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July 19, 2017

Two Blocks on an Inclined Plane

Try this beautiful problem, useful for Physics Olympiad based on Two Blocks on an Inclined Plane.

The Problem:

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)

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