When Do Sand Particles Slip Off a Vibrating Plate?

In summary, the study investigates the conditions under which sand particles begin to slip off a vibrating plate. It explores the influence of vibration frequency, amplitude, and particle size on the behavior of the sand. The research finds that the slip occurs when the forces acting on the particles, including inertial forces from the vibration, exceed the frictional forces holding them in place. Understanding these dynamics has implications for various applications in material handling and engineering.
  • #1
heroslayer99
33
6
Homework Statement
What is the max amplitude before the sand particles slip off?
Relevant Equations
a = -w^2 x
A horizontal metal plate connected to a vibration generator is oscillating vertically with simple
harmonic motion of period 0.080 s and amplitude 1.2 mm. There are dry grains of sand on the
plate. The frequency of the vibrating plate is kept constant and its amplitude is slowly increased
from zero. The grains of sand start to lose contact with the plate when the amplitude is
D. State and explain the necessary conditions when the grains of sand first lose contact
with the plate. Hence calculate the value of D.I have calculated that the acceleration of the plate is -(2pi x 1/(0.08))^2 (x) but I do not know where to go from here, any reading material / hints will be very helpful.
 
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  • #2
What is the acceleration of a grain just as it loses contact?
 
  • #3
haruspex said:
What is the acceleration of a grain just as it loses contact?
This seems like the typical problem that contains the condition "loses contact" which physicomathematically is being translated to "The normal force from the plate to the grain becomes zero"?
 
  • #4
Delta2 said:
This seems like the typical problem that contains the condition "loses contact" which physicomathematically is being translated to "The normal force from the plate to the grain becomes zero"?
How am I meant to calculate the normal force
 
  • #5
haruspex said:
What is the acceleration of a grain just as it loses contact?
I dont know :(
 
  • #6
heroslayer99 said:
I dont know :(
What will be its acceleration after losing contact then?
 
  • #7
heroslayer99 said:
How am I meant to calculate the normal force
You don't find some bizarre formula for Normal force, you just do newton's 2nd law for a grain and then set normal force to zero and see how the equation simplifies.
 
  • #8
heroslayer99 said:
Homework Statement: What is the max amplitude before the sand particles slip off?
Relevant Equations: a = -w^2 x

A horizontal metal plate connected to a vibration generator is oscillating vertically with simple
harmonic motion of period 0.080 s and amplitude 1.2 mm. There are dry grains of sand on the
plate. The frequency of the vibrating plate is kept constant and its amplitude is slowly increased
from zero. The grains of sand start to lose contact with the plate when the amplitude is
D. State and explain the necessary conditions when the grains of sand first lose contact
with the plate. Hence calculate the value of D.I have calculated that the acceleration of the plate is -(2pi x 1/(0.08))^2 (x) but I do not know where to go from here, any reading material / hints will be very helpful.

If the plate is moving vertically, what force would cause the sand particles to move horizontally across the plate to fall off?

(or did you misread the problem?) :wink:

EDIT -- or did you mean "lose contact" with the plate, instead of "slip off"? I can use my Mentor powers to see from your location that there should be no language translation issues... :smile:
 
  • #9
berkeman said:
If the plate is moving vertically, what force would cause the sand particles to move horizontally across the plate to fall off?
I assure you that they would indeed start to drift off the plate. Bouncing around will lead to some rotational, and hence horizontal, motion.
 
  • #10
heroslayer99 said:
Relevant Equations: a = -w^2 x
What is value of ##x## when the acceleration has its largest magnitude?
 
  • #11
I think the problem wants us to focus on the vertical oscillation of the grains, together with the plate, and not in some sort of Brownian horizontal motion that the grains might do and slip off the plate.
 
  • #12
Delta2 said:
I think the problem wants us to focus on the vertical oscillation of the grains, together with the plate, and not in some sort of Brownian horizontal motion that the grains might do and slip off the plate.
Sure, but the title is not inappropriate.
 
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  • #13
haruspex said:
Sure, but the title is not inappropriate.
I think he misinterpreted the statement of the problem, and in the thread title he put something according to his misinterpretation. Probably the exact wording of the problem doesn't contain the words slip off. And it doesn't seem to , if we take the exact wording of the problem to be what is in the paragraph following the relevant equations statement.
 
  • #14
Apologies for any confusion I have caused, I figured out that the acceleration of the sand particles when they lose contact is g, and hence the plate's acceleration must be greater than g, when it is at its max vertical displacement
 
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FAQ: When Do Sand Particles Slip Off a Vibrating Plate?

What factors determine when sand particles slip off a vibrating plate?

The primary factors include the amplitude and frequency of the vibrations, the size and shape of the sand particles, the material and surface texture of the plate, and the angle of inclination of the plate. These variables collectively influence the frictional forces and the inertia of the particles.

How does the amplitude of vibration affect the slipping of sand particles?

Higher amplitude vibrations increase the energy imparted to the sand particles, making it more likely for them to overcome static friction and slip off the plate. Conversely, lower amplitude vibrations may not provide sufficient energy for the particles to move.

Why does the frequency of vibration matter for sand particles slipping off a plate?

The frequency of vibration affects the timing and the rate at which energy is transferred to the sand particles. Higher frequencies can lead to more rapid oscillations, possibly causing the particles to slip more easily, while lower frequencies might not provide enough momentum for the particles to overcome friction.

How do the size and shape of sand particles influence their slipping behavior?

Larger and irregularly shaped particles have more surface area in contact with the plate, which can increase friction and make slipping less likely. Smaller and more uniformly shaped particles typically slip more easily due to reduced frictional forces.

What role does the surface texture of the vibrating plate play in the slipping of sand particles?

The surface texture of the plate affects the friction between the plate and the sand particles. A rougher surface increases friction, making it harder for particles to slip off, while a smoother surface reduces friction, allowing particles to slip more readily.

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