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Chapter 9: Q107P (page 255)

A 6100 kgrocket is set for vertical firing from the ground. If the exhaust speed is 1200 m/s, how much gas must be ejected each second if the thrust (a) is to equal the magnitude of the gravitational force on the rocket and (b) is to give the rocket an initial upward acceleration of 21m/s2?

Short Answer

Expert verified

a) Therate of consumptionis 50 kg/s

b) The rate of consumption with the additional effect due to gravity is1.6脳102kg/s

Step by step solution

01

Listing the given quantities

The value ofexhaust speed is 1200 m/s

Mass of the rocket is 6100 kg

Initial upward acceleration of21m/s2

02

Understanding the concept of launching the rocket

To successfully launched a rocket from the ground, fuel is consumed at a rate that results in a thrust big enough to overcome the gravitational force

Formula:

The thrust is given by T =Rvrel

Where, R is the rate of the fuel consumption

is the speed of the exhaust gas relative to the rocket

03

 Calculation of the rate of consumption

(a)

T=RvrelR=TVrel=MgVrel=(6100kg)(9.8m/s2)1200m/s=49.8kg/s鈮�50kg/s

The rate of consumption is 50 kg/s

04

Calculation of the rate of consumption with the additional effect due to gravity

(b)

(Rvrel-Mg=Ma)R=M(g+a)Vrel=(6100kg)(9.8m/s2+21m/s2)1200m/s=56.6kg/s鈮�1.6脳102kg/s

The rate of consumption with the additional effect due to gravity is1.6脳102kg/s

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