Identical cylinders of weight and radiusare pushed by a series of moving arms. The coefficient of friction between all surfaces is . Denoting by the magnitude of the acceleration of the arms, derive an expression for (a) the maximum allowable value of if each cylinder is to roll without sliding, (b) the minimum allowable value of if each cylinder is to move to the right without rotating. Part (c) Let, and between all surfaces. Determine the horizontal component of the force exerted on each cylinder when the acceleration is (1) to the right and (2) 10 to the right. Benchmark solutions for part (c) are given as (1) 1.456 lb to the right, (2) 2.66 lb to the right. For part (c), your solution should be coded into MATLAB so it can easily be run for alternate cases. Part (d) Plot the horizontal component of the force exerted on each cylinder for different ranges of acceleration, which illustrate the various case of rolling and sliding obtained in parts (a) and (b).

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.