Dynamics problem involving an inclined plane and Friction

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SUMMARY

The discussion revolves around a dynamics problem involving an inclined plane and friction, specifically addressing the forces acting on a block on an accelerating wedge. The key equations derived include f + Wx - Fy = 0 and μ(mgcosθ + macosθ) - masinθ = 0, which relate the frictional force, gravitational components, and the net force. The confusion arises regarding whether the acceleration pertains to the block or the inclined plane, with the consensus that the wedge's acceleration affects the normal force and thus the maximum frictional force. Participants emphasize the importance of clearly defining reference frames and axes to resolve the problem accurately.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of friction coefficients, specifically static friction (μs)
  • Familiarity with inclined plane dynamics
  • Ability to analyze forces in different reference frames
NEXT STEPS
  • Study the effects of acceleration on normal force in inclined planes
  • Learn about static and kinetic friction coefficients in detail
  • Explore the concept of reference frames in dynamics problems
  • Practice solving problems involving inclined planes with varying accelerations
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Students of physics, particularly those focusing on mechanics, educators teaching dynamics concepts, and anyone interested in solving complex problems involving inclined planes and friction.

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Homework Statement
An inclined plane shown in the figure has the acceleration intensity of a, to the right. Show that the block will slide on the plane if a > g tan ( θ - α ), where μs ( static friction) = tan θ is the static friction coefficient between the contact surfaces.
Hi, it's a simple(maybe) question.
Relevant Equations
F= ma
f= μN
So after trying to calculate the horizontal forces to solve it:

f + Wx(gravity force component of x) - Fy ( the Force that is supposedly giving the the acceleration) = 0

It got to me that the question said "plane has the acceleration" is that even possible? Unless the plane is another object like a ramp, but the plane itself? it's like considering the Earth's movement?!
I kept trying to prove continuing the horizontal forces. If a= g tan ( θ - α ) it means it won't move, so friction will be the μs= tan θ and the Fnet will be zero.

f + Wx - Fy =0

μN + mgcos θ - masinθ = 0

μ(mgcosθ + macosθ) - masinθ =0
And it just went on to a complex thing, I tried a couple of times, the results were close of g tan ( θ - α ), but I got to be doing something wrong.

Summarizing, could anyone tell me is the acceleration of the block or the plane? Is the block is sliding down or up (what??) and am I even close with that thought?
Figure given:
Sem título.jpg
 
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You are supposed to assume that something, doesn't matter what, is causing the wedge to accelerate to the right. This reduces the normal force on the block, and hence reduces the max frictional force.
Just consider the acceleration of the block and the forces on it.
Choose either an inertial frame or the reference frame of the wedge.
For axes, choose either horizontal and vertical or parallel and normal to the plane.
Whichever you choose, please specify your choices and define your variables. I am unclear as to what some mean in your post.
 

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