Calculate the size of the precipitates at which the cross over from dislocation bowing between precipitates to dislocation cutting the precipitates occurs giving rise to equal strength increase. Assume the shear modulus G=26 GigaPascals, lattice parameter of aluminum is 0.406 nm and surface energy of the precipitates is 1000 mJ/m2. What is the effect of additional ledge energy that we did not include in the analysis. A ledge is produced when a dislocation cuts through the precipitate.