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 790N and a deflection of 1.1cm . 1. To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50 kg for the mass of the hand. V=? *note answer is not 56, I can't figure out what I am doing wrong 2. If the hand is moving this fast and comes to rest in a distance of 1.1 cm, what is the average force on the hand? F=? *note answer is not 760 N.

Explanation / Answer

F d

It is analogous to a harmonic oscillation..or a spring...

F = kx

790 = k * 0.011

So, K = 71818.181 N/m

So, max energy = 1/2 * k * d,max^2 = 4.345 J

SO, the energy of the hand must be same as this...imagine it ti be a spring...max velocity is as mean position...(here..when the hand hits the board)...

so 1/2 * m*V^2 = 1/2*K*A^2....as in spring...

SO, V = 4.1689 m/s

If the hand is not moving this fast...Avg force = 0.5 * K * A = 395 N

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