A `30 kg` mass is intially at rest on floor of a truck . The coefficient of static friction between the mass and the floor of truck in `0.3` and coefficient of kinetic friction is `0.2` . Intially the truck is travelling due east at constant speed.Find the magnitude and direction of the friction force acting on the mass , if : (take `g = 10 m//s^(2))`
(a) the truck acdceleration at `1.8 m//s^(2)` eastward
(b) the truck acdceleration at `3.8 m//s^(2)` westward

Explanation

(a) When the truck acceleration eastward force of friction on mass is earwards.
`f_("required") = "mass" xx "acceleration" = (30) xx 1.8)`
`= 54 N`
Since it is greater than `mu_(s) mg`
`:. f = 54 N`
(b) When the truck acceleration eastward force of friction on mass is westwards.
`f_("required") = "mass" xx "acceleration" = 30 xx 3.8`
`= 114 N`
Since it is greater than `mu_(s) mg`. Hance
`f = f_(k) = mu_(k) mg = 60 N` (westwards)