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D-res
Hangin from Sagan's uvula
Registered: May 2004
Location: Milwaukee, WI
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Re: Re: Conceptual Physics Question
| quote: | Originally posted by Omega_M
For a heavier object, the force of gravity is significantly more than the lighter object |
Wording your sentence like this can be potentially misleading for those unfamiliar. While you're correct in saying heavier objects will exert more downward force than lighter objects, one must keep in mind that the downward acceleration of gravity (-9.8m/s^2) is the same for all objects, regardless of weight.
In regards to question 2...
Even though terminal velocity has already been defined in this thread, I'll explain it again for the sake of this post. An object is in free fall. Given it's mass and keeping in mind the constant downward acceleration of gravity, it's exerting say (hypothetically, of course) 1000N of downward force. When the air resistance, the upward force, reaches 1000N, downward acceleration stops and terminal velocity is reached.
Although the downward force exerted by objects with more mass will reach higher speeds than those with less mass before air resistance can equalize the forces, objects with less mass have lower terminal velocities because air resistance can equalize the forces quicker. It is because of this that it would seem object A would reach terminal velocity sooner. Two objects accelerating downward at the same velocity will travel neck and neck. One of the objects, however, has a lower terminal velocity than the other and in this sense, would seemingly reach terminal velocity while the other object continued accelerating. Because terminal velocity is affected by more factors than just an objects mass however, the amount of drag each object creates is the deciding factor in this problem.
The larger an object, the more drag it creates. We know theshapes of both objects are identical. However, their relevance to one another in regards to dimensions (L x W x H) is not addressed in the problem. Although various people have brought up the idea of a vacuum, we can disregard this possibility since the problem states that both objects are dropped from a high altitude.
Since air resistance affects the amount of time needed to reach terminal velocity by creating a positive, increasing upward force on both objects, it can be assumed that the object which creates more drag will equalize it's forces quicker, achieving terminal velocity, yet drag causes moderately rapid deceleration and in turn, terminal velocity requires more time to reach. Because air resistance is determined by multiple criteria, such the object's respective surface areas (larger objects create more drag than smaller ones), the speed the object is traveling (higher speeds = more air resistance), or changes in air pressure as the object falls (higher alt-> lower pressure, lower alt-> higher pressure) and because the information required to determine each objects drag wasn't included with the original problem, we can't accurately answer the question with ONLY the information provided.
A small object with very little mass may not require much drag to reach terminal velocity, but due to its small mass and size, wont create as much drag as, say, an object multiple times its size. ex: A 100k/g plastic cube measuring 5'x5'x5' will take longer to reach terminal velocity than a 105k/g plastic cube measuring 20'x20'x20' because the second cube, while having slightly more mass, creates a LOT more drag due to its much larger surface area. Of course if the larger cube were much denser and it's mass was significantly higher, we can assume once again that it would take longer to reach terminal velocity than the smaller cube.
If you'd like to assume that the object that has less mass is also, coincidentally smaller in size, we can assume it's terminal velocity is lower, but what if its mass is so small that the force of air disrupts its downward velocity and instead causes the object to bend and contort, changing both it's speed and its direction of travel? As someone else mentioned, a piece of paper would have a different terminal velocity than that of a piece of sheet metal, but there are a few factors we would have to consider first...
A. A piece of sheet metal has more mass than a piece of paper. Although the acceleration of gravity is unchanging and constant, the upward force of air resistance will have less effect on the sheet metal and would take longer to match the downward force of gravity with the upward force of air. But wait, an object with more drag will create more upward force and slow the objects acceleration quicker. The more drag an object creates, the lower its terminal velocity will be.
B. The piece of paper is less rigid, thus its more likely to bend as a direct result of air resistance. Changing shape will change the distribution of air resistance on the different surfaces of the object and in turn change its aerodynamic properties and its overall direction of travel. The more rigid piece of sheet metal would fall downward and probably wouldn't change direction as often, as easily, or as significantly as the paper, but because of its rigidity, it has the potential to create more air resistance, depending on what surfaces are facing downward. In the event the sheet metal became parallel with the ground, it would create more drag than the paper, which would bend and change shape as a direct result of air resistance.
A piece of paper, while having less mass, would probably "fly around in the wind" too much to reach terminal velocity because it's constant changes in velocity (keep in mind velocity is speed PLUS a direction) wouldn't allow it to continually accelerate downward towards terminal velocity. The rigidity of a piece of sheet metal could potentially cause similar problems. Although a piece of paper and a piece of sheet metal COULD potentially fit into this problem, due to their similar shapes but different masses, they're bad examples because their structural characteristics, especially their respective masses and rigidities, cause them to behave erratically in free fall, instead of maintaining a single, predominant direction of travel.
*sigh*
...that was a lot of thinking
Last edited by D-res on Dec-18-2006 at 16:52
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 Dec-18-2006 16:45 
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astroboy
Supreme tranceaddict
Registered: Nov 2001
Location: Melbourne
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| quote: | Originally posted by Caela
My Guesses :
1. A
(laser is smaller, light is more concentrated, less light particles = faster speed?) |
Incorrrect. The speed of light is a constant, no matter what the source. He's asking for the rate at which the light spreads. Lasers beams hardly spread at all because laser light is made up of a single frequency of light. Sunlight has the widest spectrum of light and therefore spreads the fastest.
| quote: | 2. C
(terminal velocity has a universal speed for every object...can't remember the exact number though) |
Incorrect. For every object terminal velocity is the point at which the upward air resistance on an object (that is the force of the air molecules colliding with the falling object) is equal to the downward force on the object.
| quote: | 3. B
(less air pressure at the bottom of the ball, since the top is leading the rest of it through the air, resulting with more velocity under the ball, since it is driving the ball in the direction it's moving). |
others have already explained this well
| quote: | | As the baseball moves through the air, the air pressure in the direction of motion is more than on the other side. Locally, the air molecules get compressed at the top and they create higher pressure in comparison to the pressure at the bottom. A small pocket of low pressure in the bottom of the baseball will be quickly filled in by the surrounding air, and this will result in higher velocities at the bottom. |
| quote: | 3, B - As the ball climbs into the air, more air molecules will be resisting its climb, as it has to push through the air to rise up. It will displace molecule below it creating the slip stream effect.
I agree it is worded awkwardly too, but from the choices it will have more velocity underneath it. |
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Dec-18-2006 23:28 
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