Question

a bucket of water of mass 20kg is pulled at a constant velocity up to a platform 40 meters above the ground. this takes 10 minutes , during which time 5kg of water drips out at a steady rate through a hole in the bottom . find the work required to raise the bucket to the platform.

Answer 1

from the information above, we know the average mass of the bucket of water may be m=20-5/2=17.5kg. as the bucket of water is pulled at a "constant velocity" , the mechanical energy is in conservation. in other words, the work required to raise the bucket to the platform transformed into the potential energy of the bucket of water. thus the answer should be W=mgh=17.5*9.8*40=6860J, irrelevant to the time.

Answer 2

thank u . u got the right answer. but do you know how i can do this problem using calculus

Answer 3

i'm sorry, network problem just now.

Answer 4

its fine take ur time . ty for helping me

Answer 5

hey if u want you want u can use http://www.twiddla.com/515340 to work out the problem

Answer 6

the rate of the dripping wate, according to the problem, is 5kg/10min=5kg/600s=1/120 kg/s(convenient to use ISU here). you can consider a function on the mass of the bucket of water to the time as m(t)=20-t/120.

Answer 7

from t=0 to 600, m(t)dx=(20-t/120)dx=20dx-(t/120)dx=20t-t^2/240=10500kg*s. W=mgh=m(t)dx*gh/t=10500*9.8*40/600=6860J

Answer 8

i'm terribly sorry for wasting you so much time... just mixed up with the Newton-Leibniz Formula.

Answer 9

its fine no worries

Answer 10

isnt the function suppose to b in terms of force, not mass

Answer 11

it is the same... actually..

Answer 12

hey do u think u can help me with another problem

Answer 13

id love to, you can ask that question on the left column.

Answer 14

k ty