Movin' Around

If you saw the title of my post today and thought that I was going to start talking about dancing, you are sadly mistaken.  I'm afraid that dancing doesn't really have to do with physics... or maybe it does.  If you fall, that has to do with gravity, and that's physics, right?

Anyway, now that I've gotten completely off track, let me start over.  This week in class, we started to learn about movement.  Again, it's not the dancing kind, it's the buggy car kind!

Let me explain before you go around thinking I've gone completely nuts.  All I mean, is that this week, we did the Buggy Car Lab!  Sounds like a fun name, right?  So far, I think this has been the best lab.  However, I think that's mostly due to the fact that all of the other labs have been kind of basic and not much about moving around.  They were mainly about measurements.

On the other hand, this time, we were asked, "What relationship exists between the time the buggy runs and its position?" This meant that we would get to work with a little car and measure how far it would go in a certain amount of time.  I must admit, it isn't too bad for a lab, although I'm still looking for something with a little more pizzazz.

The Process

Before we began, we had to figure out how in the world we were going to do this lab.  Of course, we were left to ourselves to figure this out, so we started talking.

As a group, we decided to run the buggy by and meter stick and some tape.  For every five seconds we were to make a mark at the point where the buggy was at.  Afterward, we decided to measure the distance from the starting point to each of the marks.  However, there was a catch.  Our teacher decided that we had to do this all in one continuous run.  That being said, we weren't allowed to stop the buggy and make the mark.  We had to do it while it was moving.

Surprisingly, it actually wasn't that hard.  We got it done in record time, but just when we thought we were done, our teacher gave us another task to do.  We were now to start 40cm. behind our original starting point.  This wasn't really hard either, as you may have guessed, and again, we finished quickly.  The only problem was our data.

Got 99 Problems, What to do With Our Graph, Sadly, is One

First and second sets of data on the left and graph on the right.

We weren't really sure what to do with it.  Of course, all the information was right, but we weren't sure if we should add the data point (0,0).  As a group, we decided that for the first set of data, we should use (0,0) because it makes logical sense.  If you are at the starting point and your time is 0 seconds, then you obviously haven't moved from that point, so you are also at 0cm.  On the other hand, for the second set of data, the buggy was 40cm. away from the starting point, so at the time of 0 seconds, the buggy was at 40cm. 

We still weren't sure about this predicament, especially for the second set of data.  Then came the graph problems.  The first graph for the first set of data was obvious because the data increased at a constant rate, but for the second graph with the second set of data, we weren't sure if we should make the first two points at -40cm. and -5cm., or at 40cm. and 5cm.

This is probably the point at which I should explain the idea of reference point and position.  Reference point it the point at which, by looking at it, you can tell that the object moved.  For example, if your friend is standing 2 meters away from the whiteboard and then he moves so that he is now 5 meters away from the whiteboard, you know for a fact that he moved because he is now 3 more meters away from the whiteboard than when he started.  In this scenario, the whiteboard was your reference point because you saw that he moved 3 more meters away from it. 

For position, you must use your reference point.  Let's say that your reference point is the place where another person started.  If that person moved 10 meters North of that point, his position is now 10 meters North of that point.  Basically, position involves the distance away from the reference point, as well as the direction which the object traveled.

To relate all this to my lab, we weren't sure if the distance or postion from the reference point (or the starting point) would be -40cm. and -5cm. for the second set of data because it was in the opposite direction.  In the end, my group decided to go with positive, for now.

Graphing

This time around, our first set of points was graphed as a linear, direct, and proportional line, but our second set of points seemed to look like an absolute value graph.  We will have to bring this up, as well as the other controversial topics, in our next class discussion.

Reflection

This week, I have decided to try a new idea. I have begun to ask questions during our class discussions, even if I already know the answer. I think this will help me, as well as my fellow students.  Also, I am still doing well at participating and understanding the topic at hand.  Movement doesn't seem like a topic that will be very hard to pick up.  The only really odd thing to me is that, last year when I took physics, I don't remember going into so much depth in the idea of movement.  Is this better for me?

Estimating Using Powers of Ten

On Thursday, my teacher decided on teaching us how to estimate using powers of ten.  On an unrelated topic, before we began, our class switched seats, so I'm with a new group.  I like this group, but I also liked my old one.  We had some fun times together, but I think this group will also have its fun moments.

To get back on topic, my teacher showed us the powers of ten first.  After all, you can't do anything unless you know the fundamentals.

