Phy 201
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I have a few general questions and another specific question for Phy 201.
General:
1) How is it that acceleration is independent of velocity? I sort of understand position, but acceleration is kind of based on the final velocity divided by the time so how can it be independent from it?
Acceleration is based on change in velocity, not on final velocity. The rate at which velocity changes doesn't depend on how fast you're moving.
The statement should have been that the acceleration is independent of the instanenous velocity, and also of the average velocity.
On a given time interval, it is possible to choose any average velocity and any average acceleration you wish. The two can be chosen independently and neither will contradict the other. Whatever average velocity and acceleration you choose, you can find a corresponding initial and final velocity that match your choice.
2) There is not a specific equation for tension right? We would just have to figure this out based on the acceleration that we need or some other example?
Your rubber band calibration graphs can be fit fairly well with a linear function, typically much better with a third-degree polynomial function. Either of these would provide a usable, if not quite precise, equation for the tension of the rubber band as a function of its length. So in this sense there can be an equation for the tension of an object.
If you're talking about tension in the context of an Atwood machine, for example, you find the tension in the string based on an analysis of forces and accelerations. I think this is what you're referring to.
3) If we want to find gravitational pull horizontal vector, we take weight(cos(theta)) where weight would be m(g) correct?
You're probably asking about a mass on an incline.
When the xy coordinate system is rotated so the positive x axis is directed parallel to and up the incline, the weight vector makes angle 270 deg - theta with the positive x axis, where theta is the angle of incline.
The x and y components of the weight are therefore m g cos(270 deg - theta) and m g sin(270 deg - theta).
The former is the weight component parallel to the incline, the latter the component perpendicular to the incline.
If the positive x axis is parallel to but down everything is pretty much the same, but the incline the angle is 270 deg + theta.
4) If i am trying to find the angle with the x axis for a vector and you give me the information that theta is 15 degrees for example, then do I need to figure out what quadrant it is in by thinking about the directions of the vectors? I am pretty sure this is right.
You don't say what the angle theta is measure with respect to, and that makes all the difference.
If theta is the angle with the x axis, then if theta is 15 degrees, then it's 15 degrees. However I don't think this is what you mean.
If theta is the angle with the horizontal direction, and the x axis is in its default orientation (horizontal to the right, as opposed to the orientation we use with an object on an incline), then the angle might be 15 degrees above or below either the positive or negative x axis, so the vector might be in any of the four quadrants (at any of the angles 15, 165, 195 or 345 degrees). If you know the signs of the x and y components of the vector, you can figure out which quadrant it's in.
Finally I am extremely confused about a question i saw on a practice test:
A system consists of a cart pulled along a constant-velocity ramp by the force of gravity on a single paper clip, whose mass is much less than that of the cart, attached by a thread over a pulley with negligible friction. If the system accelerates at 5.9 cm/s2, and if F = m a describes the relationship among net force F, mass m and acceleration a, give the acceleration of each of the following:
The same system but with 8 paper clips instead of one.
For economy of words I'll speak of the paper clip as accelerating the system, but it is in fact the force exerted by gravity on the paper clip which has this effect.
If a single paper clip hanging over the pulley accelerates the system at a certain rate, then would 8 paper clips hanging over the pulley result in a greater or lesser acceleration? How many time greater or lesser? What therefore would be the acceleration?
The same system but with a single paper clip and a cart of twice the mass.
If a single paper clip accelerates the original cart at a certain rate, then would that same paper clip give a doubled mass a greater or a lesser acceleration?
The same system but with a single paper clip with a cart of half the mass.
If a single paper clip accelerates the original cart at a certain rate, then would that same paper clip give half the mass a greater or a lesser acceleration?
The same system but with 7 paper clips and a cart of 17 times the mass.
What would be the acceleration of the same system but with a number of paper clips whose mass equals that of cart?
How would the slope of a graph of total paper clip weight vs. acceleration for the original system (for a small number of paper clips) compare with a slope of a similar graph for a system with half the cart mass, and how would it compare for the slope of a system with 7 times the cart mass?
I have no idea where to start from this. I am assuming that acceleration must me related to mass since f=m(a) but are you asking for specific numbers for just representations? If specifics could you point me in the right direction?
You are told how much acceleration we get from a single paper clip. You are asked how much acceleration we get from other numbers of paper clips, and also for different multiples of the cart mass.
I've rephrased selected questions to make the conclusions a little more obvious. You're welcome to submit your solutions, question, etc..