Air resistance will play a role in how far the projectile lands, however, if it did have a significant effect, I would think the bigger cannon ball would be impacted more than the smaller bullet (assuming that there shapes are similar).
I don't recall that air resistance has a significant...
The actual distance a projectile (bullet, cannonball, etc) travels will depend on the angle at which it is fired. As long as the gravitational forces do not change, mass has no play into determining where and in what time the projectile lands. It can be shown that in order to maximize the...
I would find the factor of 2 to be normal as it is cancelled out by the 1/2. The purpose of 1/2 is to eliminate the double counting. This is typical for pair interaction potentials.
If you're comparing with the book, there is a possibility of a typo.
Best to express the term in brackets (where the sigmas and R's are in) as something like U_ij and then manually perform a double sum and collect like terms. You should see the N pop out. Note that for this to work U_ij = U_ji as you stated.
By draw, I think you mean visualization. Ovito or AtomEye should do the trick. They are free software used by research scientists. You can find them through google.
I would not worry to much about the CC transcript. Admissions to Ph.D. programs look at other things besides the transcripts such as letters of recommendations, research and work experience, GRE test scores and your letter of intent (that being a written letter by you on why you want to attend...
BTW triboelectricity is not piezoelectricity. Piezoelectricity uses crystal like materials to generate power when they are subjected to stress, where as triboelectricity uses materials that are brought into contact to generate power.
Energy Density = Power/Area. It is a metric that describes how good a power technology is. If you have 98 Watts/Square meter and you had 1 square meter of triboelectric material, you should expect 98 Watts of power. Or if you have 2 square meters of triboelectric material, you should expect 98 X...
I can answer the second question. At far off distances the grid should look like a uniformly charged plane. This results in the potential being equivalent to that of a uniformly charged plane.
Triboelectricity happens as a result of taking two different materials and rubbing them together. After rubbing, one material gives up its electrons to the other material. This results in one material becoming negatively charged and the other becoming positively charged. When you separate the...
May I suggest you first figure the magnetic field (or magnetic flux density) on each wire due to the other wire. The magnetic field can be obtained using Amps Law. From the magnetic field you can then obtain the magnetic force which in this case is given by F=I*L*B where I is current, L is the...
If you want to do pure research or teach Physics, then Physics is the way to go. If you want to design and build things, then Engineering is the way to go. For Physics, I'll have to caution you that if you want to conduct pure research in Physics, you will need a Ph.D. Not to say you cannot get...