Motion
As a class, we have recently started our motion unit in physics. To begin with, my partner and I brainstormed some ways of describing motion:
-Is there a pattern to the object's movement?
-What path does it take?
-What forces are acting on the object's movement?
-What is its rate of movement? (how many inches or centimeters does it cover in a specific amount of time?)
-What is the quality of movement? (Modern Dance term, mind. Very scientific) Does it roll? Bounce? Swing?
Out of curiosity, I searched the internet asking the same question: How can we describe motion? There seemed to be a common idea in all the websites I found, summed up here: How they do it
Seems pretty simple, but not very specific. Speed/velocity just isn't enough information, particularly if we are to apply it to objects such as planets and galaxies.
Relative Motion
We had a class assignment to create a video portraying relative motion and think of some "deep" questions to ask the class upon presentation.
This is our video:
Brought to you by Andrea Tate, Elly Bryant, Alley Bowers and myself.
The questions are as follows:
1. What motion do you see?
2. How does the motion differ from the person in the background to the two spinning girls?
3. Describe the motion of the spinning girls in relation to each other and in relation to the creeper in the background.
Some relevant but disorganized thoughts:
-Say the distance between the spinning girls is unchanging as they rotate. Are they moving compared to each other, then?
-Does this mean that Andrea-Creeper the only one moving relative to the spinning girls?
Things to ponder.
Graphitude
Lets do some definitions, first off.
Qualitative data: data that shows general trends or patterns, not individual amounts. Quantitative data: data that shows accurate amounts and measurements.
We have been discussing graphs in class over the past week. From our discussions, I have gathered that:
-a motion map is an effective method of physically representing the motion of an object. The distance is established, and the object is drawn at intervals to represent where it is at certain times. -Advantage: actually shows you the object's path. -Disadvantage: Not as exact or quantitative as it could be. A motion map is more qualitative, meaning that it gives you the gist of things.
-an x-t graph is a more quantitative way of representing data. When representing movement, units of measurement are given for distance (typically x-axis) and time (typically y-axis). The slope of the data, or the difference between the points, is the speed. -Advantage: Data can be quantitatively displayed. -Disadvantage: If the data being displayed isn't perfectly linear, the slope represents average speed instead of the actual changing speed. Also, the dots of data plotted on an x-t graph do not actually show you the objects path--for example, a graph with a diagonal line going upwards to the right does not mean that the object moved upwards to the right. X-t graphs show changes in position and distance, not the actual path of the object, and this can be confusing to someone with little experience reading graphs or interpreting data. Examples (graphs created by me, with the aid of this website):
Graph A: Constant Speed
Preview of your graph
The object portrayed in this graph starts at zero seconds, zero meters. Once in motion, it goes five meters per one second--meaning that it's slope is 5 meters over 1 second. This also means that the speed of the object, which is the same as the slope, is 5 meters per second.
The difference between the plotted points is consistently 5 over 1, meaning that the slope and therefore the speed of the object is constant. Its shape is due to the fact that the object moves the same number of meters each second as time goes by.
Graph B: Increasing Speed
Preview of your graph
In this graph, the object in motion increases by changing amounts. From 0 to 1 seconds, the object moves 0.5 meter. From 1 to 2 seconds, the object moves 1 meters, and from 2 to 3 seconds, the object moves 1.5 meters. The distance between the rest of the points increases by 0.5 meters for each second. From this we know that the slope is not staying the same over time, but increasing, meaning that the speed of the object is increasing over time as well. The shape of the graph is due to the fact that the object is moving more meters per second as time goes by.
Graph C: Decreasing Speed
Preview of your graph
In this graph, the difference between 1 and 2 seconds is 4 meters. The difference between 2 and 3 seconds is 3.5 meters, and the difference between 3 and 4 seconds is 3 meters. The difference between the points decreases by 0.5 meters each seconds. From this we can see that the slope is decreasing as time passes, meaning that the speed is decreasing as well. The shape of the graph is due to the fact that as time goes by, the object moves fewer meters each second.
From the advantages and disadvantages of these two methods of showing data, I have concluded that both would be useful to use if the intention was to provide the most complete and understandable representation of the data. However, if I had to choose one as being the most useful to me, I would pick the x-t graph, because of its accuracy and the fact that I understand and am able to read it.
This Thing You Call "Relative Motion"
So we did the project and whatnot, but what does it mean? And why does it matter?
Well, relative motion is defined as the motion of an object relative to another object.
For motion to occur, there must be something to compare the motion to--otherwise, how could you possibly know that it was moving? Think about how we describe a moving object--it got closer to me. It went away from the bus. For motion to occur, there has to be a change in distance, yes? And to measure this distance, we need a zero. This is the object/point in space that the object in motion is moving relative to. On a graph, it is the zero point (aptly named, this zero).
