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# Physics/Dynamics

Question
A rocket of mass 1000 kg exhausts gases at a rate of 4 kg/sec with a velocity 3000 m/s. The thrust developed on the rocket is-
(a)12000 N     (b)120 N   (c)800 N  (d)200 N

Hello again Ankit,

We're going to examine one second of time. Momentum is conserved throughout that second. At the beginning of that second, the rocket's initial velocity is Vi and the final velocity at the end of that second is Vf. In one second, 4 kg of exhaust gases are ejected out the nozzle at the rear at a velocity of -3000 m/s.
Initial momentum = final momentum
1000 kg*Vi = 996 kg*Vf + 4 kg*(-3000 m/s)

Impulse equals change in momentum. The rocket's change in momentum is final momentum - initial momentum. We can rearrange the above equation to get an expression for the change in momentum.
996 kg*Vf - 1000 kg*Vi = 4 kg*3000 m/s
Since impulse is also equal to force*time, we can say that
4 kg*3000 m/s = F*t = F*1 s

Therefore,
F = 4 kg*(3000 m/s) / 1 s = 12,000 kg.m/s^2 = 12,000 N

I hope this helps,
Steve

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Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University