.32/(0.25*2*9.8*cos30)
              = 1.49 m

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