Hovercraft B/C

photolithoautotroph
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Re: Hovercraft B/C

Sorry for the wait, had to grind to keep my GPA afloat for the past few days.
What is the optimal angle for a projectile to be launched at to maximize range? height? time?
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Tesel
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Re: Hovercraft B/C

The range equation is $R = \frac{v_0^2}{g}sin(2\Theta)$. Thus, to maximize range, we need to get the maximum value of $sin(2\Theta) = 1$. The resulting angle is 45 degrees.
For height and time, the angle should be 90 degrees. Both of these are based on the initial vertical velocity; the maximum vertical velocity occurs when all initial velocity is in the vertical direction.

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photolithoautotroph
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Re: Hovercraft B/C

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Tesel
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Re: Hovercraft B/C

Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

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Re: Hovercraft B/C

Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?

photolithoautotroph
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Re: Hovercraft B/C

Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.
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Tesel
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Re: Hovercraft B/C

Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.
I should have clarified the question a lot better.
But yes, you made the right assumptions, and that was the correct use of Poiseuille's Law. Correct!

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Re: Hovercraft B/C

Consider a pipe with radius r.

If an ideal fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?

If a non-ideal, viscous fluid is flowing through the pipe, how would the flow rate change if the radius was increased to 2r?
Both fluids would go through twice as slowly?
I haven't done enough fluid dynamics to be sure, but I can guess: for an ideal fluid the flow rate would change to 4Q (Q=Av) and for a non-ideal, viscous fluid, the flow rate would change to 16Q (Poiseuille's Law)? Less sure about the second one but either could be wrong. At least I don't actually have to do this for real.

photolithoautotroph
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Re: Hovercraft B/C

If nobody posts a question in this long, you can.
Derive a formula for the acceleration of the blocks in a real atwood machine with two masses of mass $m1$ and $m2$and a pulley in the shape of a uniform disk of mass $M$ and radius $r$. The string is massless. Ignore friction.
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IvanGe
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Re: Hovercraft B/C

If nobody posts a question in this long, you can.
Derive a formula for the acceleration of the blocks in a real atwood machine with two masses of mass $m1$ and $m2$and a pulley in the shape of a uniform disk of mass $M$ and radius $r$. The string is massless. Ignore friction.
a = m1g - m2g / m1+ m2
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