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Arrive at an expression for power and velocity. Given some examples for the same. |
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Answer» Solution :(i) The work done by a force `vec(F)` for a displacement `d vec(r )` is `W = int vec(F).d vec(r )""`…(1) Left hand side of the EQUATION (1) can be written as `W=int dW = int(dW)/(dt)dt` (multiplied and DIVIDED by dt)` ""` .....(2) (ii) Since, velocity is `vec(v)=(d vec(r ))/(dt),d vec(r )= vec(v )dt`. Right hand side of the equation (1) can be written as `int vec(F).d vec(r )= int(vec(F).vec(v))dt[vec(v)=(d vec(r ))/(dt)]""` ....(3) Substituting equations (2) and (3) in equation (1), we get `int(dW)/(dt)dt = int (vec(F).vec(v))dt int((dW)/(dt)-vec(F).vec(v))dt = 0` (iii)This relation is true for any ARBITRARY value of dt. This implies that the term within the bracket MUST be equal to zero, i.e., `(dW)/(dt)= vec(F).vec(v)=0`(or)`(dW)/(dt)=vec(F).vec(v)` |
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