state the relation between radius of ball bearing and terminal velocity
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What does your intuition tell you about the relationship? Do you think a sphere with cross sectional area A = pi (D/2)^2 or with cross sectional area a = pi (d/2)^2 where d < D are the respective diameters will fall the fastest? Think it through. If you drop a balloon with D > d and you drop that same balloon with d < D, which one will fall the fastest after dropping, say, from an eight foot ceiling to the floor? They both weigh the same; so only the respective cross sectional areas will make a difference.
Step 1: Based on your expertise (because you've studied your homework) and intuition (because you are observant) the first thing for all investigative work is to specify a hypothesis. Hypothesis is just a fancy name for educated guess. This is the thing you are setting out to prove to be not false. (For reasons you will uncover when you take statistics, we never prove anything to be true. The best we can do with it is prove something to be "not false.") Provide a bit of background info on why you made the hypothesis. This is where invoking some equations might be helpful, but if there are none simply invoke your observations; you know, like Newton did when that apple landed on his head.
EXAMPLE: We intend to show that terminal speed varies inversely with the square of the sphere's diameter.
As acceleration a = g (1 - D/W), where g = 9.81 m/sec^2, D is drag force, W is weight, and D = 1/2 rho Cd A V^2 we see that drag and, therefore, acceleration depends in part on the cross sectional area A of a falling body. A = pi (d/2)^2 for a sphere, where d is the diameter. So drag D depends on d^2, meaning for a given velocity V, drag will be higher for spheres with bigger diameters. That, in turn, means terminal velocity, where a = 0, will be reached at a slower velocity V for larger diameters. That is, terminal velocities should vary inversely with the square of the diameters, which is what we intend to show with this investigation.
Step 2. Design the tests (together the experiment) to show your hypothesis (or not). Describe both the tools (what you will be using) and the process (what you are doing). In designing your experiment ensure you block out all factors other than the dependent speed (V) and the independent D (diameter). For example, you do not want the spheres to be different weights because the weights might also enter into the terminal speed. And you do not want to do the experiment where air currents etc. could affect the outcomes.
EXAMPLE: Describe the following experiment. Choose one spherical balloon and blow it up to different diameters. Then drop the balloon at each diameter to measure the time to drop (t). As you know the distance to drop h, you can find the average velocity upon impact V = h/t. Point out how using the same balloon blocks out the effects of weight as the weight remains the same for each test (drop).
Step 3. Record and analyze your results. Keep the data for each test, including the conditions (e.g., height, diameter) and results (e.g., time to drop). Then analyze what you collected to look for trends and relationships that prove or do not prove your hypothesis as specified in Step 1. Use tables of data for your test data and graphs, where meaningful, for your analysis.
EXAMPLE: Do, say, 10 tests; so you'll have ten data points. Each point will be a different diameter D and a time to drop t. More tests would be useful if you can stretch the balloon, say, 30 times for 30 diameters or even drop the balloon, say, three times per test and take the average time to drop T = SUM(t)/3 for each diameter. In statistics and experiments, more data is always better.
Using your hypothesis and your understanding of terminal velocity, plot out your data accordingly. If you believe V ~ 1/D^2, then plot V vs 1/D^2 to see what kind of curve you get. If it is more or less a straight line, then your guess, the hypothesis, is probably not false. Otherwise, back to the drawing board with a new guess. But, this is important, showing a hypothesis is not true is OK. It eliminates that possibility from further consideration. Discoveries are often found through the process of elimination.
Step 4. Based on your data and analyses, write up your conclusions and recommendations. At the very least conclude whether the hypothesis was shown to be not false or not. Then if you have ideas on further experiments or a better way to do this one, make recommendations.
Answer:
What does your intuition tell you about the relationship? Do you think a sphere with cross sectional area A = pi (D/2)^2 or with cross sectional area a = pi (d/2)^2 where d < D are the respective diameters will fall the fastest? Think it through. If you drop a balloon with D > d and you drop that same balloon with d < D, which one will fall the fastest after dropping, say, from an eight foot ceiling to the floor? They both weigh the same; so only the respective cross sectional areas will make a difference.
Step 1: Based on your expertise (because you've studied your homework) and intuition (because you are observant) the first thing for all investigative work is to specify a hypothesis. Hypothesis is just a fancy name for educated guess. This is the thing you are setting out to prove to be not false. (For reasons you will uncover when you take statistics, we never prove anything to be true. The best we can do with it is prove something to be "not false.") Provide a bit of background info on why you made the hypothesis. This is where invoking some equations might be helpful, but if there are none simply invoke your observations; you know, like Newton did when that apple landed on his head.
Explanation: