A hammer of mass is moving at speed when it strikes a nail of negligible mass th

Question

A hammer of mass is moving at speed when it strikes a nail of negligible mass that is stuck in a wooden bloc? A hammer of mass M is moving at speed v_o when it strikes a nail of negligible mass that is stuck in a wooden block. The hammer is observed to drive the nail a distance L deeper into the block. (A) Find the magnitude F of the force that the wooden block exerts on the nail, assuming that this force is independent of the depth of penetration of the nail into the wood. You may also assume that v_0>>sqrt(2gL), so that the change in the hammer's gravitational potential energy, as it drives the nail into the block, is insignificant. Express the magnitude of the force in terms of M, v_0, and L.

Explanation / Answer

here,

mass of hammer is M

penetration depth is L

initial velocity is v0

let the deaccelration due to wooden block be a

using third equation of motion

v^2 - u^2 = 2*a*s

v0^2 = 2 * a * L

a = vo^2/( 2 *L)

force , f = *a

f = M*vo^2/( 2 *L)

the magnitude of force is M*vo^2/( 2 *L)

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