1
$\begingroup$

I would be interested to measure a very small force, say in the order of $10^{-12}\ \mathrm{N}$? Is this possible? What equipment is needed?

My setup

Assume that I have a relatively heavy machine say between 5-10 kg that I want to measure if it produces this thrust, which according to calculations should be of this feeble magnitude. But (according to the predictions) this should be periodic, with a frequency of about 200Hz and it should last for about a quarter of the time period. I should also mention that this apparatus is expected to vibrate (a little), since inside a disk is supposed to be rotated at about 12k rpm.

My research

I have read about torsion balance as a possible method. I am also thinking about some piezo-electric crystals. Would be feasible?

What piezoelectric cells would be recommended? I read that the Atomic Force Microscopy devices are also implemented using piezoelectric materials.

$\endgroup$
1
  • $\begingroup$ Just one man's "wild" idea: don't atomic force microscopes use this technique? $\endgroup$ Nov 26, 2021 at 2:54

2 Answers 2

7
$\begingroup$

The question is, a $10^{-12}\rm\,N$ force applied to what. A force of $10^{-12}\rm\,N$ applied to a hydrogen atom, with mass $10^{-27}\rm\,kg$, would produce an acceleration $F/m = 10^{+15}\rm\,m/s^2$.

A torsion pendulum is absolutely a way to allow very feeble forces to cause observable, macroscopic motion. My favorite underrated classic paper is Beth’s 1936 experiment which transferred angular momentum from a beam of circularly polarized light to a torsion pendulum. There was a parity-violation experiment in the 1960s that used a torsion pendulum as a detector for circular polarization in photons emitted from a parity-violating weak interaction process. And the 2001-ish proposal that gravity might be non-Newtonian at short distances has been mostly ruled out by torsion-pendulum measurements of gravitational attraction between coin-sized test masses.

In all of those cases, you accumulate the very small force by doing the experiment many times, repeating at a frequency near the resonant frequency of the pendulum.

For more direct measurements of very tiny forces, you might read about the operation of an atomic force microscope.

$\endgroup$
3
  • 1
    $\begingroup$ Another very notorious but perhaps more mundane example is the Einstein-de Haas effect, which establishes a direct connection between "intrinsic" angular momentum and spatial/rotational angular momentum $\endgroup$
    – lurscher
    Nov 26, 2021 at 1:42
  • 2
    $\begingroup$ Just to add to something you said, often measuring a small effect that is varying in time at a known frequency is easier than measuring a small effect that is constant. $\endgroup$
    – Andrew
    Nov 26, 2021 at 2:17
  • $\begingroup$ For an excellent of the story that @lurscher refers to, read Galison's "How Experiments End." $\endgroup$
    – rob
    Nov 26, 2021 at 2:18
1
$\begingroup$

Not to answer your question completely but on the AFM point- we can model the AFM cantilever as a spring in contact mode. The spring constant can be ~0.2 N/m or lower.

Now you can, without much work get z-direction sensitivities of 0.1 nm without too much trouble, taking into account experimental noise.

Very roughly speaking this gives a resolution of 0.02 nN or 20 pN. So, not far off for measuring forces on a tiny cantilever. However, for a mass that size I'm not sure it's possible.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.