Asst _8_query

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18:42:27 QUESTION FROM STUDENT--Please define the differnece between Fnet and Force. See if you can answer this question.

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RESPONSE --> Force refers to a single action capable of accelerating an object. Fnet is the sum of all forces.

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18:42:45 ** Net force is the sum of all forces acting on an object. If you're pushing your car you are exerting a force, friction is opposing you, and the let force is the sum of the two (noting that one is positive, the other negative so you end up with net force less than the force you are exerting). Your heart rate responds to the force you are exerting and the speed with which the car is moving; the accel of the car depends on the net force. **

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RESPONSE --> OK

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18:43:17 In terms of the equations of motion why do we expect that a * `ds is proportional to the change in v^2, and why do we then expect that the change in v^2 is proportional to Fnet `ds?

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RESPONSE --> Don't get this one.

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18:44:42 ** It's very important in physics to be able to think in terms of proportionality. To say that y is proportional to x is to say that for some k, y = k x. That is, y is a constant multiple of x. To say that a * `ds is proportional to the change in v^2 is to say that for some k, a * `ds = k * ( change in v^2)--i.e., that a * `ds is a constant multiple of the change in v^2. In terms of the equations of motion, we know that vf^2 = v0^2 + 2 a `ds so a `ds = 1/2 (vf^2 - v0^2), which is 1/2 the change in v^2. So a `ds is a constant multiple (1/2) of the change in v^2. Formally we have a `ds = k ( change in v^2) for k = 1/2. Now since Fnet = m a we see that Fnet is proportional to a for a given mass m, and it follows that Fnet `ds = k * change in v^2, for the appropriate k (specifically for k = mass / 2. **

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RESPONSE --> Huh?

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18:44:58 How do our experimental results confirm or refute this hypothesis?

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RESPONSE --> I'm lost

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18:47:44 ** We didn't actually do this part of the experiment, but on a ramp with fixed slope a `ds is simply proportional to `ds. When we measured `dt for different distances from rest down the same ramp, we were then able to determine the average and final velocities. The change in v^2 for each timing would be from 0 to vf^2. The change would therefore be just vf^2. If a `ds is proportional to the change in vf^2 then a graph of vf^2 vs. a `ds should be linear. Since a is constant we don't even need to determine it--a graph of vf^2 vs. `ds would be linear. This would confirm the hypothesis. **

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RESPONSE --> oh

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Reasoning by proportionality is generally challenging for students in all physics courses. Students in 200-level courses are expected to master that sort of reasoning, but I don't hold 121 students to it. The bottom line here is that F `ds is determined not by the change in velocity v, but by the change in the squared velocity v^2, and it turns out that energy of motion is therefore proportional to v^2, not just to v. So for example something moving twice as fast has 2^2 = 4 times the energy per unit of mass; something moving 3 times as fast has 3^2 = 9 times the energy per unit of mass; etc.. Store this idea away, but don't worry about the details the proportionality reasoning.