a 3.5kg block is accelerated by a (horizontally) compressedspring whose spring c

Question

a 3.5kg block is accelerated by a (horizontally) compressedspring whose spring constant is 640 N/m. After leaving thespring at the spring's relaxed length, the block travels over ahorizontal surface, with a coefficient of kinetic friction of 0.25,for a distance of 7.8 m before stopping. a) What is the increase in the thermal energy of theblock-floor system? b) What is the maximum kinetic energy of the block? c) Through what distance is the spring compressed before theblock begins to move? a 3.5kg block is accelerated by a (horizontally) compressedspring whose spring constant is 640 N/m. After leaving thespring at the spring's relaxed length, the block travels over ahorizontal surface, with a coefficient of kinetic friction of 0.25,for a distance of 7.8 m before stopping. a) What is the increase in the thermal energy of theblock-floor system? b) What is the maximum kinetic energy of the block? c) Through what distance is the spring compressed before theblock begins to move?

Explanation / Answer

a. Increase in thermal energy of block floor system = workdone against friction
H = Ff * d = k * m * g *d = 0.25 * 3.5 * 9.8 * 7.8 = 133.77 J
b. According to law of conservation of energy, maximum k.e. =change in heat energy
Kmax = H = 133.77 J
c. Also K.E. of block = P.E. stored in spring
133.77 J = (1/2) * k * x2
x2 = 2 * 133.77 / 640
compression in spring x = sqrt (0.418) = 0.646m = 64.6 cm

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