Dynamics Homework problem - help!
Xano
Registered User regular
Registered User regular
Here's the problem so far guys, any help is appreciated.
The 20,500-lb helicopter is at rest on the ground at time t = 0. Its pilot advances the throttle so that the upward thrust exerted by the rotor as a function of time t is:
T = 18000+1000t lb.
Plot the height of the helicopter as a function of time for t = 0 to t = 6 seconds.
Ok, Here's where I'm aiming at thus far:
I know Sum of F = MA.
I know the mass (20,500/32.2), and the forces (weight acting down/ Thrust acting up at time t). I just need to solve for a(t), then integrate it to get the v(t), and then once more to get x(t). I did all this, but my answers don't seem reasonable when I plug in my time values.
Thanks for any help!
The 20,500-lb helicopter is at rest on the ground at time t = 0. Its pilot advances the throttle so that the upward thrust exerted by the rotor as a function of time t is:
T = 18000+1000t lb.
Plot the height of the helicopter as a function of time for t = 0 to t = 6 seconds.
Ok, Here's where I'm aiming at thus far:
I know Sum of F = MA.
I know the mass (20,500/32.2), and the forces (weight acting down/ Thrust acting up at time t). I just need to solve for a(t), then integrate it to get the v(t), and then once more to get x(t). I did all this, but my answers don't seem reasonable when I plug in my time values.
Thanks for any help!
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Xano on
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Could you post the work you have done so far?
>_>
However, the initial force downwards is
20500g => 9.81*20500
Compare this to
18000 + 1000t force upwards.
Equate the two.
t = 183.105 secods before it gets off the ground.
Ok, so basically. I cannot help you due to some kind of unit conflict that makes no sense to a man who works in metric. Sorry fella.
after 2.5 seconds the force is 1000t
also, since you have a non uniform force, you can't use F=ma, you need to use f = m dv/dt swap the dt to the other side and integrate to get: mv = 500t^2 - 500(2.5^2) (you integrate from t=2.5 to t=t)
your mass is 20500/32.17 or 637.24. solve for v and you get v= .785t^2 - 4.9. v=dx/dt so you integrate again to get x = .261544t^3 - 4.9t +8.1633.
so your final function is
H = 0 for t<=2.5
H = .261544t^3 - 4.9t +8.1633 for t>2.5
Holy shit I cannot believe they actively teach in imperial measurements.
They're all just numbers and units, the process of getting the answer should be the same.
That said, they're not supposed to be using US-standard for measuring in any science classes anymore. I think, when doing equations with gravity, this is the one stupid exception to that.
The ability to work in different unit systems is really crucial, even if you work in metric, because you might need to convert between CGS and MKS, etc. The value of g you used is in [m/s^2] which is why your answer makes no sense. Trust me when I say that you need to learn unit analysis. You won't always have convenient problems given to you by professors where you just use the numbers and don't worry about the units.
Unit analysis is also an excellent way of checking your final result when working a problem--if you're trying to calculate a time and get units of time-distance then you have a problem.
engineering still uses us standard for most everything.
my intro to aero course made us use slugs and the like. in fact, aside from the theory courses most of them were in us standard.
also,
lb or lbf are forces
slugs or lbm are masses.
lb is a pain because sometimes people do use it as a mass without labeling it lbm. so look at the context of the problem. since the helicopter weighs 20500, its a weight which is a force.
Only engineering in the USA uses metric.
Engineering in all the countries I work in (everywhere other than the USA) uses metric.