## Hovercraft B/C

photolithoautotroph
Member Posts: 15
Joined: April 8th, 2018, 6:21 pm
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State: PA

### 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
Exalted Member Posts: 161
Joined: January 30th, 2016, 8:03 pm
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State: MI

### 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
Member Posts: 15
Joined: April 8th, 2018, 6:21 pm
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State: PA

### Re: Hovercraft B/C

i wish i was good Events 2019: Expd, Water, Herp
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Tesel
Exalted Member Posts: 161
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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?

2018 MI Mission Possible State Champions

UTF-8 U+6211 U+662F
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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
Member Posts: 15
Joined: April 8th, 2018, 6:21 pm
Division: C
State: PA

### 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 wish i was good Events 2019: Expd, Water, Herp
Rip states 2019

Tesel
Exalted Member Posts: 161
Joined: January 30th, 2016, 8:03 pm
Division: C
State: MI

### 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!

2018 MI Mission Possible State Champions

CMS AC
Member Posts: 151
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State: NJ

### 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
Member Posts: 15
Joined: April 8th, 2018, 6:21 pm
Division: C
State: PA

### 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
Member Posts: 196
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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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