Okay, so if I use 1/2mv2top+mg2r=1/2mv^2bottom, and top: Ftension= mv2/r - mg bottom: Ftension= mv2/r + mg I get Tension at bottom = mv^2(top)/r+4mg/r+mg, which simplifies to Tbottom=Ttop + 6mg.
As for the time, I'm not really sure what to do with that. T=2*pi*r/v, but that is constant...
Homework Statement
A bucket of water (10kg) is swung vertically. Radius is 1 m. It takes 1 second to spin the bucket in a full circle.
a. How much force has to be exerted at the top of its motion?
b. How much force must be exerted at the bottom?
Homework Equations
vtop=sqrt(gr)
top: Ftension=...
So in essence it's just
KE+Wdrag+EPE=GPE
Okay, cool. I get the 13.24 m/s as well.
Thank you for all your help! Not only in answering this question (finally) but also with those concepts that my physics teacher failed to properly teach...
51v2+144.12+(.5*167*34.9281)+(102*9.8*12.01)=102*9.8*22.37
51v2+144.12+(2916.49635)+(12005.196)=22361.052
sqrt (143.0439147)= 11.96
I guess I still have some numbers wrong in there then?
KE+Wdrag+EPE+GPE=GPEinitial
.5mv^2+144.12+(.5*167*144.2401)+(102*9.8*12.01)=102*9.8*22.37
I'm getting a square root of a negative again.. what am I doing wrong?
Edit: for the elastic potential energy, if I use 5.91 instead of 12.01, I get 11.96 m/s.
Drag would be in opposite direction of mg, so it would be addition then? I'm not very good at envisioning these things.
Should it just be N then, and not N m?
Is 15.25 m/s any closer? 167x+12=mg, x=5.9
Fspring-Wdrag=mg
I'm always confused as to whether I should add or subtract drag.
167x-12x=mg
x=6.45 m
Well x represents displacement from equilibrium, so it's the extra distance that the cord has stretched beyond the 6.1m?
Using this I get velocity to be about 15.59 m/s, unless I"m still...
Well when acceleration is zero there's no net force. However there's still gravity acting on it along with elastic potential energy...? So these would all be equal?
I have no idea... I've never heard of a continuous variable before and a quick search doesn't really return how you would find the maximum.
Oh wait, is this integrals? If so, it's way beyond the math my class level should capable of.
Would it make sense to set KE+Wdrag+GPE equal to the initial...
Oops, I actually have 21.838 written down. Was it just a typo or should I completely redo the calculation?
I thought maximum velocity would be at this point because kinetic energy starts being transferred to elastic energy as the cord then stretches.
I'm doing sqrt (118.1247059) to get the...