A 2kg hollow sphere with a 30cm diameter is welded onto a thin 5kg rod that is 1.3m in length to form a hybrid scepter-staff for a narcissistic king. The king will often balance it in his palm with the sphere up and then let it fall over and swing down. What is the difference in linear speed of the center of mass and the outer edge of the sphere when the staff-scepter is at the bottom?
At what angle from the vertical does the weld have to accelerate the sphere faster than gravity?

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