A 4.9-N hammer head is stopped from an initial downward velocity of 3.2 m/s in a

Question

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.

Calculate the downward force F exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward.

Explanation / Answer

mass of 4.9 N hammer head = 4.9/9.8 = m = 0.5 kg KE of hammer striking nail = 1/2mV² = (0.5)(0.5)(3.2)² = 2.56 J Work done by hammer = Favg x distance = Favg(0.0045) = 2.56 Favg = 2.56/0.0045 = 569 N ˜ 570 N ANS Favg = 2.56/0.0012 = 2130 N ˜ 2100 N ANS Comment:the speed (3.2 m/s) of the hammer as it strikes nail includes the effect of the hand force of 15 N. ie this final speed (3.2 m/s) is caused by the effect of hammer weight + hand force.

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