Amass, m , and spring, k, are at rest in a gravity field, about to be struck by a mass, m, falling from a height, h. the mass, m, sticks to m , and the two move downward. the variable, x, keeps track of the displacement after impact. sketch the general motion of x for some period of time after impact. how many equations do you think are needed to describe this system mathematically? if the system ever came to rest, what would be the deflection of the spring?

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j