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In the above question 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. |
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) implies int_(0)^(l)(dV)/(F-Kv)=int_(0)^(t)(dt)/(m)` `-[ln(F-KV)]_(0)^(v)=(t)/(m) implies ln((F-kV)/(F))= -(Kt)/(m)` `F-KV=Fe^(-kt//m) implies V=(F)/(K)(1-e^(-kt//m))` |
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