A B 7.5 m h 20 m C The roller coaster car having a mass of 210-kg has a speed of 3 m/s at A. Determine the minimal height h of A if the track is designed so that the car does not leave it at B.

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The image depicts a roller coaster diagram with the following details:

- The roller coaster car has a mass of 210 kg.
- The car is initially moving with a speed of 3 m/s at point A.
- The diagram features a loop with a radius of 7.5 m at point B.
- The height from the ground to point B is represented as 20 m.
- The height from point C to the top is labeled as \( h \).

**Objective:**
Determine the minimal height \( h \) of point A such that the car does not leave the track at point B.
Transcribed Image Text:The image depicts a roller coaster diagram with the following details: - The roller coaster car has a mass of 210 kg. - The car is initially moving with a speed of 3 m/s at point A. - The diagram features a loop with a radius of 7.5 m at point B. - The height from the ground to point B is represented as 20 m. - The height from point C to the top is labeled as \( h \). **Objective:** Determine the minimal height \( h \) of point A such that the car does not leave the track at point B.
**Problem Statement:**

A jet aircraft has a total mass of 21-Mg (megagrams) and a center of mass at point G. 

- The thrust provided by the engines at take-off is given as 2T = 9 kN and T' = 1.4 kN.

**Dimensions and Forces:**

- The distance from the thrust line (2T) to point G is 2.3 m.
- The distance from the nose wheel A to point G is 6 m.
- The total length from the tail (horizontal position of T') to the front is 9.2 m (2.5 m + 6 m + 0.7 m).
- The distance from point B to point A is 3 m.

**Task:**

Determine the reaction on the nose wheel at point A, neglecting friction.

**Diagram Explanation:**

The diagram displays an aircraft on a runway with forces and distances labeled. The force 2T acts horizontally from the aircraft’s side near the tail. The T' force acts slightly above this line. The aircraft is supported at two points, wheels A and B, with the distances provided between these points and the center of mass, G. The thrust and dimensions indicate that the problem is about analyzing moments around a point to find an unknown reaction force at point A.
Transcribed Image Text:**Problem Statement:** A jet aircraft has a total mass of 21-Mg (megagrams) and a center of mass at point G. - The thrust provided by the engines at take-off is given as 2T = 9 kN and T' = 1.4 kN. **Dimensions and Forces:** - The distance from the thrust line (2T) to point G is 2.3 m. - The distance from the nose wheel A to point G is 6 m. - The total length from the tail (horizontal position of T') to the front is 9.2 m (2.5 m + 6 m + 0.7 m). - The distance from point B to point A is 3 m. **Task:** Determine the reaction on the nose wheel at point A, neglecting friction. **Diagram Explanation:** The diagram displays an aircraft on a runway with forces and distances labeled. The force 2T acts horizontally from the aircraft’s side near the tail. The T' force acts slightly above this line. The aircraft is supported at two points, wheels A and B, with the distances provided between these points and the center of mass, G. The thrust and dimensions indicate that the problem is about analyzing moments around a point to find an unknown reaction force at point A.
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