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Two blocks of masses $$4kg$$ and $$8kg$$ are connected by a string and slide down a $$30^\circ$$ inclined plane. The coefficient of kinetic friction between the $$4Kg$$ block and the plane is $$0.25$$; that between the $$8Kg$$ block and the plane is $$0.35$$.
(a) Calculate the acceleration of each block.
(b) Calculate the tension in the string.
Discussion:

Since the larger block has the larger coefficient of friction it will need to be pulled down the plane.

For the small block, $$4(sin30^\circ-(0.25)cos30^\circ)-T=4a$$
$$\Rightarrow 4a=11.11N-t$$
For larger block, $$15.44+T=8a$$
Now, adding the two relations $$26.55N=12a$$
$$a=2.21m/s^2$$
We can find the tension $$T=2.27N$$