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 860N and a deflection of 1.6cm .

1. To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50kg for the mass of the hand.
v= ________

2. If the hand is moving this fast and comes to rest in a distance of 1.6cm , what is the average force on the hand?
F=___________

Explanation / Answer

The work done against the board when it breaks = F x d = (860)(1.5E-2) = 12.90 J A hand of mass = 0.50 kg must have the same energy in order to break board: 1/2mV² = 12.90 V² = 12.90/(0.5)(0.5) V² = 51.6 V = 7.18 m/s ANS Assuming constant deceleration: V = v2ad = 7.18 V² = 2ad = (7.18)² = (2)(a)(1.5E-2) a = 51.6/2(1.5E-2) = 1720 m/s² {deceleration of hand} Favg = ma = (0.5)(1720) = 860 N ANS same as force necessary to break board

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