MC question (2 Viewers)

[khfreakau]

Hey guys, this is a question from my half yearly where I disagree with the given answer, was wondering what you guys thought.

Ultimately, the factor limiting the maximum speed of a rocket is:
a) the amount of fuel it carries
b) the speed of ejection of the gases
c) the mass of the rocket
d) the length of the rocket

 

[x_cp3]

Quite ambiguous. What did you put?

 

[khfreakau]

I put B, apparently the answer's A.

 

[x_cp3]

I was thinking it was either A or B too. What did the majority put in ur grade?

 

[ohexploitable]

Quite ambiguous. What did you put?

Why? The answer is obviously A to me...

 

[khfreakau]

Why? The answer is obviously A to me...

Can you explain why? I don't understand how the amount of fuel carried limits the MAXIMUM speed of the rocket....

 

[ohexploitable]

I was thinking it was either A or B too. What did the majority put in ur grade?

Not B. If I was in a rocket where the propulsion system is me blowing air out of a straw, I would eventually get close to the speed of light if a) I had enough air (fuel supply) and b) if I could live that long lol.

 

[ohexploitable]

Can you explain why? I don't understand how the amount of fuel carried limits the MAXIMUM speed of the rocket....

More fuel = more total thrust throughout the whole journey.

F=ma, m is constant (lets stick with non-relativistic speeds lol) so,



but,



So, more fuel = more thrust = more force = more acceleration = more speed.

 

[khfreakau]

More fuel = more total thrust throughout the whole journey.

So, more fuel = more thrust = more force = more acceleration = more speed.

The underlying problem I see in that argument is the assumption that the thrust is sufficient to keep the rocket at a constant acceleration. As time goes on, if the amount of fuel is infinite, then you should agree that as t->infinity, then v->c. However we KNOW this is not the case due to mass dilation and energy-mass equivalence.

In other words, if you have a certain amount of fuel with a certain thrust, there is only a certain speed that you can achieve. If you have that same amount of fuel with a GREATER thrust, then the maximum speed that can be achieved is greater.

 

[ohexploitable]

The underlying problem I see in that argument is the assumption that the thrust is sufficient to keep the rocket at a constant acceleration. As time goes on, if the amount of fuel is infinite, then you should agree that as t->infinity, then v->c. However we KNOW this is not the case due to mass dilation and energy-mass equivalence.

In other words, if you have a certain amount of fuel with a certain thrust, there is only a certain speed that you can achieve. If you have that same amount of fuel with a GREATER thrust, then the maximum speed that can be achieved is greater.

lol...

The underlying problem with that statement is that it completely violates the principle of conservation of energy. Energy cannot be created or destroyed etc.

Lets say you have 1kg of fuel, when that fuel is consumed it will release a certain amount of energy, this amount is constant and independent of time. That 1kg of fuel will release the same amount of energy regardless of whether it's consumed in a few nanoseconds or over the span of a hundred years.

 

[ohexploitable]

The amount of thrust changes how quickly you can reach the maximum speed, not the actual maximum speed.

 

[MikeK]

In other words, if you have a certain amount of fuel with a certain thrust, there is only a certain speed that you can achieve. If you have that same amount of fuel with a GREATER thrust, then the maximum speed that can be achieved is greater.

If there is no drag or any other force acting upon the rocket other than the engine, then the final kinetic energy will be equal to the total amount of chemical energy released by the fuel.

Time is irrelevant.

 

[ohexploitable]

The underlying problem I see in that argument is the assumption that the thrust is sufficient to keep the rocket at a constant acceleration.

Constant acceleration is not required.

As time goes on, if the amount of fuel is infinite, then you should agree that as t->infinity, then v->c. However we KNOW this is not the case due to mass dilation and energy-mass equivalence.

There is nothing wrong with this statement.

 

[khfreakau]

lol...

The underlying problem with that statement is that it completely violates the principle of conservation of energy. Energy cannot be created or destroyed etc.

Lets say you have 1kg of fuel, when that fuel is consumed it will release a certain amount of energy, this amount is constant and independent of time. That 1kg of fuel will release the same amount of energy regardless of whether it's consumed in a few nanoseconds or over the span of a hundred years.

