### 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:** \[ F = 60 \times 10^3 \, \text{N} \] \[ \text{KE} = \frac{1}{2} \times 10,000 \, \text{kg} \times (60 \, \text{m/s})^2 \] \[

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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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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