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Calculate the minimum force required to drag a body of mass m, resting on a horizontal surface. The coefficient of friction between the body and the surface is mu. |
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Answer» Solution :Let the applied force be F, acting at an angle `theta` with the HORIZONTAL FIG. `f_(2)` = force of limiting friction, mg = weight of the body and R = NORMAL force. For equilibrium, `R+F sintheta = mg """or"`, R = mg - F sin`theta` and F cos `theta = f_(s) = mu R= mu (mg- F sin theta`) or, F cos `theta +muF sin theta = mu`mg `:. F = (mu mg)/(cos theta+musin theta)` Value of F will be minimum when ( cos`theta +mu sin theta`) is maximum. `:. (d)/(d theta) (cos theta +mu sin theta) = 0 ` or , - sin `theta +mucos theta = 0 """or", tan theta = mu ` `:.sin theta = (mu)/(SQRT(1+mu^(2))),"and cos"theta = (1)/(sqrt(1+mu^(2)))` `:. F_("min")= (MUMG)/((1)/(sqrt(1+mu^(2)))+(mu^(2))/(sqrt(1+mu^(2))))=(mumg)/(sqrt(1+mu^(2)))" ""and"theta= tan^(-1)mu` 
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