Question

A hammer of mass M is moving at speed v_0 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. Find the work W done on the hammer by the nail. Express your answer as a function of F and L, where F is the force the nail exerts on the hammer. Don't forget to consider the sign of your answer. Find the change in kinetic energy of the hammer. Express your answer in terms of M and v_0. 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 >> squareroot 2g L, so that the change in the hammer's gravitational potential energy, as it drives the nail into the block, is insignificant. Express your answer in terms of M, v_0, 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.

Answer 1

(a).Workdone: W = FL (b) Kinetic energy: (c).Magnitude of Force: From kinematic equations V2-u2 =2as 2L Using newtons )" law 2L2L M 0.5(102 2L 2(0.02) = 1250 N F 1250 - 280.89 lb 4.45 N F 280.89 1b