a. Estimate the force with which a karate master strikes a board, assuming the hand's speed at the moment of impact is `10.0ms^(-1)`, decreasing to `1.00ms^(-1)` during a `0.002 s` time internal of contact between te hand and the board. The mass of his and and arm is `1.00 kg` . b Estimate the shear, assuming this force it exerted on a `1.00 cm` thick pine board that is `10.0 m` wide. c. If we maximum shear stress a pine board can support before breaking is `3.60xx10^(6)N//m^(2)`, will the board break?

Explanation

We will use the impulse momentum theorem to find the force on the had, which is equal in magnitude to the force on the board. Then the definition of shear stress wil let us compute that quantity to se if it is large enough to break the board.
The impulse momentum theorem descrbes the force of te board on his hand.
`Ft=mv_(f)-mv_(i)`
`F(0.002s)=(1.00kg)(1.00ms^(-1)-10.0ms^(-1))`
and `F=-4500N`
a. Therefore, the force of his hand on board is `4500 N`.
b. That force produces a shear stress on the area that is exposed whn the board snaps:
Stress`=F/A=(4500N)/((10^(-1)m)(10^(2)m))=4.50xx10^(6)Ns^(-1)m^(-2)`
c. yes, this is larger than `3.60 MNm^(2)` and suffiices to break the board.
We do not have the right combination of information to use the work kinetic energy theorem to find the force. We could compute the acceleration of the hand and use Newton's second law to find the same `4.50 kN` force, but writing the impulse-momentum theorem is more direct. The area in stress `=` force `//` area of the layers of molecules between which the stress produces distortion (strain).