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Finding the acceleration of a pulley system including an inclined plane

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Homework Statement
A diagram of a pully with a rope, on one end of a rope hangs a mass (m) and on the other is another mass (twice the mass of the first - 2m) that sits on an inclined plane tilted 17 degrees to the horizontal. The mass on the inclined plane has a coefficient of kinetic friction of 0.21. They want you to calculate the acceleration of the system.
Homework Equations
Fnet = (m)(a)
This question showed up on my grade 12 physics test.

The problem I have with this question is that I did not know the direction that the system would accelerate in, so I just solved as though the mass on the inclined plane would accelerate the system. I expected that if it would accelerate the other way the acceleration would be negative. But it turns that the magnitude of the acceleration changes depending on which you assume the system will accelerate because the force of friction will be in a different direction depending on the acceleration.

My question is how do you tell which way the system will accelerate before solving the problem, because it did not accelerate towards the inclined plane, so I got the wrong magnitude.
 

haruspex

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Homework Statement: A diagram of a pully with a rope, on one end of a rope hangs a mass (m) and on the other is another mass (twice the mass of the first - 2m) that sits on an inclined plane tilted 17 degrees to the horizontal. The mass on the inclined plane has a coefficient of kinetic friction of 0.21. They want you to calculate the acceleration of the system.
Homework Equations: Fnet = (m)(a)

This question showed up on my grade 12 physics test.

The problem I have with this question is that I did not know the direction that the system would accelerate in, so I just solved as though the mass on the inclined plane would accelerate the system. I expected that if it would accelerate the other way the acceleration would be negative. But it turns that the magnitude of the acceleration changes depending on which you assume the system will accelerate because the force of friction will be in a different direction depending on the acceleration.

My question is how do you tell which way the system will accelerate before solving the problem, because it did not accelerate towards the inclined plane, so I got the wrong magnitude.
Write the equations entirely symbolically. These will be valid regardless because you can decide the sign of the frictional force later.
Try setting that to zero. Which sign results for the acceleration?
 

kuruman

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To say what @haruspex suggested somewhat differently: Find the direction of the acceleration pretending that there is no friction. If the block accelerates in a given direction under this assumption, it will not accelerate in the opposite direction when friction is "turned on". Therefore the force of friction will be in the opposite direction to the friction-free acceleration.
 

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