Consider a particle moving in a circle performing non-uniform motion.Consider one revolution of the particle.In that revolution the net displacement is zero(you should use Fnet.d).So,net work done by the net force is zero.But by work energy theorem the work done is not coming out to be zero.
Please tell me which theory is right here and why?
1I think the Work-Energy Theorem is correct.
dW = Fdx
W = 0∫2πr (Fdx)
= F 0∫2πr (dx)
= F [x]02Ï€r
= F(2Ï€r)
=2Ï€rF......................................this is a positive value.
So Work done is not zero...(please verify)
1oho.You have taken distance travelled.You have to take net dispacement.Which is equal to zero.
1let me make it pretty clear...
answer urself these two questions which force and which diosplacement are u tlking about n u will get ur answer!
btw both the theories are correct!it's just tht u r messing up with identification of "which work" are u calculating!
its ok if u realize what slipped in ur thought process...if not after sometime i will post a long reply regarding this "APPARENT PARADOX"
1just a hint
non-uniform motion so work done by tangential force is ∫F.dl and note u can't take F out of integration here as u were thinking tht ∫dl=0 but the force itself is varying in direction(and if by ur grace maybe even in magnitude [3]...just kidding)
1did u not read the hint?
yaar long wala will take some time i already had spent time i allocated for long reply with rahul :P
1Sorry,the direction of the net force is changing.I took F.dr but it is F vector.dr vector.
Thank you