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"Block A with a mass of 10kg rests on a 30 degrees incline. The coefficient of kinetic friction is 0.20. The attached spring is parallel to the incline and passes over a massless, frictionless pulley at the top. Block B, with a mass of 8kg, is attached to the dangling end of the string. The acceleration of B is (magnitude and direction)?"

Now, I know how to solve these problems. First you determine the direction of acceleration (80N dangling vs. (100sin30N + 0.20*Normal (for friction))). Once you know this, you simply make the system of equations:

Here, acceleration is up incline for Block A, down for Block B (and assuming g=10N/kg):

mAa = T-100sin30-(0.20*100cos30)

mBa= mBg- T

Then solve for a.

But, in going through countless posts about this online, I've seen people claim that they don't have to determine the direction of acceleration beforehand. They simply assume it (either up the incline or down the incline), then if the acceleration comes out negative at the end, they say it's simply the same magnitude, but in the opposite direction as assumed.

The problem with this is that if, say, the acceleration this problem were down the incline for Block A/up for Block B, then the equations would be (correct me if I'm wrong):

mAa = 100sin30-(0.20*100cos30)-T

mBa = T - mBg

And in calculating this, one realizes that the answer (including magnitude) is different.

Now, I know that all of this confusion can be averted by simply calculating yourself the direction of acceleration first (in fact, the direction is often stated in problems), then making the system of equations. However, as I've seen many people online claim that this isn't necessary, or always assuming that Block A accelerates up the incline, I'm a bit confused. In my numerous calculations (as an aside, I've been thinking so much about them that last night I even dreamed about this one stupid problem), if one randomly assumes a direction to the acceleration, and it comes out negative, then you've assumed incorrectly, and must change the assumed direction and recalculate (which will give you a different answer).

For example, in the problem above, the answer is .69 m/s2 downwards for Block B, but 2.6 m/s2 and -2.6m/s2 are other commonly-had responses.

Sorry for the long post. Any ideas?