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Motivated by a problem arising in the mining industry, we estimate the energy ε(η) that is needed to reduce a unit mass to fragments of size at most η in a fragmentation process, when η→0. We assume that the energy used in the instantaneous dislocation of a block of size s into a set of fragments (s 1,s 2,...) is s βφ(s 1/s,s 2/s,...), where φ is some cost function and β a positive parameter. Roughly, our main result shows that if α>0 is the Malthusian parameter of an underlyingdoi:10.1239/aap/1118858639 fatcat:lzzhpuyrdrg7fa4hx7a2zbfoya