Uncategorized: Practice Problem & Solution
A block of mass (10text{ kg}) is in contact against the inner wall of a hollow cylindrical drum of radius (1text{ m}). The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : ((g = 10text{ m/s}^2)) (2019)
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
The normal force (N) provides centripetal force, so (N = momega^2 R). For the block not to fall, friction (f = mu N) must balance its weight (mg). Thus, (mu momega^2 R = mg). This simplifies to (omega^2 = frac{g}{mu R}). Substituting values: (omega = sqrt{frac{10}{0.1 times 1}} = sqrt{100} = 10text{ rad/s}).
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