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Terminal Velocity of a Ball Given Velocity and Acceleration 
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#1
Dec1712, 12:05 AM

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1. The problem statement, all variables and given/known data
A steel ball is dropped from a great height. When its velocity is 20m/s its acceleration is 7.35 m/s^2. What is it's terminal velocity? 2. Relevant equations V  V_o = at F = ma (Air resistance isn't given, so I don't think drag force can be used.) 3. The attempt at a solution 1. I know the final net force must equal 0. 2. The answer is 40 m/s, but I am unsure of how to get this answer. 3. I tried calculating drag force and taking the limit as time approaches infinity, but I must be making an error. 


#2
Dec1712, 01:02 AM

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#3
Dec1712, 01:09 AM

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Well I know air resistance is proportional to velocity, but I don't see how I can find air resistance without knowing surface area, mass, density, temperature, etc.



#4
Dec1712, 01:32 AM

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Terminal Velocity of a Ball Given Velocity and Acceleration
You can find b/m for the given conditions. Then, what does v have to be if a = 0 ? BTW: Are you sure about the answer of 40 m/s ? If so, then I conclude that the air resistance follows a different law . 


#5
Dec1712, 02:13 AM

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v = mg/b
1. What does b stand for? 2. I'm sure it is 40 m/s. I came up with multiple answers, but they were all smaller than 40 m/s. 3. They don't give a value for mass. (If I understand what b stands for, I may be able to figure it out.) 


#6
Dec1712, 02:28 AM

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The forces acting on the falling ball are gravity and air resistance, which is proportional to velocity and opposite to it.
Writing up Newton's second law, F=ma=mgkv. The acceleration is a=g(k/m) v. You know that a=7.35 m/s^{2} when v=20 m/s. Plug in: you will find k/m. The ball will reach the terminal velocity when the two forces  gravity and air resistance  cancel, that is, the acceleration is zero: g(k/m) v=0. You know k/m, how big is v? If the given result is 40 m/s then the air resistance is taken proportional to v^{2}. Do the same procedure, replacing v by v^{2}. 


#7
Dec1712, 02:31 AM

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If you assume that the drag force (air resistance) is proportional to v^{2}, you will get 40 m/s for your answer. This whole thing is essentially just working with proportiona. 


#8
Dec1712, 03:57 AM

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Thank you so much! I forgot that air resistance can be proportional to v and v^2.



#9
Dec1712, 09:55 AM

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a=gkv, a is a function of veolcity(assumption) k is a constant and then we can find k, by using given data.
then find a=0, which kv=g, you can find out v which is terminal veolcity. 


#10
Dec1712, 01:30 PM

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In the given problem it appears that acceleration, as well as force, is proportional to v^{2} . 


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