### Mechanics Problem: Acceleration, Tension, and Speed Calculation#### Problem StatementTwo blocks are connected by a massless rope as shown below. The mass of the block on the table (\(m_1\)) is 4.5 kg and the hanging mass (\(m_2\)) is 1.5 kg. The table and the pulley are frictionless.![Diagram of two blocks connected by a rope over a pulley. m1 is on the table, m2 is hanging. a1 and a2 are indicated as the accelerations of m1 and m2 respectively.]The diagram shows:- \(m_1\) (block on the table) connected to the rope, which passes over a pulley and connects to \(m_2\) (hanging block).- \(a_1\) indicates the acceleration of \(m_1\) on the table.- \(a_2\) indicates the acceleration of \(m_2\) downward.#### Questions(a) **Find the acceleration (in m/s²) of the system. (Enter the magnitude.)** Given/Calculated Answer: **1.635 m/s²** (b) **Find the tension (in N) in the rope.** Given/Calculated Answer: **7.36 N**(c) **Find the speed (in m/s) with which the hanging mass hits the floor if it starts from rest and is initially located 1.8 m from the floor.** Given/Calculated Answer: **2.43 m/s**#### Explanation of Diagram- The diagram illustrates the setup of two masses (\(m_1\) on a table, and \(m_2\) hanging) connected by a rope over a pulley.- The direction of acceleration (\(a_1\)) for the block on the table and (\(a_2\)) for the hanging block is shown by arrows.#### Mathematical Approach and Formulae (For Educational Purpose)1. **Finding Acceleration (\(a\))**: \[ a = \frac{m_2 \cdot g}{m_1 + m_2} \] Where: - \(a\) is the acceleration. - \(m_1\) and \(m_2\) are the masses. - \(g\) is the acceleration due to gravity (9.8 m

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Two blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.5 kg and the hanging mass is 1.5 kg. The table and the pulley are frictionless. m, m2 (a) Find the acceleration (in m/s?) of the system. (Enter the magnitude.) 1.635 |× m/s² (b) Find the tension (in N) in the rope. 7.36 (c) Find the speed (in m/s) with which the hanging mass hits the floor if it starts from rest and is initially located 1.8 m from the floor. 2.43 x m/s

Two blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.5 kg and the hanging mass is 1.5 kg. The table and the pulley are frictionless. m, m2 (a) Find the acceleration (in m/s?) of the system. (Enter the magnitude.) 1.635 |× m/s² (b) Find the tension (in N) in the rope. 7.36 (c) Find the speed (in m/s) with which the hanging mass hits the floor if it starts from rest and is initially located 1.8 m from the floor. 2.43 x m/s

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

### Mechanics Problem: Acceleration, Tension, and Speed Calculation

#### Problem Statement
Two blocks are connected by a massless rope as shown below. The mass of the block on the table (\(m_1\)) is 4.5 kg and the hanging mass (\(m_2\)) is 1.5 kg. The table and the pulley are frictionless.

![Diagram of two blocks connected by a rope over a pulley. m1 is on the table, m2 is hanging. a1 and a2 are indicated as the accelerations of m1 and m2 respectively.]

The diagram shows:
- \(m_1\) (block on the table) connected to the rope, which passes over a pulley and connects to \(m_2\) (hanging block).
- \(a_1\) indicates the acceleration of \(m_1\) on the table.
- \(a_2\) indicates the acceleration of \(m_2\) downward.

#### Questions
(a) **Find the acceleration (in m/s²) of the system. (Enter the magnitude.)**

Given/Calculated Answer: **1.635 m/s²**

(b) **Find the tension (in N) in the rope.**

Given/Calculated Answer: **7.36 N**

(c) **Find the speed (in m/s) with which the hanging mass hits the floor if it starts from rest and is initially located 1.8 m from the floor.**

Given/Calculated Answer: **2.43 m/s**

#### Explanation of Diagram
- The diagram illustrates the setup of two masses (\(m_1\) on a table, and \(m_2\) hanging) connected by a rope over a pulley.
- The direction of acceleration (\(a_1\)) for the block on the table and (\(a_2\)) for the hanging block is shown by arrows.

#### Mathematical Approach and Formulae (For Educational Purpose)
1. **Finding Acceleration (\(a\))**:
\[
a = \frac{m_2 \cdot g}{m_1 + m_2}
\]
Where:
- \(a\) is the acceleration.
- \(m_1\) and \(m_2\) are the masses.
- \(g\) is the acceleration due to gravity (9.8 m

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