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a problem regarding momentum(from an entrance exam to Uni in Japan)(editted)
In the space ,A rocket with mass M moving with constant velocity of V with no external force acting on it.
1) after sometime, the rocket release the fuel mass M/2 in an instant to increase the velocity .the velocity of the fuel relative to the rocket = V
1.1) using the law of conservation of momentum find the velocity of the rocket after the increase of the velocity
1.2) after the increase of the velocity , what is the sum of the kinetic energy of the fuel gas and the rocket?
2) (2nd situation . not the time after question 1) after sometimes the rocket release the fuel gas of mass M/4 to increase velocity .after that the rocket realease another fuel gas of mass M/4 to increase velocity. both of the velocity of the fuel relative to the rocket are V.
2.3) after increases of the velocity 2 times what is the velocity of the rocket
2.4)the first time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.5)the second time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.6) after the increase of the velocity 2 times, what is the sum of the kinetic energy of the fuel gas and the rocket?
3) (3rd situation ) After sometimes the rocket release aa amount of fuel to increase it`s velocity.after that, it release the same amount of fuel as the first time to increase it`s velocity again.both of the velocity of the fuel relative to the rocket are V.
3.7) after the second time of the release of the fuel,the velocity of rocket kV ,find the value of k (k is more than 1)
3.8) from question 3.7, if the maximum amount of the fuel released is equal to M ,what is the maximum value of k
this is what i thought of using this formulae
mv = − dm (−u +v + dv ) + (m + dm )(v + dv )
and i got the answer for 1.1 = 3/2M
is it correct?
for 1.2) should sum of the kinetic energy equal to 2(1/2)(M/2)(3V/2)^2 ?
2.3) using the same formulae as 1.1 i got 5/4V and 1/5/6V
2.4,2.5,2.6,2.7 dun understand the concept= =
2.8) is it 0? because the mass of the rocket would also be reduced to 0?
sorry for not adding my own attempt at first I am new to this forum and hadnt yet to read the rule then
please ,your help will be greatly appreciated...
.....
this is the question in the entrance exam to a University in Japan...so if the question seem confusing please do ask me...i might have mistranslated somethings...thank you very much for helps
Homework Statement
Homework Equations
In the space ,A rocket with mass M moving with constant velocity of V with no external force acting on it.
1) after sometime, the rocket release the fuel mass M/2 in an instant to increase the velocity .the velocity of the fuel relative to the rocket = V
1.1) using the law of conservation of momentum find the velocity of the rocket after the increase of the velocity
1.2) after the increase of the velocity , what is the sum of the kinetic energy of the fuel gas and the rocket?
2) (2nd situation . not the time after question 1) after sometimes the rocket release the fuel gas of mass M/4 to increase velocity .after that the rocket realease another fuel gas of mass M/4 to increase velocity. both of the velocity of the fuel relative to the rocket are V.
2.3) after increases of the velocity 2 times what is the velocity of the rocket
2.4)the first time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.5)the second time of release of fuel gas to increase the velocity of the rocket,what is the velocity of the fuel relative to the space
2.6) after the increase of the velocity 2 times, what is the sum of the kinetic energy of the fuel gas and the rocket?
3) (3rd situation ) After sometimes the rocket release aa amount of fuel to increase it`s velocity.after that, it release the same amount of fuel as the first time to increase it`s velocity again.both of the velocity of the fuel relative to the rocket are V.
3.7) after the second time of the release of the fuel,the velocity of rocket kV ,find the value of k (k is more than 1)
3.8) from question 3.7, if the maximum amount of the fuel released is equal to M ,what is the maximum value of k
The Attempt at a Solution
this is what i thought of using this formulae
mv = − dm (−u +v + dv ) + (m + dm )(v + dv )
and i got the answer for 1.1 = 3/2M
is it correct?
for 1.2) should sum of the kinetic energy equal to 2(1/2)(M/2)(3V/2)^2 ?
2.3) using the same formulae as 1.1 i got 5/4V and 1/5/6V
2.4,2.5,2.6,2.7 dun understand the concept= =
2.8) is it 0? because the mass of the rocket would also be reduced to 0?
sorry for not adding my own attempt at first I am new to this forum and hadnt yet to read the rule then
please ,your help will be greatly appreciated...
.....
this is the question in the entrance exam to a University in Japan...so if the question seem confusing please do ask me...i might have mistranslated somethings...thank you very much for helps
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