# Pressure = Force/Area

1. May 9, 2006

### michiko

I understand that is the equation. I'm comparing two different scenarios based on the same sample. Hitting the sample with something with a smaller tip will have larger pressure because all the pressure is concentrated on that little tip. Doing the same with something larger would mean less pressure, is that correct? Then why am I getting a graph that defies the law of physics? My results show greater sample deformation with the larger object rather than the smaller one. Why?

2. May 9, 2006

### Chi Meson

Perhaps the larger object is moving at the same speed as the smaller object? If so, then more force is exerted.

3. May 9, 2006

### michiko

Is there an equation that connects speed with the force? I'm doing a course on Chemistry so I don't really know about physics stuff.

4. May 9, 2006

### antonantal

Yes, there is an equation that connects speed with force:

F = d(mv)/dt ,
F being the force, m the mass, v the speed, and t the time.

But I don't think this equation will be of any help.

First of all, you can't compare the two deformations unless the impact surface is the same because the sample, being a solid body, will not distribute the pressure evenly on it's entire surface, and because of this, when hitting the sample with something with a smaller tip there will be a bigger deformation on a smaller surface of the object and when doing the same with something larger there will be a smaller deformation on a bigger surface of the object (the actual deformation being the same in both cases).
A better approach would be an energetical one: No matter what the shape of the hitting object is, it has an amount of kinetic energy
E = (mv^2)/2 .
Now, if after the impact none of the objects move anymore (as likely happens in your experiment), it means that all the energy is consumed by deformating the object (if we neglect the very small amount of energy lost in terms of heat dissipated and noise). This means that if the object has the same initial kinetic energy in both cases, no matter what shape the tip has, it will produce the same amount of deformation.

5. May 9, 2006

### michiko

I see, so how does that explain my experiment results? Since you said that there would be a smaller deformation on a larger surface with the tip that is larger and a larger deformation on a smaller surface with the smaller tip, why do I get a larger height change with the larger tip? The sample is the same sample, and does it being DNA make a difference? I cannot think of any possible explanation except for the fact that different tips used contributed to this.

6. May 9, 2006

### antonantal

Are you sure that the hitting object has the same kinetic energy in both cases?

7. May 9, 2006

### Chi Meson

Why not tell us what the experiment is? What are the objects, what are they doing before hitting the sample, what the heck is the sample anyway? What other quantites do you know about the things involved.

8. May 9, 2006

### michiko

Ok, the experiment is about AFM imaging ds DNA which are 14bp long. It's to compare between using a normal AFM tip (larger tip) and a carbon nanotube tip (smaller tip) to look at the same dsDNA molecule. Using the larger tip shows that the height is 0.5nm less than the height seen with the smaller tip. Although I understand that pressure is larger for the smaller tip because the force is exerted over a smaller area, I do not see why there is more deformation with the larger tip. Could it be that the amplitudes are different as different tips resonate at different frequencies?

Last edited: May 9, 2006
9. May 9, 2006

### Curious3141

I'm not an expert and my experience with AFM (atomic force microscopy) is limited. What I do know is that AFM is a complex modality, with many variables. It is possible to run AFM in non-contact or contact modes, in surface topography, and to measure hardness.

I don't know the exact nature of the tips you're using here, but if you're doing surface topography, a few possibilities spring to mind. A larger tip will presumably have lower resolution (it will tend to average out the surface features) than a smaller tip. While the smaller tip can read the grooves of DNA better (hence, a smaller height value), the larger tip may just be averaging things out.

The other possibility is the softness of the tip. A harder tip will compress less when in contact with the surface, giving a greater height (greater cantilever deflection), while a softer tip will give a smaller height (I think).

Best to get the opinion of someone very familiar with AFM, it's a specialty unto itself.

10. May 9, 2006

### michiko

Alright. Thanks for the help anyway!