Change the chapter
Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of $3.00 \times 10^9 \textrm{ N/m}^2$ (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)
Question by OpenStax is licensed under CC BY 4.0.

$2360 \textrm{ N}$

Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 11, Problem 13 (Problems & Exercises) (1:09)

Sign up to view this solution video!


No votes have been submitted yet.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 11, Problem 13 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. We want to know what force needs to be exerted on a nail by a hammer in order to exert a pressure of three times ten to the nine newtons per squared meter, given that the tip of the nail has a diameter of one millimeter, which I converted to meters by multiplying by ten to the minus three. So pressure is force divided by area, we can solve this for F by multiplying both sides by A, so force is the pressure times the area. So that’s pressure times pi r squared because this is the area of a circle, the circular tip of the nail, but we don’t know what the radius is but we can substitute it with diameter divided by two, which gets squared and the denominator two gets squared so we have four in the denominator. So we have pressure times pi times diameter squared over four, and this is going to be the force. So three times ten to the nine newtons per squared meter times pi times one to ten to the minus three meters diameter of the nail squared, divided by four, this gives 2360 newtons.