Question #42353

A system consists of a heavy base of mass $M$ resting on the horizontal floor of an elevator. A motor rigidly attached to the base drives a massless rod of length $L = 0.5 \text{ m}$ with a point mass $m = 2 \text{ kg}$ at its free end. The rod rotates in a vertical plane with a constant angular velocity $\omega = 10 \text{ rad/s}$. The elevator accelerates upwards with a constant acceleration $a = 5 \text{ m/s}^2$. Assume $g = 10 \text{ m/s}^2$. What is the maximum internal torque $\tau_{\text{max}}$ the motor must provide to maintain the constant angular velocity, and what is the minimum mass $M_{\text{min}}$ of the base required so that it never loses contact with the elevator floor?