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 0.45cm 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.

Part A

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.

Part B

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 same as on part A. What then is the 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

(A)
u = 3.2 m/s
v = 0
s = 0.45 * 10^-2 m

V^2 = u^2 - 2*a*s
0 = 3.2^2 - 2*a*(0.45 * 10^-2)
a = 1137.8 m/s^2

Force = m*a
F = 4.9/9.8 * 1137.8 N
F = 568.9 N

Total Force, F = 568.9 + 15
Total Force, F = 583.9 N
Total Force, F = 584 N

(B)
u = 3.2 m/s
v = 0
s = 0.12 * 10^-2 m

V^2 = u^2 - 2*a*s
0 = 3.2^2 - 2*a*(0.12 * 10^-2)
a = 4266.7 m/s^2

Force = m*a
F = 4.9/9.8 * 4266.7 N
F = 2133.4 N

Total Force, F = 2133.4 + 15
Total Force, F = 2148.4 N

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