My teacher got a very, very large number for this problem. I\'mconfused because

Question

My teacher got a very, very large number for this problem. I'mconfused because she gave us F=ma to use but I think there isanother formula I must use. I can't figure out what one though.

While chopping down his father's cherry tree, George discoveredthat if he swung the axe with a speed of 25 m/s it would embeditself 2.3 cm into the tree before coming to a stop. If the axehead has a mass of 2.5 kg, how much force was the tree exerting onthe axe head upon impact

Please show step by step solution and all formulae

I know how to find the force of the axe, but not the force of thetree exerting on the axe......please help

Explanation / Answer

. 01.   Formulae: 02.      d = d0 +(v0)*(t) + (1/2)*(a)*(t2) 03.      v = v0 +(a)*(t) 04.      F = m*a . 05.   Using '02' 06.      2.3 cm = 23.0E-3meters = 0.0 meters + (25 m/s)*t + (1/2)*(a)*(t2) 07.   Using '03' 08      0.0 m/s = (25 m/s) + (a)*(t)      ;   solvefor a 09.      a = (-25 m/s)/(t) 10.   Substitute '09' into '06' 11.      23.0E-3 meters = (25m/s)*t + (1/2)*[(-25 m/s)/(t)]*(t2) 12.      23.0E-3 meters = (12.5m/s)*(t)      ;   solvefor t 13.      t = (23.0E-3 meters)/(12.5m/s) = 1.84E-3seconds      ;   thisis the amount of time before the axe stops 14.   Substitute '13' into '09' 15.      a = (-25.0 m/s)/(1.84E-3seconds) = -13586.96m/s2       ;   thisis the deceleration of the axe head 16.   Opposing force of tree: 17.      F = (2.5kilograms)*(13586.96 m/s2) = 33967.39 Newtons .

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