What is the optimal angle for a projectile to be launched at to maximize range? height? time?
What is the optimal angle for a projectile to be launched at to maximize range? height? time?
The range equation is [math]R = \frac{v_0^2}{g}sin(2\Theta)[/math]. Thus, to maximize range, we need to get the maximum value of [math]sin(2\Theta) = 1[/math]. 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. 
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?
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.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.
Next question, please.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.
Derive a formula for the acceleration of the blocks in a real atwood machine with two masses of mass [math]m1[/math] and [math]m2[/math]and a pulley in the shape of a uniform disk of mass [math]M[/math] and radius [math]r[/math]. The string is massless. Ignore friction.
a = m1g - m2g / m1+ m2If 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 [math]m1[/math] and [math]m2[/math]and a pulley in the shape of a uniform disk of mass [math]M[/math] and radius [math]r[/math]. The string is massless. Ignore friction.
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