You are assuming 100% efficiency which is never the case. I'm simply stating that if the efficiency was improved such that the thrust was greater and less of the fuel was wasted, then the maximum speed would be greater.

The amount of thrust changes how quickly you can reach the maximum speed, not the actual maximum speed.

Disagree. A greater thrust is a greater force.

If

then agreeably a greater thrust would result in a greater acceleration.
Your statement that it would change how quickly you can reach the maximum speed is probably correct, I don't want to have to calculate what force is needed to accelerate a mass to a certain speed, but the problem is, a LESSER THRUST would mean that the rocket would not be able to apply the force required to reach a certain speed.

For example, if a rocket with a certain thrust T could attain a maximum speed 0.2c when its thrust is applied, then rocket with thrust T+x where x is some value would be able to attain a speed greater than 0.2c, yet not by much. When the thrust is infinite, then the rocket should be able to reach the speed of light (or just below it, technically).

Your statements are correct for nonrelativistic speeds, but not for relativistic ones, which can't be ignored if we are seeking the MAXIMUM speed of the rocket.

cf bottom of page 88 of Physics 2.

Note in figure 5.14 that as the speed of an object approaches the speed
of light c, its mass approaches an infinite value. It is this enormous
increase in mass that prevents any object from exceeding the speed of
light. This is because an applied force is required to create acceleration.
Acceleration leads to higher velocities, which eventually leads to
increased mass. This means that further accelerations will require evergreater
force. As mass becomes infinite, an infinite force would be
required to achieve any acceleration at all. Sufficient force can never be
supplied to accelerate beyond the speed of light.

The greater the thrust, the greater the force.

 

[ohexploitable]

You are assuming 100% efficiency which is never the case. I'm simply stating that if the efficiency was improved such that the thrust was greater and less of the fuel was wasted, then the maximum speed would be greater.

100% efficiency is the case in HSC Physics, just like how we disregard air resistance etc. There is no wasted fuel in HSC Physics.

Disagree. A greater thrust is a greater force.

No.

Greater thrust results in greater instantaneous force but not total force.

 

[stampede]

Hey guys, this is a question from my half yearly where I disagree with the given answer, was wondering what you guys thought.

Ultimately, the factor limiting the maximum speed of a rocket is:
a) the amount of fuel it carries
b) the speed of ejection of the gases
c) the mass of the rocket
d) the length of the rocket

keyword in question is ultimately.

ultimately, no matter how fast them gases are flying out of the rocket, achieving maximum speed will depend on how much fuel you have.

In other words, if you have a certain amount of fuel with a certain thrust, there is only a certain speed that you can achieve.If you have that same amount of fuel with a GREATER thrust, then the maximum speed that can be achieved is greater.

dont talk about having a certain amount of fuel and then comparing thrusts.

imagine a formula 1 car had 1 litre of petrol and schumacher floored the fuck out of his car, till it was only able to reach 200km/h before running out of fuel

now imagine me carjacking you and driving your shit toyota corolla, with a full tank, and flooring it till i hit 210km/h before the car dies on me.

the answer is a

debate me not for i will always win.

(nah im kidding this is an interesting q, and very tricky, keep debating if u feel the need because i can understand why youd think its b, but ill try to help u comprehend, also excuse my rudeness if it offends you)

 

[khfreakau]

100% efficiency is the case in HSC Physics, just like how we disregard air resistance etc. There is no wasted fuel in HSC Physics.

No.

Greater thrust results in greater instantaneous force but not total force.

First statement - well that's just retarded, no point in studying Goddard who improved fuel efficiency.

Second statement - the instantaneous force is what is relevant at relativistic speeds though. If you had exerted a total force of 1000000N up to that point, but the rocket only exerts 100N thrust per second, then at a certain speed it can't accelerate any further since there is more mass than it can move (work done).

 

[stampede]

Constant acceleration is not required.

you're on the right track with your argument, but this statement is wrong.

without an increasing or constant acceleration (if a is not >= 0 ), velocity will not be increasing, and you obviously want velocity to increase to achieve maximum speed

 

[ohexploitable]

Just a note, we're both misusing the word 'thrust', thrust is just a name for a particular type of force but we are using it to describe the rate that force is applied i.e. Newtons per second.

 

[stampede]

also guys, its a rocket, a real one not a bullshit relativistic one, you have over thought the q way too much