Question #202253

A body of mass m falls from rest through a medium which exerts a frictional drag force bv proportional to a frictional force F. Expand the velocity in power series up to t^4, at what time does the body reach 1/e of it terminal velocity, find it displacement, expand the displacement in power series up to t^4


1
Expert's answer
2021-06-03T09:17:44-0400

F=mgbv,F=mg-bv,

mdvdt=mgbv,m\frac{dv}{dt}=mg-bv,

dvdt=mgbvm,\frac{dv}{dt}=\frac{mg-bv}{m},

dvmgbv=dtm,\frac{dv}{mg-bv}=\frac{dt}{m},

v=mgb(1ebmt).v=\frac{mg}{b}(1-e^{-\frac bm t}).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS