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in the above equation if a constant force F is applied on the rod.Find the velocity of the rod as a function of time assuming it started with zero initial velocity. |
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Answer» Solution :`m(dv)/(dt)=F-ilB`...(1) `i=(Blv)/(R+r)` ..(2) `m(dv)/(dt)=F-(B^(2)l^(2)V)/(R+r)` LET `K=(B^(2)l^(2))/(R+r)` `UNDERSET(0)overset(v)INT(dV)/(F-Kv)=underset(0)overset(t)int(dt)/(m)` `-1/K[ln(F-KV)]_(0)^(v)=t/m` `ln((F-kV)/F)=-(Kt)/m` `F-KV=F_(e)^(-kt//m)` `V=F/K(1-(e)^(-kt//m)` 
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