A small box of mass m1 is sitting on a board of mass m2 and length L (Figure 1)
ID: 1427791 • Letter: A
Question
A small box of mass m1 is sitting on a board of mass m2 and length L (Figure 1) . 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).
Express your answer in terms of some or all of the variables s, m1, m2, g, and L. Do not include Ff in your answer.
Explanation / Answer
As the system accelerates from the applied
force, the box experiences a force against
friction equal to m1*a. When that force
exceeds the frictional force, the box will
slide. Fr = µs*m1*g, so
m1*a = µs*m1*g
a = µs*g
The applied force is given by F = (m1+
m2)*a, so
F = µs*g*(m1 + m2)