**Problem Description:**A 10 kg crate is pushed against a spring at point A and released from rest. Upon release, it moves 2 m along a rough horizontal section (d), then enters a smooth loop with a 100 cm radius vertical loop. On the rough surface, the coefficient of friction $ \mu_k $ is 0.2, and the spring is initially compressed by 60 cm.**Questions:**a. What is the velocity of the crate at the top of the loop, D?b. What is the minimum spring constant, $ k $, for which the crate remains in contact with the loop?**Diagram Explanation:**The diagram presents a surface with a rough section labeled “rough” and a spring labeled with a spring constant $ k $. Initially, the crate is held at point A against the compressed spring. The spring is aligned horizontally. The rough section extends from A over a distance $ d $ and is followed by a smooth circular loop with a designated radius of 100 cm leading up to point D at the top.Key features include:- The spring on the left, indicating the starting point and the spring compression.- The rough horizontal path from A where friction is present.- A large circular loop where the crate will travel, characterized by a smooth surface.- Various labeled points (A, B, C, D, E) throughout the circuit.This setup is designed to explore principles of energy conservation, friction, and circular motion.

DA 10kg crate is pushed against the spring at A and released from rest. Upon release, On the rough surface, p is 0.25, and the spring is initially compressed 60 cm. moves 2 m along a rough horizontal section (d), then into a smooth p 100 cm radius vertical loop What is the velocity of the crate at the top of the loop, D? What is the minimum spring constant, le, for which the crate remains in contact with the loop A b. C D smooth B d الله E rough A

DA 10kg crate is pushed against the spring at A and released from rest. Upon release, On the rough surface, p is 0.25, and the spring is initially compressed 60 cm. moves 2 m along a rough horizontal section (d), then into a smooth p 100 cm radius vertical loop What is the velocity of the crate at the top of the loop, D? What is the minimum spring constant, le, for which the crate remains in contact with the loop A b. C D smooth B d الله E rough A

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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Question

**Problem Description:**

A 10 kg crate is pushed against a spring at point A and released from rest. Upon release, it moves 2 m along a rough horizontal section (d), then enters a smooth loop with a 100 cm radius vertical loop. On the rough surface, the coefficient of friction $ \mu_k $ is 0.2, and the spring is initially compressed by 60 cm.

**Questions:**

a. What is the velocity of the crate at the top of the loop, D?

b. What is the minimum spring constant, $ k $, for which the crate remains in contact with the loop?

**Diagram Explanation:**

The diagram presents a surface with a rough section labeled “rough” and a spring labeled with a spring constant $ k $. Initially, the crate is held at point A against the compressed spring. The spring is aligned horizontally. The rough section extends from A over a distance $ d $ and is followed by a smooth circular loop with a designated radius of 100 cm leading up to point D at the top.

Key features include:
- The spring on the left, indicating the starting point and the spring compression.
- The rough horizontal path from A where friction is present.
- A large circular loop where the crate will travel, characterized by a smooth surface.
- Various labeled points (A, B, C, D, E) throughout the circuit.

This setup is designed to explore principles of energy conservation, friction, and circular motion.

Expert Solution

Step 1

Given data:

$m = 10 k g d = 2 m ρ = 100 c m μ_{s} = 0.25 x = 60 c m$

Need to determine the velocity of the crate at D and minimum value of spring constant.

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Solved in 2 steps

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