For example:
There are two cars parked next to each other in a parking lot, one red and one white. The red car starts up and drives forwards, away from the white car. Relative to the white car, the red car is moving, because the distance between them is changing. In this scenario, the white car is the zero and the red car is the object in motion.
But wait. If the definition of motion is a change in distance, wouldn't the white car be moving relative to the red car, too, even if it isn't the one driving away?
Yes. Exactly.
If you were to use the red car as the zero and the white car as the object in motion, the white car would be moving relative to the red car. In every situation, if object a is moving relative to object b, then the opposite is true as well. It just depends on where you place your zero.
So, keeping these ideas in mind, let's set up another scenario.
Now the red car and the white car are both driving down the road, the white one behind the red one, both going 35 miles per hour.
Because of their identical speed, the distance between them is not changing--but they're both being driven. Are they moving, relative to each other?
No.
The same rule still applies. If there is no change in distance between them, then, relative to each other, neither car was moving.
HOWEVER. This does not mean that neither car was moving--relative to other things.
Think of all the things that the cars' distances are increasing or decreasing from--the point in the parking lot at which they began driving, a sign that they pass by on the road, a hitchhiker left in the dust. So many possibilities.
Bottom line: If the distance is changing between objects, then they are bothing moving relative to each other.
And...why does it matter? Because all motion is relative. Without an object to compare it to (a zero), it is impossible describe (much less perceive) the motion of another object. Graphs cannot be made. Measurements cannot be taken. And the nice thing is, if you've ever described the motion of anything, you've been using the idea of relative motion your whole life without even realizing it.
How does it affect science?
To quote from this website:
"Motion means continuous change of position of an object with respect to an observer. To another observer in a different frame of reference the object may not be moving at all, or it may be moving in an entirely different manner. The motions of the planets were found in ancient times to appear quite complicated in the laboratory frame of reference of an observer on Earth. By transferring to the frame of reference of an imaginary observer on the Sun, Johannes Kepler showed that the relative motion of the planets could be simply described in terms of elliptical orbits. The validity of one description is no greater than the other, but the latter description is far more convenient."
Basically, it helps us to better understand the motion of objects by being able to use different reference points to perceive it.
Parallax
I am looking at a flower vase at the end of the next room, perhaps fifteen or twenty feet away.
It appears to be right in the middle of my line of vision.
Viewing with left eye: The vase seems more left-ish.
Viewing with right eye: The vase seems much more to the right.
Switching back and forth between using one eye or the other, but never both at one time, the vase appears to be jumping from left to right and right to left, depending on the eye. But the vase isn't actually moving, is it?
This phenomena can be described as parallax, "the apparent displacement of an observed object due to a change in the position of the observer." (link)
Think about it. You aren't a cyclops. Your eyes are positioned a small space away from each other. When observing with both eyes, we see an object in a single place, but when we switch between using one eye or the other, the apparent difference in the position of the object shows that each eye percieves it from a different angle.
On a larger scale, you could stand to the right of a chair. The chair, obviously, appears to be at your left.
Move behind the chair and it appears to be directly in front of you.
Move to the left of the chair, and now it is on your right.
Just like before, the observed object has not changed its position, but the observer has.
However, distance makes a difference as to how you perceive an object. If I do the same thing that I did to the vase with the house outside of the window, all the way across the street, it doesn't seem to "move" at all. Why? My eyes are still perceiving the house from different points, right?
Fact is, the farther away an object is, the less its position will seem to change. Relative to the distance between my eyes and the house, the distance between my eyes is very small. To notice any change in postion, I would have to view the house from two points that are farther apart, like from one end of the block to the other. Likewise, the greater the distance is between the points of observation, the more the position of the observed object will appear to have changed.
So, when observing an object close to you that is aligned with a distant object and observing it from each individual eye, the close object will appear to move a lot in comparison to the distant object. They will no longer be aligned. This fact is particularly useful to astronomers.
How is parallax used?
Astronomers can use parallax to determine the distance to stars. It might seem like a far stretch from looking at a vase in your living room, but the principal is the same.
using motion parallax to measure distance to a nearby star
(Info and image pertaining to astronomy obtained from this website. Anything in quotations is text taken directly from the site.)
In this case, a person's eyes are not far enough apart to experience parallax when looking at a star. A much greater distance is needed--like the diameter of the earth's path around the sun, as shown at left.
"The parallax angle, P, is measured by comparing the nearby star's position to the stable position of distant background stars."
Basically, the astronomers use the known characteristics of triangles to determine the angles and therefore distances of the triangles created by the points of observation, the star being observed, and the distant stars being used as background reference points.
Using the operations of sine, cosign or tangent, if one of the other angles of the triangle is known (like the distance from the earth to the sun) ans the angles have been found, the distance from the earth to the star is able to be calculated.
