Adhesive Force of an oscillating surface

[kakarot1905]

Hi

An oscillating plate, something like this:
[URL]http://www.physicsclassroom.com/class/waves/h4.gif[/URL]
has an adhesive surface.

Suppose a particle is stuck to the plate, what is the Adhesive Force on the particle over time [equation]

I know that the break-off force is equal to 10N
But the adhesive force should vary with the tensile force acting on it, so it must be less than 10N at some time during the periodic oscillation...

I thought it was equal to normal force experienced by the particle [-mass*(acceleration due to periodic oscillation - gravity)] but would that mean it would double the weight?!

 

[Valerie Park]

The adhesive force on the particle over time can be expressed as F = μN, where F is the adhesive force, μ is the coefficient of friction between the plate and the particle, and N is the normal force experienced by the particle. The normal force is equal to the mass of the particle multiplied by the net acceleration (acceleration due to the periodic oscillation minus gravity). Therefore, the equation for the adhesive force over time would be F = μ(m*(a - g)), where m is the mass of the particle, a is the acceleration due to the periodic oscillation, and g is the acceleration due to gravity. As the periodic oscillation increases in magnitude, so too will the adhesive force.