Rolling: Practice Problem & Solution
A solid cylinder of mass $3\text{ kg}$ is rolling on a horizontal surface with velocity $4\text{ m s}^{-1}$. It collides with a horizontal spring of force constant $200\text{ Nm}^{-1}$. The maximum compression produced in the spring will be: (2012 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Rolling. Understanding the underlying formula is key to arriving at the correct answer below:
By mechanical energy conservation, kinetic energy converts to spring potential energy: $\frac{3}{4}mv^2 = \frac{1}{2}kx^2$. Substituting the values gives $x = 0.6\text{ m}$.
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