Correct Answer - Option 2 : 4600 N
The correct answer is 4600 N.
CONCEPT:
-
Rocket: A rocket works by expelling gases from one end at a very high velocity.
- The escaping gas has a very high speed and this with its mass translates to a very large momentum. due to the principle of conservation of momentum the body of the rocket is pushed forward.
- The propulsion of all rockets is explained by Newton's third law of motion.
- A rocket's acceleration depends on three major factors:
- Exhaust velocity
- Rate the exhaust is ejected
- Mass of the rocket
The amount of thrust (Ft) produced by the engine is given by:
Ft = v × \(\frac{dm}{dt}\)
Where v is the speed of exhaust gases with respect to rocket and \(\frac{dm}{dt}\) is fuel consumption rate or mass per unit time
The acceleration (a) of the rocket is given by:
a = Ft/M
Where M is the mass of the rocket and Ft is the thrust
CALCULATION:
Given that:
M = 850 kg, Fuel consumption rate = \(\frac{dm}{dt}\) = 2.3 kgs-1
Speed of the exhaust gases relative to the rocket engine (v) = 2000 ms-1
Thrust produced by the engine = Ft = v × \(\frac{dm}{dt}\) = 2000 × 2.3 = 4600 N