Two Blocks on an Inclined Plane

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.

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 \(T=2.27N\)

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