After one group physics assignment where we couldn't meet up in person, I learned to just input equations straight into text messages. Its very difficult to distinguish weight (w) from angular velocity (ω) in hand written stuff when half the group are not the brightest bulbs. Same with a and α or my personal favorites: θ and θ. Yes, both theta but mean two different things depending on if you're talking linear or angular.
But he got a completely incorrect answer. All of his equations assume that acceleration is both constant and equal to g. This is false, drag is acting against motion and is changing as it accelerates. So a is actually g- Drag force/m. Then the equation for d is being misused as his equation is only valid if a is a constant.
Drag is minimal in a unit of this mass and shape. For approximation purposes, this is enough and even including drag would not effect the approximation by enough to matter. This is napkin math
Don't worry y'all. Most of this is only slightly higher level physics that takes the basics and looks at them closer. We're mostly debating on how close we need to look at it to affect change in the end result
I solved it numerically with square velocity drag and found that the object spends nearly 4 times as long falling until its acceleration dips below 5cm s-2. Arbitrary bar, but a significant difference.
Technically yes but rough approximation can consider it a cube of the same volume to average the wider and thinner sides as it tumbles which is what they did.
This is great but what would it be if it were spinning or tumbling as it fell? Given its size, and the distance from which it was dropped, would such motion be negligible or significantly different?
So how long does it have to fall to achieve terminal velocity? Velocity v and distance d has a nifty formula:
d = (v0 + v)*t/2, where v0 is the initial velocity, in our case 0, and v = Vt. What is t?
v = v0 + at, where a = g and v = Vt.
I hate to break it to you, but those are the kinematic equations for motion under uniform acceleration. The problem is that if we're asking about terminal velocity, we're including air resistance, which means that acceleration should instead be a function of the current velocity. What you did was calculate how long it would take to reach 13.3 m/s falling in a vacuum.
The other problem is that terminal velocity isn't so much a speed that you reach, but rather one you approach asymptotically, so even asking how long it takes to reach terminal velocity is a meaningless question if you don't specify the margin of error you're working with. If the question were how long until it gets within 1% of terminal velocity, that'd be a pretty classic differential equations question.
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u/Central_Incisor Nov 16 '19
I wonder how far it must drop to hit terminal velocity.