Ch 09: Work and Kinetic Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 09: Work and Kinetic Energy

Problem 50b

Chapter 9, Problem 50b

A 737-800 jet airliner has twin engines, each with 105 kN thrust. A 78,000 kg jet reaches a takeoff speed of 70 m/s in a distance of 1100 m. What is the increase in thermal energy due to rolling friction and air drag?

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Identify the work-energy principle: The work done by all forces acting on the jet is equal to the change in its kinetic energy plus the energy lost to friction and air drag. The equation is: \( W_{net} = \Delta KE + E_{thermal} \).

Calculate the change in kinetic energy (\( \Delta KE \)) of the jet: \( \Delta KE = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 \), where \( m \) is the mass of the jet (78,000 kg), \( v \) is the final velocity (70 m/s), and \( u \) is the initial velocity (0 m/s).

Determine the total work done by the engines: \( W_{engines} = F_{thrust} \cdot d \), where \( F_{thrust} \) is the total thrust from both engines (\( 2 \cdot 105 \ \text{kN} = 210 \ \text{kN} \)) and \( d \) is the distance over which the force is applied (1100 m).

Relate the work-energy principle to find the thermal energy: Rearrange the equation \( W_{net} = \Delta KE + E_{thermal} \) to solve for \( E_{thermal} \): \( E_{thermal} = W_{engines} - \Delta KE \).

Substitute the values for \( W_{engines} \) and \( \Delta KE \) into the equation for \( E_{thermal} \) to calculate the increase in thermal energy due to rolling friction and air drag.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thrust and Drag Forces

Thrust is the force produced by the engines to propel the aircraft forward, while drag is the resistance force acting opposite to the direction of motion, caused by air friction. In this scenario, the total thrust from the engines must overcome both the drag and rolling friction to achieve the required takeoff speed.

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the thrust must account for the energy lost to friction and drag, as well as the energy required to accelerate the jet to its takeoff speed.

Thermal Energy and Energy Losses

Thermal energy refers to the energy generated as heat due to friction and drag forces acting on the aircraft. As the jet accelerates, some of the mechanical energy is converted into thermal energy, which can be quantified to determine the increase in thermal energy due to these resistive forces during the takeoff process.

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