Motion
As a class, we have recently started our motion unit in physics. To begin with, my partner and I brainstormed some ways of describing motion:
-Is there a pattern to the object's movement?
-What path does it take?
-What forces are acting on the object's movement?
-What is its rate of movement? (how many inches or centimeters does it cover in a specific amount of time?)
-What is the quality of movement? (Modern Dance term, mind. Very scientific) Does it roll? Bounce? Swing?
Out of curiosity, I searched the internet asking the same question: How can we describe motion? There seemed to be a common idea in all the websites I found, summed up here:
How they do it
Seems pretty simple, but not very specific. Speed/velocity just isn't enough information, particularly if we are to apply it to objects such as planets and galaxies.
Relative Motion
We had a class assignment to create a video portraying relative motion and think of some "deep" questions to ask the class upon presentation.
This is our video:
Brought to you by Andrea Tate, Elly Bryant, Alley Bowers and myself.
The questions are as follows:
1. What motion do you see?
2. How does the motion differ from the person in the background to the two spinning girls?
3. Describe the motion of the spinning girls in relation to each other and in relation to the creeper in the background.
Some relevant but disorganized thoughts:
-Say the distance between the spinning girls is unchanging as they rotate. Are they moving compared to each other, then?
-Does this mean that Andrea-Creeper the only one moving relative to the spinning girls?
Things to ponder.
Graphitude
Lets do some definitions, first off.
Qualitative data: data that shows general trends or patterns, not individual amounts.
Quantitative data: data that shows accurate amounts and measurements.
We have been discussing graphs in class over the past week. From our discussions, I have gathered that:
-a motion map is an effective method of physically representing the motion of an object. The distance is established, and the object is drawn at intervals to represent where it is at certain times.
-Advantage: actually shows you the object's path.
-Disadvantage: Not as exact or quantitative as it could be. A motion map is more qualitative, meaning that it gives you the gist of things.
-an x-t graph is a more quantitative way of representing data. When representing movement, units of measurement are given for distance (typically x-axis) and time (typically y-axis). The slope of the data, or the difference between the points, is the speed.
-Advantage: Data can be quantitatively displayed.
-Disadvantage: If the data being displayed isn't perfectly linear, the slope represents average speed instead of the actual changing speed. Also, the dots of data plotted on an x-t graph do not actually show you the objects path--for example, a graph with a diagonal line going upwards to the right does not mean that the object moved upwards to the right. X-t graphs show changes in position and distance, not the actual path of the object, and this can be confusing to someone with little experience reading graphs or interpreting data.
Examples (graphs created by me, with the aid of this website):
Graph A: Constant Speed
The object portrayed in this graph starts at zero seconds, zero meters. Once in motion, it goes five meters per one second--meaning that it's slope is 5 meters over 1 second. This also means that the speed of the object, which is the same as the slope, is 5 meters per second.
The difference between the plotted points is consistently 5 over 1, meaning that the slope and therefore the speed of the object is constant. Its shape is due to the fact that the object moves the same number of meters each second as time goes by.
Graph B: Increasing Speed
In this graph, the object in motion increases by changing amounts. From 0 to 1 seconds, the object moves 0.5 meter. From 1 to 2 seconds, the object moves 1 meters, and from 2 to 3 seconds, the object moves 1.5 meters. The distance between the rest of the points increases by 0.5 meters for each second. From this we know that the slope is not staying the same over time, but increasing, meaning that the speed of the object is increasing over time as well. The shape of the graph is due to the fact that the object is moving more meters per second as time goes by.
Graph C: Decreasing Speed
In this graph, the difference between 1 and 2 seconds is 4 meters. The difference between 2 and 3 seconds is 3.5 meters, and the difference between 3 and 4 seconds is 3 meters. The difference between the points decreases by 0.5 meters each seconds. From this we can see that the slope is decreasing as time passes, meaning that the speed is decreasing as well. The shape of the graph is due to the fact that as time goes by, the object moves fewer meters each second.
From the advantages and disadvantages of these two methods of showing data, I have concluded that both would be useful to use if the intention was to provide the most complete and understandable representation of the data. However, if I had to choose one as being the most useful to me, I would pick the x-t graph, because of its accuracy and the fact that I understand and am able to read it.
This Thing You Call "Relative Motion"
So we did the project and whatnot, but what does it mean? And why does it matter?
Well, relative motion is defined as the motion of an object relative to another object.
For motion to occur, there must be something to compare the motion to--otherwise, how could you possibly know that it was moving? Think about how we describe a moving object--it got closer to me. It went away from the bus. For motion to occur, there has to be a change in distance, yes? And to measure this distance, we need a zero. This is the object/point in space that the object in motion is moving relative to. On a graph, it is the zero point (aptly named, this zero).
