1. The layout of an elevator system is given below: The motor has inertia \( J_{m} \), the main pulley has radius \( R_{p} \) and inertia \( J_{p} \), the car has mass \( M_{c} \) and the counterweight has mass \( M_{r w} \). Note that the motor shaft and the rope are stiff. Neglect friction. a. Describe the motion of the system. In which direction does the car move when the motor turns counter-clockwise? In which direction does the counterweight move? b. Obtain relationships between the speeds of the motor \( \omega_{m} \), the pulley \( \omega_{p} \), the car \( M_{c} \), and the counter-weight \( M_{c w} \)
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When the motor turns counter-clockwise, it causes the main pulley to rotate in the same direction (counter-clockwise). As a result, the rope wrapped around the pulley is pulled upwards on the side attached to the car and downwards on the side attached to the Show more…
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One elevator arrangement includes the passenger car, a counter weight, and two large pulleys, as shown in FlGURE $11-50 .$ Each pulley has a radius of 1.2 $\mathrm{m}$ and a moment of inertia of 380 $\mathrm{kg} \cdot \mathrm{m}^{2} .$ The top pulley is driven by a motor. The elevator car plus passengers has a mass of $3100 \mathrm{kg},$ and the counterweight has a mass of 2700 $\mathrm{kg} .$ If the motor is to accelerate the elevator car upward at $1.8 \mathrm{m} / \mathrm{s}^{2},$ how much torque must it generate? Hint: The two pulleys move together, so you can model them as a single pulley with the sum of the moments of inertia.
A pulley system is attached to an elcvator as shown in figure. The elevator starts to move up with an accolcration $a$. Column-I (a) $\Lambda$ cceleration of $m_{1}$ in elevator frame (b) Accelcration of $m_{1}$ in ground frame (c) Distance covered of $m_{1}$ in clevator frame (d) Distance covered of $m_{1}$ in ground framc Column-II (p) $\frac{\frac{1}{2}\left(m_{2}-m_{1}\right) g t^{2}}{\left(m_{1}+m_{2}\right)}+\frac{1}{2} a t^{2}$ (q) $\frac{1}{2}\left[\frac{m_{2}-t h_{1}}{\left(m_{1}+m_{2}\right)}(g+a)\right] t^{2}$ (r) $\left(\frac{m_{2} \quad m_{1}}{m_{1}+m_{2}}\right) g+a$ (s) $\frac{\left(m_{2} \quad m_{1}\right)}{\left(m_{1} \mid m_{2}\right)}(g+a)$
Laws of Motion and Friction
Section D
(1I) An Atwood machine (Fig. 16) consists of two masses, $m_{\mathrm{A}}=7.0 \mathrm{kg}$ and $m_{\mathrm{B}}=8.2 \mathrm{kg}$ . connected by a cord that passes over a pulley free to rotate about a fixed axis. The pulley is a solid cylinder of radius $R_{0}=0.40 \mathrm{m}$ and mass 0.80 $\mathrm{kg}$ . (a) Determine the acceleration $a$ of each mass. (b) What percentage of error in $a$ would be made if the moment of inertia of the pulley were ignored? Ignore friction in the pulley bearings.
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