Sliding motion for adjacent blocks along an inclined plane
This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
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The scenario here is of two adjacent dry cuboidal blocks as shown in the figure, on an incline of a fixed inclined plane making an angle with the horizontal.
The upper mass is denoted as , and the coefficients of static and kinetic friction between that mass and the incline are denoted and . The lower mass is denoted as , and the coefficients of static and kinetic friction between that mass and the incline are denoted and .
The extremes are (whence, the plane is horizontal) and (whence, the plane is vertical).
We assume that the block undergoes no rotational motion, i.e., it does not roll or topple. Although the diagram here shows a block with square cross section, this shape assumption is not necessary as long as we assume that the block undergoes no rotational motion.
Behavior assuming system initially at rest
Note that the answer in the third column must be yes if the first two columns are yes and no if the first two columns are no.
In cases where the two masses separate, their kinematics can be studied separately. In cases where the masses stay together, they can be collapsed into a single mass whose kinematics can be studied.
|Is ?||Is ?||Is ?||Is ?||Behavior||Do stay together?|
|Doesn't matter||Yes||Yes||Doesn't matter||Both blocks remain stationary.||Yes|
|Yes||No||Doesn't matter||Doesn't matter||slides down, stays stationary.||No|
|No||Doesn't matter||No||Yes||Both slide down, but slides down faster, with accelerations and for respectively.||No|
|No||Doesn't matter||No||No||Both slide down together, with acceleration .||Yes|