A slingshot consists of a light leather cup attached between two rubber bands. If it takes a force of 32 N to stretch the bands 1.2 cm, what is the equivalent spring constant of the two rubber bands?

In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. a rider is towed at a constant speed by a rope that is at an angle of 15 ∘ from horizontal. the tension in the rope is 1900 n. the force of the sail on the rider is 30∘ from horizontal. what is the weight of the rider? express your answer with the appropriate units.

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 that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?