Example 3:

The box B sits on the bed of a truck which is going around a turn of radius _{}. At this instant the truck has a speed _{}. If the coefficient of friction between B and the bed is _{}, calculate the maximum rate at which the truck’s speed can
increase without making the box slip.
Solution:

_{}
_{}
_{}
Slip condition,
_{}
Substitute (2) into (4), we get
_{}
Substitute (5) into (1) and (3), we get
_{}
_{}
Substitute (8) into (7), we get
_{}
_{}