A block is placed on a horizontal surface. The block is pushed by applying a force F which acts at an angle of theta with the vertical . How much force will be required to move the block if friction coefficient mu ? Discuss the fact it tan theta lt mu.

A block is placed on a horizontal surface. The block is pushed by appl

1.	A block is placed on a horizontal surface. The block is pushed by applying a force F which acts at an angle of theta with the vertical . How much force will be required to move the block if friction coefficient mu ? Discuss the fact it tan theta lt mu.
Answer» <P> Solution :Normal reaction force , N = (mg+Fcos`THETA`) `:.` Minimum required force (horizontal ) to move the block, `P_("min") = MU(mg +Fcostheta`) Now, `("required force" (P_("min")))/("applied horizontal force (P)")= (mu (mg +Fcos theta))/(Fsin theta)` If `tantheta lt mu` than `(P_("min"))/(P)gt("mgtan"theta+tantheta.Fcostheta)/(Fsintheta)gt(mg)/(Fcostheta)+1gt1` `[because costhetagt0`] i.e., `PltP_("min")` `:.` The block remains STATIC.