**Problem 9.65** Consider the system of two blocks shown in the figure. The mass of block A is 10 kg, and the mass of block B is 80 kg. The blocks are connected by a string that passes over a pulley. The pulley is a uniform solid disk with a radius of 0.20 m and a moment of inertia of $4.0 \, \text{kg} \cdot \text{m}^2$. **Part A** If the pulley is rotating with an angular speed of 8.0 rad/s after the block has descended 12.0 m, what is the answer with the appropriate units? **Figure Description:** The diagram illustrates two blocks connected by a string over a pulley. Block A is on a horizontal surface, while Block B is hanging vertically. The pulley is pictured as a disk. Block A and Block B are labeled, and arrows indicate the direction of possible movement. --- (Copyright © 2020 Pearson Education Inc. All rights reserved.)

Problem 9.65 Consider the system of two blocks shown in the figure. The mass of block A is 10 kg, and the mass of block B is 80 kg. The blocks are connected by a string that passes over a pulley. The pulley is a uniform solid disk with a radius of 0.20 m and a moment of inertia of $4.0 \, \text{kg} \cdot \text{m}^2$. Part A If the pulley is rotating with an angular speed of 8.0 rad/s after the block has descended 12.0 m, what is the answer with the appropriate units? Figure Description: The diagram illustrates two blocks connected by a string over a pulley. Block A is on a horizontal surface, while Block B is hanging vertically. The pulley is pictured as a disk. Block A and Block B are labeled, and arrows indicate the direction of possible movement. --- (Copyright © 2020 Pearson Education Inc. All rights reserved.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Problem 9.65**

Consider the system of two blocks shown in the figure. The mass of block A is 10 kg, and the mass of block B is 80 kg. The blocks are connected by a string that passes over a pulley. The pulley is a uniform solid disk with a radius of 0.20 m and a moment of inertia of $4.0 \, \text{kg} \cdot \text{m}^2$.

**Part A**

If the pulley is rotating with an angular speed of 8.0 rad/s after the block has descended 12.0 m, what is the answer with the appropriate units?

**Figure Description:**

The diagram illustrates two blocks connected by a string over a pulley. Block A is on a horizontal surface, while Block B is hanging vertically. The pulley is pictured as a disk. Block A and Block B are labeled, and arrows indicate the direction of possible movement.

---

(Copyright © 2020 Pearson Education Inc. All rights reserved.)

Expert Solution

Step 1

Given,

Mass of B $\to m_{B} = 5 k g$

Pulley radius $\to r = 0.200 m$

Pulley M.I. $\to I = 1.40 k g m^{- 2}$

Angular speed $\to ω = 8 r a d / s$

Step 2

From equation of motion

$m_{b} g - T = m_{b} a m_{a} a = T \Rightarrow m_{b} g - m_{a} a = m_{b} a \Rightarrow m_{b} g = (m_{b} + m_{a}) a \Rightarrow a = \frac{m_{b} g}{(m_{b} + m_{a})} . . . . . (1)$