I just want to gain a ballpark estimate for how much force an MRI machine can generate on a small object such as a nail.. lets say the magnet is 1-2 Tesla. Very rough estimates are ok.
It depends on the volume of the nail. Of the order of 3N/cm^3 (for iron/steel nails). In terms of acceleration, the volume cancels, and we get something like 45g, where g is the gravitational acceleration on earth. It is important to have an inhomogeneous field - I assumed a typical length scale of 1m here.