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airship has higher maximum speed at high altitudes, but also less thrust produce...

Apr 9, 2024

airship has higher maximum speed at high altitudes, but also less thrust produced from the engine why

Solution

Consider the air density at high altitudes: At higher altitudes, the air density is lower, which reduces the drag force on the airship. The drag force can be expressed as

F_{drag} = \frac{1}{2} C_d \rho v^2 A

where

C_d

is the drag coefficient,

\rho

is the air density,

v

is the velocity, and

A

is the cross-sectional area. Lower

\rho

means lower

F_{drag}

Relate thrust to engine performance: The engine's thrust depends on the air density because engines use air to burn fuel. At high altitudes, the lower air density means less oxygen for combustion, resulting in less thrust. The thrust

T

can be related to the mass flow rate

\dot{m}

and the velocity

v

of the exhaust gases as

T = \dot{m} v

. With less air intake,

\dot{m}

decreases, leading to lower thrust

Balance forces for maximum speed: The maximum speed is achieved when the thrust equals the drag force. At high altitudes, even though the thrust is lower, the reduced drag allows the airship to maintain a higher maximum speed

Answer

The airship has a higher maximum speed at high altitudes due to reduced air density, which lowers the drag force. However, the engine produces less thrust at these altitudes because of the reduced air density affecting combustion.

Key Concept

Dynamics deals with the study of forces and their effect on motion, including the relationship between drag force and air density, as well as how engine thrust is affected by air density.

Explanation

The airship's higher maximum speed at high altitudes is due to the reduced drag force resulting from lower air density. The engine produces less thrust because the lower air density provides less oxygen for fuel combustion.