A 4.9-N hammer head is stopped from an initial downward velocity of 3.2 m/s in a distance of 0.45 cm by a nail in a pine board. In addition to its weight, there is a 15-N downward force on the hammer head applied by the person using the hammer. Assume that the acceleration of the hammer head is constant while it is in contact with the nail and moving downward. (a) Draw a free-body diagram for the hammer head. Identify the reaction force to each action force in the diagram. (b) Calculate the downward force exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward. (c) Suppose the nail is in hardwood and the distance the hammer head travels in coming to rest is only 0.12 cm. The downward forces on the hammer head are the some as in part (b) What then is the force exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward?
Solution 52P Step 1 of 5: a) Step 2 of 5: b)To find the acceleration of the hammer head We have equation 2 2 vy=v +0y (y yy ) 0 v =0 y v0y-3.2 m/s (y y )=-0.0045 m 0 v2 ay= 0y 2(y0 ) 2 = (3) 2(0.0045) 2 =1.138 m/s Step 3 of 5: The mass of the hammer head is, m=Fa =4.9(9.8) = 0.50 kg