The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will

(i) Estimate the force with which a karate master strike a board, assuming the hand’s speed at the moment of impact is 10.0 m $s-1$, decreasing to $1.00\mathrm{}\mathrm{m}\mathrm{}\mathrm{s}-1$ during a $0.002\mathrm{}\mathrm{s}$ time internal of contact between the hand and the board. The mass of his hand and arm is $1.00\mathrm{}\mathrm{k}\mathrm{g}$.

(ii) Estimate the shear, assuming this force it exerted on a $1.00 \mathrm{cm}$ thick pine board that is $10.0 \mathrm{cm}$ wide.
(iii) If the maximum shear stress that a pine board can support before breaking is $3.60\times {10}^6 \mathrm{N}/{\mathrm{m}}^2$, will the board break?

A rod pulled with forces $F_1$ and $f_2$ at its ends. Find the:

(i) Tension at a distance $x$ from left and at the rod,

(ii) longitudinal and shearing stresses at the given cross-section $PQ$ if the cross-section of the rod is $A_0$,
(iii) conditions for maximum longitudinal and shearing stresses at the given cross-section $PQ$.

Drawings A and B show two cylinders that are identical in all respects, except that one is hollow. Identical forces are applied to each cylinder in order to stretch them. Which cylinder, if either, stretches more?