Question

QUESTION 2 a) (5 p) Interpret the rocket equation dv(OM(t)=-udMO (EQ.1) within framework of the law of momentum conservation, written in a closed system, here M(t) is the rocket mass, at time t, whereas M(t) is by definition, dM(t)=M(t+dt)-M(t): -dM(t)=dM(t), is the mass of the gas thrown by the rocket through the infinitely small period of time dt; on the other hand, dv(t) is, still by definition, dv(t)=v(t+dt)-vít).i.e. the increase in the velocity of the rocket through the period of time dt: u is the relative velocity of the exhaust gas, with respect to the rocket b) (10 p) with [EQ.1] show that aM(t)=Ru [EQ.2). Here R is dM(t)/dt, i.e. the mass of the gas thrown out by the rocket through the unit period of time of concern; interpret this equation, and justify it, quickly. 2 c) (10 p) Suppose that. R is a constant. Then calculate R to start to lift a payload of 100 tonnes, against Earth's acceleration g; u -2.5 km/s, g=10m/s. Note, in order to produce force one has to spend energy and using it throw out momentum. Attach File Browse My Computer Browse Content Collection

Answer 1

I have solved your problem which is shown below:

Answer: Rocket propulsion is based on the principal of conservation of momentum assuming that there is no external force are acting on it. In rocket propulsion gases are produced by combustion of fuel in the combustion chamber like in this experiment liquid CO2 changes to gases CO2 are ejected out from the pipe. The force with which gas is ejected in the downward direction provides a reaction force on the rocket in the upward direction. Due to this force the cart moves forward.

The mass of the whole system doesn’t change but as the time passage the mass of the rocket decreases (excluding ejected gas). Some mass change into form of energy which leads to energy mass conversion.

The linear momentum of the ejected gas in the backward direction or in case of rocket in downward direction is equal and opposite to the linear momentum of this cart in forward direction or in case of rocket in upward direction respectively. If the rate of ejection of gases is constant through the experiment the rate of change of momentum will also be constant through the experiment.

However mass of the rocket keeps decreasing so as the acceleration and velocity of the rocket keeps on increasing and in this case the velocity of the cart increases as the ejection of gases increases.

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