posted by MJ on .
The drawing shows a large cube (mass = 34 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 3.3 kg) is in contact with the front surface of the large cube and will slide downward unless P is sufficiently large. The coefficient of static friction between the cubes is 0.71. What is the smallest magnitude that P can have in order to keep the small cube from sliding downward?
As I understand it, the smaller cube does not touch the horizontal surface, and is being held above that surface by friction force appled at the interface between the cubes.
The weight of the small cube is m g. (m = 3.3 kg). The force that is applied to the big block is
P = (M + m) a, where a is the acceleration. (M = 34 kg) The force applied to the small bloack is m a. The friction force is m a u, where u is the static coefficient of friction between the blocks (0.71).
To avoid vertical slippage
m a u > m g.
a > g/u
P > (M + m) g/u