What are the accelerations of A on an incline with different scenarios?

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SUMMARY

The discussion focuses on calculating the acceleration of body A on an incline under three scenarios: at rest, moving up, and moving down. Given the weights of body A (110 N) and body B (37 N), along with friction coefficients (μs = 0.56, μk = 0.25) and an incline angle of θ = 40°, the participant successfully determined that the acceleration of A at rest is 0 m/s². However, they struggled with the calculations for A moving up and down the incline, indicating confusion regarding the application of forces and friction in these scenarios.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of static and kinetic friction coefficients
  • Basic trigonometry for resolving forces on an incline
  • Familiarity with free body diagrams
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  • Calculate the net force acting on body A using free body diagrams for each scenario.
  • Learn how to apply the equations of motion for objects on inclined planes.
  • Explore the differences between static and kinetic friction in practical applications.
  • Review examples of similar physics problems involving multiple forces and inclines.
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Students studying physics, particularly those focusing on mechanics and inclined planes, as well as educators looking for examples of problem-solving in dynamics.

Matt12345
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Homework Statement


Body A weighs 110 N, and body B weighs 37 N. The coefficients of friction between A and the incline are μs = 0.56 and μk = 0.25. Angle θ is 40°. Let the positive direction of an x-axis be up the incline.

06_38.gif


(a). Find the acceleration of A if A is initially at rest.
(... m/s^2) i

(b). Find the acceleration of A if A is moving up the incline.
(...m/s^2) i

(c). Find the acceleration of A if A is moving down the incline.
(...m/s^2) i


Homework Equations


F=ma


The Attempt at a Solution


So I am not really sure how to solve this problem at all. I have tried a few ways, none have come up with reasonable or correct answers.

I tried using...

FT = mA * g * sin(theta) - fk

where fk = mewk * FN
and setting FN = g * a

I then solved for a and came out with 134 but that was wrong and didn't make sense.

I have no idea what to do next. Can anyone help me out? That would be awsome.
 

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So I got part (a). which is 0. I don't know why I didn't try that before. I feel stupid. But parts (b). and (c). I am still not sure about.
 
Matt12345 said:
So I got part (a). which is 0. I don't know why I didn't try that before. I feel stupid. But parts (b). and (c). I am still not sure about.
This problem makes no sense. Either the block A is at rest, or it moves up the plane, or moves down the plane. It can't do all three!
 

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