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

Question

A hammer of mass M is moving at speed 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. Part 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_o >> square root 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, v0, and L. Now evaluate the magnitude of the holding force of the wooden block on the nail by assuming that the force necessary to pull the nail out is the same as that needed to drive it in, which we just derived. Assume a relatively heavy M = 0.5 kg hammer (about 18 ounces), moving with speed V_0 = 10 m/s. (If such a hammer were swung this hard upward and released, it would rise 5 m). Take the penetration depth L to be 2 cm, which is appropriate for one hit on a relatively heavy construction nail. Express your answer to the nearest pound.

Explanation / Answer

A)

We use work-energy theorem

W= KEf-KEi = F*d

1/2M(Vf2-V02) = F*L

Vf = 0m/s

-1/2MV02 = - F*L ……………negative F since it’s directed downward

1/2MV02 = F*L

F= MV02/2L

B)

F= MV02/2L = (0.5*102)/(2*0.02) = 1250 N = (1250/4.45)lb = 280.9 lb

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