For example:
There are two cars parked next to each other in a parking lot, one red and one white. The red car starts up and drives forwards, away from the white car. Relative to the white car, the red car is moving, because the distance between them is changing. In this scenario, the white car is the zero and the red car is the object in motion.
But wait. If the definition of motion is a change in distance, wouldn't the white car be moving relative to the red car, too, even if it isn't the one driving away?
Yes. Exactly.
If you were to use the red car as the zero and the white car as the object in motion, the white car would be moving relative to the red car. In every situation, if object a is moving relative to object b, then the opposite is true as well. It just depends on where you place your zero.
So, keeping these ideas in mind, let's set up another scenario.
Now the red car and the white car are both driving down the road, the white one behind the red one, both going 35 miles per hour.
Because of their identical speed, the distance between them is not changing--but they're both being driven. Are they moving, relative to each other?
No.
The same rule still applies. If there is no change in distance between them, then, relative to each other, neither car was moving.
HOWEVER. This does not mean that neither car was moving--relative to other things.
Think of all the things that the cars' distances are increasing or decreasing from--the point in the parking lot at which they began driving, a sign that they pass by on the road, a hitchhiker left in the dust. So many possibilities.
Bottom line: If the distance is changing between objects, then they are bothing moving relative to each other.
And...why does it matter? Because all motion is relative. Without an object to compare it to (a zero), it is impossible describe (much less perceive) the motion of another object. Graphs cannot be made. Measurements cannot be taken. And the nice thing is, if you've ever described the motion of anything, you've been using the idea of relative motion your whole life without even realizing it.
How does it affect science?
To quote from this website:
"Motion means continuous change of position of an object with respect to an observer. To another observer in a different frame of reference the object may not be moving at all, or it may be moving in an entirely different manner. The motions of the planets were found in ancient times to appear quite complicated in the laboratory frame of reference of an observer on Earth. By transferring to the frame of reference of an imaginary observer on the Sun, Johannes Kepler showed that the relative motion of the planets could be simply described in terms of elliptical orbits. The validity of one description is no greater than the other, but the latter description is far more convenient."
Basically, it helps us to better understand the motion of objects by being able to use different reference points to perceive it.
Parallax
I am looking at a flower vase at the end of the next room, perhaps fifteen or twenty feet away.
It appears to be right in the middle of my line of vision.
Viewing with left eye: The vase seems more left-ish.
Viewing with right eye: The vase seems much more to the right.
Switching back and forth between using one eye or the other, but never both at one time, the vase appears to be jumping from left to right and right to left, depending on the eye. But the vase isn't actually moving, is it?
This phenomena can be described as parallax, "the apparent displacement of an observed object due to a change in the position of the observer." (link)
Think about it. You aren't a cyclops. Your eyes are positioned a small space away from each other. When observing with both eyes, we see an object in a single place, but when we switch between using one eye or the other, the apparent difference in the position of the object shows that each eye percieves it from a different angle.
On a larger scale, you could stand to the right of a chair. The chair, obviously, appears to be at your left.
Move behind the chair and it appears to be directly in front of you.
Move to the left of the chair, and now it is on your right.
Just like before, the observed object has not changed its position, but the observer has.
However, distance makes a difference as to how you perceive an object. If I do the same thing that I did to the vase with the house outside of the window, all the way across the street, it doesn't seem to "move" at all. Why? My eyes are still perceiving the house from different points, right?
Fact is, the farther away an object is, the less its position will seem to change. Relative to the distance between my eyes and the house, the distance between my eyes is very small. To notice any change in postion, I would have to view the house from two points that are farther apart, like from one end of the block to the other. Likewise, the greater the distance is between the points of observation, the more the position of the observed object will appear to have changed.
So, when observing an object close to you that is aligned with a distant object and observing it from each individual eye, the close object will appear to move a lot in comparison to the distant object. They will no longer be aligned. This fact is particularly useful to astronomers.
How is parallax used?
Astronomers can use parallax to determine the distance to stars. It might seem like a far stretch from looking at a vase in your living room, but the principal is the same.
(Info and image pertaining to astronomy obtained from this website. Anything in quotations is text taken directly from the site.)
In this case, a person's eyes are not far enough apart to experience parallax when looking at a star. A much greater distance is needed--like the diameter of the earth's path around the sun, as shown at left.
"The parallax angle, P, is measured by comparing the nearby star's position to the stable position of distant background stars."
Basically, the astronomers use the known characteristics of triangles to determine the angles and therefore distances of the triangles created by the points of observation, the star being observed, and the distant stars being used as background reference points.
Using the operations of sine, cosign or tangent, if one of the other angles of the triangle is known (like the distance from the earth to the sun) ans the angles have been found, the distance from the earth to the star is able to be calculated.