In a region of space, the potential energy of the system varies with x as u = α − (βx − γ)2 , where α = 38 j, β = 1.0 j1/2m-1, γ = 17 j1/2, and x is measured in meters. a particle of mass m = 2.5 kg is initially at x0 = 11 m. assume there are no dissipative forces (friction, wind resistance, etc.) in this problem. (a) at what position is the force on the particle zero? (b) what is the potential energy of the system when the particle is at the position that you found in part (a)? is this a point of stable or unstable equilibrium?

Heat from the sun reaches earth to a. radiation b. convection c. conduction

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

Amodel rocket with a mass of 0.212 kg is launched into the air with an initial speed of 84 m/s. how much kinetic energy will the rocket have at a height of 214 m? assume there is no wind resistance. 634 j 303 j