Powers of ten:

10^-3= 0.001

10^-2= 0.01

10^-1= 0.1

10^0= 1

10^1= 10

10^2= 100

10^3= 1000

These powers of ten go on and on in both directions, but we decided to just stick with the simplest ones for now.  However, our class got confused when we were asked to round. What if our number is 500? Would we choose 10^2 as the estimation or 10^3?  To solve this questions, we figured out what 10^0.5 would be. That number is in between 10^0 and 10^1, so it should give us the number at which we would round up. Everything below that number we would round down.  The number came out to be 3.16.  We then found 10^1.5 which is 31.6, and 10^2.5, which is 316, and so on and so forth.  Basically, we now know that, for the number 500 for example, we would round up to 10^3 because it is more than 316.

Wacky Question 1

Our teacher then decided to use the wackiest questions to help teach us how to estimate using the powers of ten.  Our first question was, "How many basketballs could fit into the gym?"  Weird question right? However, it was actually quite fun to figure out.

My group and I estimated the length, width, and height of the gym to the powers of ten.

Gym Estimations:

Length: 10^1 meters

Width: 10^1 meters

Height: 10^1 meters

To figure this out, all we did was choose the most logical answer.  We then did the same thing with the diameter of the basketball, which we found to logically be 10^-1 meters.  However, what we really needed was the volume of the basketball and the gym.  For the gym, you would multiply the three dimensions and get 10^3 meters.  For the basketball, some confusion came about.  Do we put the ball into a cube and estimate the volume of the cube?  That would be pretty close to the volume of the basketball.  Or, do we use the actual formula for the volume of a sphere to be more precise?  My teacher didn't seem to mind either way, so we tried both.  Using the cube method, we got 10^-3 meters, but using the formula method, we got 10^-2 meters.  We didn't really discuss what to do when this happens, so we just figured out how many basketballs would fit in the gym using both.  To find the answer, you would do 10^3/10^-2 or 10^3/10^-3 and you would get either 10^5 basketballs or 10^6 basketballs.  Basically, you would divide the volume of the gym by the volume of a basketball to find out how many basketball would fit inside the gym.

Wacky Question 2

We also used the same process when my teacher asked us to figure out how many marbles would fit into the average UCS school bus.  Because I already showed you the process, I'm not going to do it again, but just for fun, the answer came out to be 10^7 marbles or 10,000,000 marbles.  Pretty big number right?  That would probably be really expensive to buy all the marbled to fit into one school bus.

Helpful Hints

• When dividing with numbers with exponents, subtract the exponents to get your answer.  For example, when doing 10^3/10^-3, you would do 3+ (-3) for your exponents, and your final answer would be 10^6.
• When rounding, if the number is greater than 3.16, 31.6, 316, and so on, then round up a power of ten, but if the number is less, round down a number of ten.
• When multiplying numbers with exponents, add the exponents together.  If you have 10^1 times 10^1 times 10^0, you would do 1+ 1+ 0, making your final answer, 10^2.
• Knowing the actual dimensions helps when estimating.

Reflection

Out of all the classes I have had so far in physics, I personally believe that this one was the most confusing.  I understood the general idea, but I don't think I have a firm grasp on it yet.  I've decided that I will practice until I get it down, just in case I need to use it again, which I probably will.

How to Convert!

Yesterday in class, to sum it up, all we did was convert.  Converting here, converting there. And of course, we learned different ways to do it.  

Kill Him Dead But Don't Call Me?

The first and most basic way to convert is the way almost all the elementary teachers teach it. 

KHDU(or B)DCM, or King Henry Drinks Unlimited Delicious Chocolate Milk.  I've even heard of Kill Him Dead But Don't Call Me.  That was a pretty odd one, but that's besides the point! This trick however, actually stands for the way to convert between metric units.

Kilo Hecto Deca Unit(or Base) Deci Centi Milli

All you do is take your given number, let's say 6 meters, and slide it along this set of letters.  6 meters is a unit or base, so you would start at U (or B).  You would then jump from letter to letter, moving the decimal point of the number as you go along, until you reach the unit you are converting to.  If you convert 6 meters to kilometers, you would move the decimal 3 places to the left, making the new number 0.006 kilometers.  If you converted 6 meters to millimeters, you would move the decimal 3 places to the right, making it 6,000 millimeters.  This does make logical sense though, because when you convert to a smaller number, the resulting number should be greater, and vice versa.

What, There's More!

Just when we thought we had it down, my teacher throws us a curve ball.  "Wait there's more!"  It sounds just like a TV commercial to me.  "Don't forget that for a special price, we'll throw in more units! So get to work now!"  I knew it.  I knew there was something else.  

