A 10,000 kg airplane must reach a velocity of 60 m/s to take off. If the ho rizontal force exerted by the engine of the plane is 60 Kn and neglecting other horizontal forces What is the length of the runway needed? The maximum power transferred to the airplane
A 10,000 kg airplane must reach a velocity of 60 m/s to take off. If the ho rizontal force exerted by the engine of the plane is 60 Kn and neglecting other horizontal forces What is the length of the runway needed? The maximum power transferred to the airplane
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Airplane Takeoff Calculation Problem
**Problem Statement:**
A 10,000 kg airplane must reach a velocity of 60 m/s to take off. If the horizontal force exerted by the engine of the plane is 60 kN and neglecting other horizontal forces:
1. What is the length of the runway needed?
2. What is the maximum power transferred to the airplane?
**Details to Consider:**
- Mass of the airplane (m): 10,000 kg
- Required takeoff velocity (v): 60 m/s
- Force exerted by the engine (F): 60 kN (kilonewtons)
**Required Calculations:**
1. **Length of the runway needed (d):**
To find the length of the runway, we use the work-energy principle. The work done by the force in moving the airplane along the runway must equal the kinetic energy needed for takeoff.
\[ \text{Work} = \text{Force} \times \text{Distance} = F \cdot d \]
The kinetic energy (KE) the airplane needs is given by:
\[ \text{KE} = \frac{1}{2} m v^2 \]
Equating the work to the kinetic energy:
\[ F \cdot d = \frac{1}{2} m v^2 \]
2. **Maximum power transferred to the airplane (P):**
Power is the rate of doing work and can be calculated using the formula:
\[ P = F \cdot v \]
### Explanation of Terms:
- **Force (F):** The push or pull exerted by the engine.
- **Distance (d):** The length of the runway required to reach the takeoff speed.
- **Velocity (v):** The speed at which the airplane must be traveling at the end of the runway.
- **Power (P):** The engine's power output necessary to get the airplane to takeoff speed.
### Example Calculations:
1. **Runway Length Calculation:**
\[ F = 60 \times 10^3 \, \text{N} \]
\[ \text{KE} = \frac{1}{2} \times 10,000 \, \text{kg} \times (60 \, \text{m/s})^2 \]
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c07220d-ca17-4b4a-9c07-9176cc38cf32%2F1c235607-5471-4202-b880-90cd8b9c73b5%2Fe4enjd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Airplane Takeoff Calculation Problem
**Problem Statement:**
A 10,000 kg airplane must reach a velocity of 60 m/s to take off. If the horizontal force exerted by the engine of the plane is 60 kN and neglecting other horizontal forces:
1. What is the length of the runway needed?
2. What is the maximum power transferred to the airplane?
**Details to Consider:**
- Mass of the airplane (m): 10,000 kg
- Required takeoff velocity (v): 60 m/s
- Force exerted by the engine (F): 60 kN (kilonewtons)
**Required Calculations:**
1. **Length of the runway needed (d):**
To find the length of the runway, we use the work-energy principle. The work done by the force in moving the airplane along the runway must equal the kinetic energy needed for takeoff.
\[ \text{Work} = \text{Force} \times \text{Distance} = F \cdot d \]
The kinetic energy (KE) the airplane needs is given by:
\[ \text{KE} = \frac{1}{2} m v^2 \]
Equating the work to the kinetic energy:
\[ F \cdot d = \frac{1}{2} m v^2 \]
2. **Maximum power transferred to the airplane (P):**
Power is the rate of doing work and can be calculated using the formula:
\[ P = F \cdot v \]
### Explanation of Terms:
- **Force (F):** The push or pull exerted by the engine.
- **Distance (d):** The length of the runway required to reach the takeoff speed.
- **Velocity (v):** The speed at which the airplane must be traveling at the end of the runway.
- **Power (P):** The engine's power output necessary to get the airplane to takeoff speed.
### Example Calculations:
1. **Runway Length Calculation:**
\[ F = 60 \times 10^3 \, \text{N} \]
\[ \text{KE} = \frac{1}{2} \times 10,000 \, \text{kg} \times (60 \, \text{m/s})^2 \]
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning