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I understand that the hammer applies a force on the nail (of magnitude say, 25 N). The force is then transmitted through the nail onto the wood and thus, the nail exerts a force of 25 N on the wood.

But then according to Newton's third law of motion, the wood would apply a force on the nail (of mag. 25 N).

In theory, this force on the nail by hammer (25 N) and the force on the nail by wood (-25 N) must cancel each other and the nail shouldn't move (supposing it was at rest when it was hammered).

However, in reality, the nail does move and gets embedded. How is this possible?

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I understand that the hammer applies a force on the nail (of magnitude say, 25 N). The force is then transmitted through the nail onto the wood and thus, the nail exerts a force of 25 N on the wood.

If that is assumed, then indeed the nail won't move.

First, this is quite a weak force, equivalent to weight of 2.5kg. I think that won't drive nail in most of woods. Maybe styrofoam. Wood needs much larger force.

Second, in addition, you assume that the nail acts with equal force on the wood to the force it experiences from the hammer. This implies that net force on the nail is zero. And with this assumption of equality, it would be zero even if the force of the hammer was hundred times larger (which in practice would be enough to drive the nail into the wood).

That assumption is correct only as long as the nail is at rest, or moves uniformly. But this is not what happens for large enough force. The nail accelerates, because the wood can't provide equal force to the force of the hammer. The wood fibers give way to the nail, and this means there has to be a limit to the force the fibers can exert on the nail, and this limit has been reached.

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  • $\begingroup$ Thanks for your answer ! $\endgroup$
    – Golden_Hawk
    Commented Feb 24, 2023 at 2:57
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The force is then transmitted through the nail onto the wood and thus, the nail exerts a force of 25 N on the wood.

Some of the force does this, but not all. Some of the force instead is used to accelerate the nail.

You could hang a nail in the air from a light thread and tap it with a hammer. Although very light, you can feel the force from the hammer striking the nail, so the hammer is producing a non-zero force on the nail.

But since the nail is in the air, it's not transmitting the force to anything. Instead the force goes into accelerating the nail.

In the wood the same thing happens. Some of the force accelerates the nail and that means that slightly less than that amount of force is opposed by the block.

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The hammer applies a force to the nail head. that force is transmitted to the pointed end of the nail, in contact with the piece of wood. because the nail point is extremely small, the pressure applied to the piece of wood right under the nail point is huge- big enough to pry the wood fibers apart and allow the nail point to start penetrating the wood.

Now note that the piece of wood is lying on a stout workbench which, being heavy, reflects the impulse force delivered by the hammer blow right back into the piece of wood, causing the wood between the nail tip and the workbench surface to get crushed. in goes the nail.

To guarantee that the hammer blow will bounce off the workbench and back into the wood requires that the inertia of the bench be a certain amount bigger than that of the hammer. for a very large piece of wood, the inertia of the wood will suffice.

If you are clever enough, you can actually calculate the mass ratio (workbench/hammer) needed to get the hammer blow to bounce off the bench and crush that which is between the bench and the hammer.

BTW this determines how heavy an anvil must be for use with a 5 pound hammer, while working hot iron. The solution of this problem is left as an exercise for the interested reader, and will count for half your grade for the term.

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  • $\begingroup$ Thanks for your answer ! $\endgroup$
    – Golden_Hawk
    Commented Feb 24, 2023 at 2:58
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look, the wooden piece does apply the same amount force on the nail, but the effect of force also depends on the type of material used, in this case, the Young's modulus of iron is more than that of wood, and that means that the change in dimensions of iron nail will be far less than that of wood, you can calculate strain using the following formula

formula

Here A represents the area on which the restoring force F is being applied and Y is Young's modulus

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See first of all there is no equal and opposite reaction also here the surfaces are not perfectly flat enough for example take a look on a tip of nail it’s pointed so here the geometry plays a key role if it would have been something flat and as same as wooden block it wouldn’t go in instead it would bounce and stay where it was. Wooden block has Young’s modulus and the pressure applied by the nail is way larger than the stress that wooden block can handle so that’s why the wooden block gets deformed and the nail pierces through it pressure and stress have same dimensions and units.

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