A spring with spring constant k = 205 N/m is used as a launcher for a small bloc

Question

A spring with spring constant k = 205 N/m is used as a launcher for a small block whose mass is 10 g. The block is placed against the compressed spring in a horizontal arrangement on a smooth horizontal surface. The spring, with the block, is compressed 6 cm and then released.

a) Find the speed of the block just as it leaves the spring. Answer in m/s

(b) The block encounters a rough surface as it leaves the spring. How much work does friction do in bringing the block to an eventual stop? Answer in J

(c) The block slides a distance of 6.0 m before stopping. What is the coefficient of kinetic friction between block and surface?

Explanation / Answer

a) Since the elastic force is a conservative one, the energy conservation can be applied. When the body is at rest and the spring is compressed, the energy is completely of potential nature being E = (1/2) K x^2 = 0.369 J. It is converted integrally into kinetic energy, so that E = (1/2) m v^2 => v = sqrt(2 E/m) = 8.59 m s^-1.

b) The work done by friction force is equal to the energy possessed when it started to move, i.e. just 0.369 J

c) Since F_fr = mu_k F_norm = mu_k mg, and W = F_fr Dx = mu_k mg Dx, it follows mu_k = W/(m g Dx) = 0.62.

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