   Chapter 6, Problem 57P

Chapter
Section
Textbook Problem

A typical person begins to lose consciousness if subjected to accelerations greater than about 5g (49.0 m/s2) for more than a few seconds. Suppose a 3.00 × 104-kg manned spaceship’s engine has an exhaust speed of 2.50 × 103 m/s. What maximum burn rate |ΔM/Δt| could the engine reach before the ship’s acceleration exceeded 5g and its human occupants began to lose consciousness?

To determine
The burn rate of a fuel in an engine.

Explanation

Given Info: Mass of an engine is m=3.00×104kg and acceleration of ship is a=49.0 m/s2 , exhaust speed of an engine is ve=2.50×103m/s and instantaneous thrust of a rocket engine is T=1.47×106N .

Explanation:

Take the net force as instantaneous thrust.

The expression for net force by Newton’s Second law is,

Fnet=ma

• Fnet is the net force of an engine.
• m is the mass of an engine.
• a is the acceleration of ship.

Rewrite the above equation for thrust.

T=ma (1)

• T is the instantaneous thrust of a rocket engine.

Substitute 3.00×104kg for m and 49.0m/s2 for a in equation (1).

T=(3.00×104kg )(49.0m/s2)=147×104N=1.47×106N

The expression for thrust is,

T=|veΔmΔt|

• T is the instantaneous thrust of a rocket engine

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