Show that if the net force on a particle constrained to move in 1 dimension depends only on position, f-f), the newton's second law can be solved to find v as a function ofx given by: 1 dv2 2 dx v2-si +副0f(x')dx'. note: use the chain rule: dt- = 2dte b) consider a mass constrained to move along x-axis and subject to a net force f =-kx, where k > 0 is a constant. the mass is released form rest at x xo at t-0. use the equation for velocity from part a) to find (x) = . separate the variables and integrate to obtain the time dependence of the position of this mass. hint: when solving the awkward integral you will obtain, use first the suband then ucos 0 in subsequent integral. dt dx dt dx

Part 1: a magnetic levitation or maglev train rides rails without touching them. explain how this works using your data. include the appropriate magnet drawing in your answer. part 2: two objects are near a bar magnet. one is about 1 cm away, while the other is 6 cm away. compare and contrast the magnetic force that affects each object. use your data to answer the question

The experiment was repeated many years later but the gases were mixed in a different type of container. a white solid was obtained which was xenon fluoride. predict whether you think 1) krypton and 2) radon will react with fluorine. explain reasons for your predictions

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)