A small box of mass m 1 is sitting on a board of mass m 2 and length L. The boar
ID: 1311952 • Letter: A
Question
A small box of mass m1 is sitting on a board of mass m2 and length L. The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is ?s. The coefficient of kinetic friction between the board and the box is, as usual, less than ?s.
Throughout the problem, use g for the magnitude of the acceleration due to gravity. In the hints, use Ff for the magnitude of the friction force between the board and the box.
Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board).
Explanation / Answer
Given sufficient force , the box starts tio slide against the board which means kinetic friction comes into play.
Themaximum force of kinetic friction acting on box = usm1g. This force tends to drag the box in the forwaed direction. Therefore, when the box starts to slip it acclerates forward at the rate usg m/s2.
An equal force must be opposing the board . However, the accleration of board must be more than that of the box.
The accleration of board = (Ff - usm1g)/m2. >= usg (acc. of the box)
Ff >= usm1g+m2usg = us(m1+m2)g (Answer).