a hammer of mass M strikes a nail of mass m with velocity of u metre per second and drives it a metre into fixed block of wood . the average resistance of the wood to the penetration of nail is
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Solution
Given: mass of hammer = M kg mass of nail = m kg initial velocity of hammer = um/s distance = a meters. Resistance of wood =? Kinetic energy of hammer is (Mxu²)/2 this energy is transferred to the nail. ∴ energy of nail is equal to that of hammer. let initial velocity of nail be v. Kinetic energy of nail= (mx v² )/2 mv²/2 = Mu²/2 ∴v²=(Mxu²)/m ⇒v=u√M/m ------------(1) let the retardation of nail in the block be a₁m/s² v²=u²+2as ⇒0=v²-2x a₁xa 2xa₁=v²/a ∴a₁=v²/ax2 ⇒a₁=(u²(√M/m)²)/2x a (from equation 1) ⇒(u²xM)/2xaxm ∴a₁=(u²xM)/2xaxm so, force on wooden block is F=mx a1 =[m x (u²XM)]/2Xaxm⇒u²M/2a ∴u²M/2a is the average resistance of wood.