What is the acceleration of the two blocks on a ramp?

[TheExibo]

1. What is the acceleration of the two blocks: https://lh4.googleusercontent.com/j...13Gpemd0x2xRIVU0a-BbWCzysCnjbUK_oI6vU8dFIf27q2. F(normal)=(9.8m/s^2)(m)3. For the left block, this is the equation I get: F(net)=2.72a=2.72*9.8-F(tension)

For the right block, i get this: F(net)=5.86a=f(tension)-(9.8*5.86sin27.4)

After substitution of the two, the acceleration I get is 0.00266m/s^2 downward, but then I tried again and got 16.9m/s^2. Not sure what's going on. Friction can be ignored. Anyone else get an answer? Thanks!

 

[Hijaz Aslam]

Draw a diagram including all the forces acting on both the blocks and also include the tension experienced by the string, and try hitting the problem again.

 

[haruspex]

After substitution of the two, the acceleration I get is 0.00266m/s^2 downward, but then I tried again and got 16.9m/s^2.

The equations are right but both answers are wrong.
The second would mean the hanging block is falling faster than if the string were cut!
Please post your working.

 

[Hijaz Aslam]

There will be two tension forces, corresponding to both the blocks, trying to oppose its motion. When we add up these tension forces, after cancelling the smaller tension, the net tension is found to be towards the hanging block, that is,away from the block on the ramp.

Now imagine the whole system (which contains both the blocks) to be moving under the influence of a single net force which is a consequence of the forces experienced by both the block individually (due to gravity).

So the acceleration can be found by manipulating the net tension (actually taking the negative of the net tension, because the net force experienced by the block is in the opposite direction but with the same magnitude as the tension) and using the formula $F=ma$ .

NOTE: The force experienced due to the gravity on the block which is on the ramp is only along the plane of the ramp.

I would appreciate solving the problem by assigning arbitrary variables for the mass of both the blocks and the angle of incline of the ramp. Break down the problem into a final equation containing all these variables and substitute the values.

Your former answer ($0.00266\frac{m}{s^2}$) seems correct (and is quite reasonable) but the decimal point is misplaced. Try again!