# PS.7.1 Worked Example - Collision and Sliding on a Rough Surface

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Block 1 of mass $$\displaystyle 3m$$ is sliding along a frictionless horizontal table to the right with speed $$\displaystyle v_0$$. Block 1 collides with block 2 of mass $$\displaystyle m$$ that is moving to the left with speed $$\displaystyle v_0$$. After the collision, the two blocks stick together and the blocks enter a rough surface at $$\displaystyle x=0$$ with a coefficient of kinetic friction that increases with distance as $$\displaystyle \mu (x)=b x^2$$ for $$\displaystyle 0\leq x\leq d$$, where $$\displaystyle b$$ is a positive constant. The blocks come to rest at $$\displaystyle x=d$$. The downward gravitational acceleration has magnitude $$\displaystyle g$$. Determine an expression for the initial speed $$\displaystyle v_0$$ of the blocks.

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