Assume the following represents an isolated system. A box with a mass of m = 0.3

Question

Assume the following represents an isolated system. A box with a mass of m = 0.3 kg starts from rest on the end of a spring. The spring has a stiffness of k = 50 N/m and is compressed a distance of 0.2 m from equilibrium. The box is released from the spring and slides across a frictionless horizontal surface until it encounters an incline. How high up the incline (h, as shown in the figure ) does the box get if, a) the incline id frictionless b) the force of kinetic friction between the incline (and only the incline) and the box is fk = 0.8 N.

Explanation / Answer

a) Using energy conservation,

all spring energy will convert into its potential energy.

kx^2 /2 = mgh

50 (0.2^2) / 2 = 0.3 x 9.81 x h

h = 0.34 m

b) friction force in incline = u.mgcos@ =0.8 x 0.3 x 9.81 x cos30 = 2.04 N

Work done by friction = -f.l

           = -2.04 x (h/sin30) = -4.08h

Now using enenrgy conservation,

kx^2/2 + friction work = mgh

50 x 0.2^2 /2 - 4.08h = 0.3 x 9.81 x h

h = 0.142 m

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