Electrical wires suspended between two towers form a catenary (see figure) modelled by the equation shown below, where x and y are measured in meters. y = 20 cosh(x/20) ? 20 ? x ? 20 the towers are 40 meters apart. find the length of the suspended cable. (round your answer to three decimal places.)

The percent efficiency of a machine can never be 100% (or greater), because in the real world some energy is always converted into a. heat b. work c. input force d. output force

The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. find the period when the length is 144 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 7pi seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.

Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. the first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. assume that the positive direction is directed from the second satellite towards the first satellite. (a) calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.(b) what is the loss of kinetic energy in this inelastic collision? (c) repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity(d) loss of kinetic energy = ?