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A carpenter swings a 3-kg hammer so that its speed is 5 m/s just before it strikes a nail. The...

Question:

A carpenter swings a 3-kg hammer so that its speed is 5 m/s just before it strikes a nail. The nail is driven 6 mm into a block of wood. Assuming that a constant force resisted the motion of the nail, what must have been the magnitude of the force?

Conservation of Energy:

Energy is conserved in our universe.

It is never lost, it only changes form.

Thus if we drop a stone from a height, it loses potential energy as it gains kinetic energy in the for of increasing velocity.

We also must be familiar with the concept of work done by a force.

It is defined as :

{eq}\displaystyle { W=\vec{F}\cdot \vec{d} } {/eq}

Answer and Explanation:

The force opposing the nail's entry into the wood does some work.

Let the magnitude of this force be :

{eq}\displaystyle{F} {/eq}

Thus the work done is :

{eq}\displaystyle{W=Fd\\ W=F\times 0.006 Nm } {/eq}

The distance is taken in meters instead of millimeters.

This work done is compensted by the energy of the hammer.

The energy is given by :

{eq}\displaystyle{ E=\frac{1}{2}mv^2\\ E=0.5(3)(5^2)\\ E=37.5 Nm\\ } {/eq}

Thus :

{eq}\displaystyle{ W=E\\ F(0.006)=37.5\\ F=6250N\\ } {/eq}

Thus the force is found to be 6250 newtons.


Learn more about this topic:

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What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
98K

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