In the figure, two 9.20 kg blocks are connected by a massless string over a pulley of radius 1.20 cm and rotational inertia 7.40 × 10-4 kg-m². The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.600 rad in 147 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T₁, and (d) string tension T₂? Assume free-fall acceleration to be equal to 9.81 m/s². T₂ T₁

In the figure, two 9.20 kg blocks are connected by a massless string over a pulley of radius 1.20 cm and rotational inertia 7.40 × 10-4 kg-m². The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.600 rad in 147 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T₁, and (d) string tension T₂? Assume free-fall acceleration to be equal to 9.81 m/s². T₂ T₁

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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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

**Figure Description:**

In this problem, two blocks, each with a mass of 9.20 kg, are connected by a massless string that is placed over a pulley. The pulley has a radius of 1.20 cm and a rotational inertia of \(7.40 \times 10^{-4} \, \text{kg}\cdot\text{m}^2\).

Key aspects to consider:
- **Pulley Properties:** The string does not slip on the pulley, and the axis of the pulley is frictionless. It is not specified whether there is friction between the table and the sliding block.
- **Initial Conditions:** From rest, the pulley turns through 0.600 rad in 147 ms, indicating that the blocks' acceleration is constant throughout this period.

**Objectives:**

Calculate the following:
(a) The magnitude of the pulley's angular acceleration.
(b) The magnitude of either block's acceleration.
(c) The tension in the string on the side connecting to the block overhanging the pulley (\(T_1\)).
(d) The tension in the string on the side of the block on the table (\(T_2\)).

**Assumption:** The free-fall acceleration is assumed to be \(9.81 \, \text{m/s}^2\).

**Diagram Details:**

The diagram shows:
- A block on a table connected by a string over a pulley to a block hanging off the edge of the table.
- The tension in the string on the side of the block on the table is labeled \(T_1\).
- The tension in the string on the side of the hanging block is labeled \(T_2\).

This setup is used to illustrate problems involving rotational dynamics, tension in strings, and kinematics.

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