Challenging Mechanics Questions: Help Needed!

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The discussion focuses on solving challenging mechanics questions related to the Saturn V rocket and a railway truck. Participants seek assistance with calculations involving thrust, resultant forces, and the effects of mass change on momentum. Key formulas discussed include F = (dm/dt)(v) for thrust and the need to account for gravitational forces in the rocket's calculations. The conversation highlights confusion around the application of these formulas, particularly regarding the variable nature of mass flow rates. Overall, the thread emphasizes the need for clarity in applying physics principles to solve the posed problems.
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We have been given a set of questions to do. Most of these I have managed fairly easily but there are some which I am really stuck on and am getting quite annoyed with now as I have been working at them for ages! Help on any of these would be really appreciated:

The Saturn V rocket which launched the Apollo space missions had the following specifications:
mass at lift-off = 3.0 x 10^6 kg
velocity of exhaust gases = 1.0 x 10^4 m/s
initial rate of fuel consumption at lift-off = 3.0 x 10^3 kg/s

1.(a) Calculate:
(i) the force (thrust) produced at lift-off
(ii) the resultant force acting on the rocket at lift-off

2.(a) An empty railway truck of mass 10000kg is traveling horizontally at a speed of 0.5m/s. (had to calculated the momentum and kinetic energy - not sure if this will help with the bit I am stuck with!)
Sand falls vertically into the truck at a constant rate of 40kg/s. Calculate the additional horizonal force which must be applied to the truck if it is to maintain a steady speed of 0.5m/s.

Thanks for anyones help - I can usually manage these kind of questions but I'm really stuck for some reason!
 
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Originally posted by Auron87
The Saturn V rocket which launched the Apollo space missions had the following specifications:
mass at lift-off = 3.0 x 10^6 kg
velocity of exhaust gases = 1.0 x 10^4 m/s
initial rate of fuel consumption at lift-off = 3.0 x 10^3 kg/s

1.(a) Calculate:
(i) the force (thrust) produced at lift-off

Ft = mv

Derive both sides

F = (\frac{dm}{dt})(v)


(ii) the resultant force acting on the rocket at lift-off
I think this means to include gravity. It should be whatever you got from part (i) - gravity.

2.(a) An empty railway truck of mass 10000kg is traveling horizontally at a speed of 0.5m/s. (had to calculated the momentum and kinetic energy - not sure if this will help with the bit I am stuck with!)
Sand falls vertically into the truck at a constant rate of 40kg/s. Calculate the additional horizonal force which must be applied to the truck if it is to maintain a steady speed of 0.5m/s.

Ft = mv

Derive both sides

F = (\frac{dm}{dt})(v)
 
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I've not met that formula before but I do understand where its from but how can you use it because you don't know time or is it necessary to work out the time or something??
 
dm/dt is a variable, not a division of 2 or 4 variables :wink:

In the first question, dm/dt is 3.0 x 10^3 kg/s

In the second question, dm/dt is 40kg/s
 
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