**Problem**A conveyor belt at the postal service deposits packages down a chute of radius \( \rho \) to be sorted. At the instant shown, package \( B \) is resting at the end of the chute while package \( A \) has just entered the chute at a height \( h \) with velocity \( v_A \). After going down the chute package \( A \) and \( B \) become stuck together. **Part A:** What is the velocity of the packages after they impact?**Part B:** Using the angular momentum form of Newton’s 2nd Law, determine how fast the velocity is increasing, \( \dot{v} \), at the instant when \( \theta = 70 \) degrees. (Hint: To compute the angular momentum, use a polar frame with \( \mathbf{v}_{A/O} = v \mathbf{e}_\theta \).)**Values:** \( g = 9.81 \, \text{m/s}^2, \, m_A = 5 \, \text{kg}, \, m_B = 8 \, \text{kg}, \, v_A = 5 \, \text{m/s}, \, h = \rho = 1.5 \, \text{m} \)**Diagram Explanation:**The diagram illustrates a smooth chute under a conveyor belt. Package \( A \) is depicted at the top of the chute entering with velocity \( v_A \), while package \( B \) is shown at rest at the end of the chute. An arrow indicates the velocity vector of package \( A \). The chute is curved with a radius \( \rho \), and angle \( \theta \) is marked at the point where package \( A \) is located. These elements are used to visualize the problem and the physical interactions as the packages move and eventually collide.

Answered: Image /qna-images/answer/088d5620-a164-4f3b-a193-30e18fa9a1d9.jpg

A conveyer belt at the postal service deposits packages down a chute of radius p to be sorted. At the instant shown, package B is resting at the end of the chute while package A has just entered the chute at a height h with velocity VA. After going down the chute package A and B become stuck together. Part A: What is the velocity of the packages after they impact? Part B: Using the angular momentum form of Newton's 2nd Law determine how fast the velocity is increasing, v, at the instant when 0 = 70 deg. (Hint: To compute the angular momentum, use a polar frame with VA/O= vêe.) Values: g= 9.81 m/s², mA = 5 kg, mB = 8 kg, VA = 5 m/s, h = p = 1.5 m CONVEYER TIC h SMOOTH CHUTE VA 9 1 at rest •B

A conveyer belt at the postal service deposits packages down a chute of radius p to be sorted. At the instant shown, package B is resting at the end of the chute while package A has just entered the chute at a height h with velocity VA. After going down the chute package A and B become stuck together. Part A: What is the velocity of the packages after they impact? Part B: Using the angular momentum form of Newton's 2nd Law determine how fast the velocity is increasing, v, at the instant when 0 = 70 deg. (Hint: To compute the angular momentum, use a polar frame with VA/O= vêe.) Values: g= 9.81 m/s², mA = 5 kg, mB = 8 kg, VA = 5 m/s, h = p = 1.5 m CONVEYER TIC h SMOOTH CHUTE VA 9 1 at rest •B

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

**Problem**

A conveyor belt at the postal service deposits packages down a chute of radius \( \rho \) to be sorted. At the instant shown, package \( B \) is resting at the end of the chute while package \( A \) has just entered the chute at a height \( h \) with velocity \( v_A \). After going down the chute package \( A \) and \( B \) become stuck together.

**Part A:** What is the velocity of the packages after they impact?

**Part B:** Using the angular momentum form of Newton’s 2nd Law, determine how fast the velocity is increasing, \( \dot{v} \), at the instant when \( \theta = 70 \) degrees. (Hint: To compute the angular momentum, use a polar frame with \( \mathbf{v}_{A/O} = v \mathbf{e}_\theta \).)

**Values:**
\( g = 9.81 \, \text{m/s}^2, \, m_A = 5 \, \text{kg}, \, m_B = 8 \, \text{kg}, \, v_A = 5 \, \text{m/s}, \, h = \rho = 1.5 \, \text{m} \)

**Diagram Explanation:**

The diagram illustrates a smooth chute under a conveyor belt. Package \( A \) is depicted at the top of the chute entering with velocity \( v_A \), while package \( B \) is shown at rest at the end of the chute. An arrow indicates the velocity vector of package \( A \). The chute is curved with a radius \( \rho \), and angle \( \theta \) is marked at the point where package \( A \) is located. These elements are used to visualize the problem and the physical interactions as the packages move and eventually collide.

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