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 \(800 \mathrm{~N}\) and a deflection of \(1.2 \mathrm{~cm}\).

a. To break the board with a blow from the hand, how fast must the hand be moving? Use \(0.50 \mathrm{~kg}\) for the mass of the hand.

b. If the hand is moving this fast and comes to rest in a distance of \(1.2 \mathrm{~cm}\), what is the average force on the hand?