A bucket weighing 100 pounds is filled with sand weighing 500 pounds. A crane li
ID: 1503392 • Letter: A
Question
A bucket weighing 100 pounds is filled with sand weighing 500 pounds. A crane lifts the bucket from the ground to a point 80 feet in the air at a rate of 2 feet per second, but sand simultaneously leaks out through a hole at 3 pounds per second. Neglecting friction and the weight of the cable, determine how much work is done. Give a formula for the weight of the sand depending on the height from the ground y. Give the force, that applies to the bucket at a height y form the ground. Use that 1 pound corresponds to 4.448 Newton in force. Calculate the work. You may use your caluclator for the end solution.Explanation / Answer
Let x = feet the bucket,
(Remember weight is the force exerted on a mass due to gravity.)
Bucket (without sand):
Force = 100 lbs.
Leaking Sand:
Force = (3 lb/sec) * (1 sec/ 2 ft) * (x ft) = 3x / 2 lbs.
Thus, the total force is given by
F(x) = 100 + (500 - 3x/2) = (600 - 3x/2) lbs
Work = integral(x = 0 to 80) (600 - 3x/2) dx
work = (600x - 3x^2/4) {for x = 0 to 80}
work = 48000 - 4800
work = 43200 ft-lb.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.