Fuel burn rate


by Simka
Tags: burn, fuel, rate
Simka
Simka is offline
#1
Oct29-06, 02:58 PM
P: 1
A rocket, mass m=4000kg, lifts off the ground vertically with acceleration of a=0.2g. The velocity of gass emmiting from it is u=1200m/s (with respect to the rocket). Find engine's reactive force and then fuel burn rate (mu).

This is what i managed to do:
rocket's speed at any moment t (with respect to the ground) is a*t
gass's speed at any moment t (with respect to the ground) is u-a*t


Mass of rocket at any time t is m-mu*t
Mass of fuel that is burned is mu*t
rocket's mass multiplied by it's speed and gass's mass multiplied by its speed are equal, so

(m-mu*t)*a*t=mu*t*(u-a*t)

and i get that m*a*t=mu*t*u

mu=(m*a)/u=6.53 kg/s

but... I was given 4 answers (5.9kg/s 9.8kg/s 39.2kg/s 19.8kg/s) and mine is wrong...

Any ideas anyone?
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
Andrew Mason
Andrew Mason is offline
#2
Oct30-06, 07:01 AM
Sci Advisor
HW Helper
P: 6,590
Quote Quote by Simka
A rocket, mass m=4000kg, lifts off the ground vertically with acceleration of a=0.2g. The velocity of gass emmiting from it is u=1200m/s (with respect to the rocket). Find engine's reactive force and then fuel burn rate (mu).

This is what i managed to do:
rocket's speed at any moment t (with respect to the ground) is a*t
gass's speed at any moment t (with respect to the ground) is u-a*t


Mass of rocket at any time t is m-mu*t
Mass of fuel that is burned is mu*t
rocket's mass multiplied by it's speed and gass's mass multiplied by its speed are equal...
You are forgetting about gravity. Use Newton's third law: The rate of change of momentum of the rocket + force of gravity = rate of change of momentum of the gas being expelled:

[tex]F_{rocket} = mg + ma = - F_{gas} = - vdm/dt[/tex]

AM


Register to reply

Related Discussions
stiochiometric air-to-fuel ratio for heavy fuel oil Engineering Systems & Design 2
Solid Propellant Burn Rate Sensitivity General Physics 8
[stars] Nuclear Fuel usage rate General Astronomy 26
Related Rate -finding the Rate of Change of an Angle Calculus & Beyond Homework 5
Measuring rate of reaction via rate of temperature change Chemistry 3