A swift blow with the hand can break a pine board. As the hand hits the board, t

Question

A swift blow with the hand can break a pine board. As the hand hits the board, the kinetic energy of the hand is transformed into elastic potential energy of the bending board; if the board bends far enough, it breaks. Applying a force to the center of a particular pine board deflects the center of the board by a distance that increases in proportion to the force. Ultimately the board breaks at an applied force of 870 and a deflection of 1.5 . Part A To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50 for the mass of the hand. Part B If the hand is moving this fast and comes to rest in a distance of 1.5 , what is the average force on the hand?

Explanation / Answer

The work done against the board when it breaks = F x d = (870)(1.5E-2) = 13.05 J A hand of mass = 0.50 kg must have the same energy in order to break board: 1/2mV

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