Aneutral kaon decays into two pions via the process k^0 → π + π − where m of k^0 =500mev/c2 and the pion masses are both 140 mev/c2. if the kaon is at rest, what are the energies (in mev), momenta (in mev/c), and velocities (in units of c) of the pions.

if the kaon moves in the lab with a kinetic energy of 600 mev, and the positive pion is emitted along the kaon’s direction of motion, find the kinetic energies (in mev) and momenta (in mev/c) of each pion.

the kaon has the same lab kinetic energy as in the previous problem, but the positive pion is emitted 45° relative to the kaon’s direction of motion (measured in the kaon’s rest frame). use conservation of energy and momentum to find the kinetic energies (in mev), momenta (in mev/c) and angles (in degrees) of each pion relative to the kaon initial direction.

An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of where qin is the refrigerator cooling rate, qout is the heat rejection rate, and is the power input. show that copm can be expressed in terms of the reservoir temperatures tc and th, the cold and hot thermal resistances rt,c and rt,h, and qin, as where rtot rt,c rt,h. also, show that the power input may be expressed as 1.39 a household refrigerator operates with cold- and hot-temperature reservoirs of tc 5 c and th 25 c, respectively. when new, the cold and hot side resistances are rc,n 0.05 k/w and rh,n 0.04 k/w, respectively. over time, dust accumulates on the refrigerator’s condenser coil, which is located behind the refrigerator, increasing the hot side resistance to rh,d 0.1 k/w. it is desired to have a refrigerator cooling rate of qin 750 w. using the results of problem 1.38, determine the modified coefficient of performance and the required power input w under (a) clean and (b) dusty coil conditions. internally reversible refrigerator qout qin w high-temperature reservoir low-temperature reservoir th th,i tc,i tc high-temperature side resistance low-temperature side resistance w qin th tc qinrtot tc qinrtot copm tc qinrtot th tc

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

If two students are running down the hall toward each other, trying to get to class, and they have the same mass and acceleration, what will happen when they collide? will their forces cancel out or will each one experience a reaction?