A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J0 (r/R), where R is the radius of the beam and J0 is the current density at the edge. Determine the value of J0.

Aray of light traveling parallel to the principal axis of a concave mirror will be reflected through the mirror's

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.