Figure-2.85 shows a block B of mass m, cart C of mass M, and the coefficient of static between the block and the cart is `mu`. Neglect frictional between wheels and axles and the rotational effects of the wheels. Determine the minimum value of F which must be applied on B such that it will not slide.

`[(mg)/(mu)(1+(m)/(M))]`

Answer

`F_("a , min") = (mg)/(mu_(s))( 1+ (m)/(M))`

Explanation

Common acceleration `a_(c) = (F_(a))/(M + m)`

as `" " F_(a) - N = ma_(c)`
`F_(a) - N = (mF_(a))/(M + m) " " ……. (i) `
as `" " mu N = mg " " ….. (ii)`
Solving Eqns. (i) and (ii) , we get `F_(a)`.