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Hammer + Nail forces! Will answer in response

by sadakaa
Tags: forces, hammer, nail
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sadakaa
#1
Sep15-08, 08:08 PM
P: 19
1. A hammer is pounding a nail straight down into a wooden board. Just before the hammer hits the nail, the speed of the hammer is 1.2 m/s. The hammer drives the nail into the wood and stops after the nail goes in a distance of 0.95 cm. The weight of the hammer head is 6N, and in addition to this weight there is a force of 14 N exerted on the hammer head by the person using the hammer. Assume that the acceleration of the hammerhead is constant while it is contact with the nail and moving downward, (i.e., while the hammer is slowing from its initial speed to zero). Calculate the magnitude of the downward force exerted by the hammer head on the nail while it is driving the nail into the wood. (Hint: By Newton’s third law, the force of the hammer head on the nail has equal magnitude to the force of the nail up on the hammer head. Ask yourself what are all the forces on the hammer head.)

2. Relevant equations

V2 = V02 + 2a(x-x0)


3. The attempt at a solution

Take up as positive, thus:

V0 = -1.2 m/s
V = 0
X0 = .0095 m
X = 0

0 = -1.22 +2(a)(-.0095)
a = 75.7895 m/s2

Now i get stuck. I set up the equation

ma = Fnormal - Fperson - Fgrav

I'm not too sure how to continue. Help!
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LowlyPion
#2
Sep15-08, 08:51 PM
HW Helper
P: 5,341
Quote Quote by sadakaa View Post
1. A hammer is pounding a nail straight down into a wooden board. Just before the hammer hits the nail, the speed of the hammer is 1.2 m/s. The hammer drives the nail into the wood and stops after the nail goes in a distance of 0.95 cm. The weight of the hammer head is 6N, and in addition to this weight there is a force of 14 N exerted on the hammer head by the person using the hammer. Assume that the acceleration of the hammerhead is constant while it is contact with the nail and moving downward, (i.e., while the hammer is slowing from its initial speed to zero). Calculate the magnitude of the downward force exerted by the hammer head on the nail while it is driving the nail into the wood. (Hint: By Newton’s third law, the force of the hammer head on the nail has equal magnitude to the force of the nail up on the hammer head. Ask yourself what are all the forces on the hammer head.)

2. Relevant equations

V2 = V02 + 2a(x-x0)


3. The attempt at a solution

Take up as positive, thus:

V0 = -1.2 m/s
V = 0
X0 = .0095 m
X = 0

0 = -1.22 +2(a)(-.0095)
a = 75.7895 m/s2

Now i get stuck. I set up the equation

ma = Fnormal - Fperson - Fgrav

I'm not too sure how to continue. Help!
Looks like you are almost there.

You have the nail pushing up with the net deceleration on the mass of the hammer head and the force of the arm and shoulder being present throughout the deceleration as well as gravity on the mass. So I would write it as

F = (75.79)*(6N)/(9.8) +14N + 6N


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