According to this commercial, the KHDU(or B)DCM doesn't really work as great as you might assume. Yay... not.  That means that there are more units than just what is on this conversion method.  And, guess what, it takes extra work as your special price!  It would actually look like this:

...Tera Giga Mega Kilo Hecto Deca Unit Deci Centi Milli Micro Nano Pico...

Plus, it gets more confusing!  First of all, it goes on forever, and second of all, once you get past Milli or Kilo, you can no longer do the sliding decimal method.  It turns out that, once you get past the two, there is actually 1,000 in each.  I know that sounds a little weird, but by this I mean that there are 1,000 kilometers in a mega meter, for example.  Now, the only problem is how to convert to these bigger numbers.

New Methods

Our teacher told us about two ways to convert between numbers instead of KHDUDCM.  Now, we can use Dimensional Analysis or cross-multiplying.

Cross-Multiplying

This is the first way we learned, which is kind of easier.  It is basically a one or two step process of multiplying two fractions or ratios, but not across. You would multiply diagonally. For example:

6/2 = x/2

You would do 6 times 2 and x times 2 making, your answer be 12=2x.

You would then divide by 2 and find your answer of x to be 6.

To convert for this problem, let's say you were converting from 2 feet to x inches.  You would set up a proportion of 2ft./x in. = 1ft./12 in.  This way,you would only come out with inches in the end.  However, this method does have its drawbacks.  For example, you cannot convert between multiple units at the same time. That's where Dimensional Analysis comes in.

Dimensional Analysis

The second way is this Dimensional Analysis method.  This way, you can keep things organized easier and convert between multiple units at the same time.  However, this way, you have to multiply across, not diagonally, and you must have the same units opposite each other so they cancel and you are only left with the units you want.  Let's say you were converting from 32km./hr. to x mi./hr. :

32km/1hr = 0.6214mi/1km = 1hr/60min. 

You would then multiply across and get 19.8848mi/60min.  This is because the km and hours would cancel and you would only be left with the units you want to get to.

Then, you would simplify to get it to x miles for every 1 hour getting 0.33mi/hr as your final answer.

Personally, I find this method to be easier.  It is easier for me to see visually and it is easier for me to check to make sure I did my work right.  However, it all depends on what is better for you. 

Also, as a little side note, when rounding, you need to round to the most appropriate number.  If the number you are coming from, like 32km, is rounded two digits already, then your answer should be rounded two digits as well.  Also, the more decimals there are, the more precise the number is. 32.0000000 is more precise than just 32.

Reflection

I think I am still doing a good job in class.  I participated in class and helped out in my group discussions.  I also have decided to do dimensional analysis as my main method because it's easier.  I have just now realized that I should be working on the things that work better for me, not the confusing way.  I believe that you should still try to understand the more confusing way, but if you just can't get it, you shouldn't force yourself to do it.

No Lab, Just Talk

This week my class and I talked even more.  This time we discussed three other labs and then we talked a little about how to convert between metric units.  These labs were the Tile Lab, the Lever Lab, and the Pendulum Lab.  Now, just to let you know, my group and I only did one of these labs, so I won't be able to put down as much on the topic as I usually would.

The Tile Lab

Before I begin, I have to say that I did do this lab, so I know at least how the procedure went.

For the Tile Lab, we were asked, "Is there a relationship between the area and the mass of the tiles?"  My group and I thought that there was, and that it would be, a linear, direct, and proportional relationship (at least that's what we drew in our predictive graph).  We then set off to work.

To measure the area, we traced the tiles on graph paper and counted the squares inside the shape to find the area.  For the mass,  we measured it on a triple beam balance.  We then recorded the information and graphed it.  According to our graph, we did end up seeing a direct and linear relationship.  Was it proportional though?

This was where our class discussion came in.  We discussed for a while.  For this discussion, we found:

• The relationship would be proportional because we would expect the graph to go through (0,0).  It makes logical sense because, if there is 0 area, there has to be 0 mass because there wouldn't be anything there.  It is also proportional because the graph would go through the origin, fitting our definition of proportional.
• We also realized that our teacher must have cut the tiles into weird and different shapes on purpose to make us see what would happen if the tiles were all different.
• We decided that it was more efficient to count squares to find the area than to do anything else. Although, another idea was brought up where we would divide the tile into smaller shapes, find the area of each shape, and then add them together. We aren't sure if that would be more efficient however, because we didn't try it.
• The five percent rule tells how good the area relates to the mass.
• We are positive that there is a relationship that is direct and linear.
• We concluded that for every square the area increased, the mass would increas by 0.1975 grams.

The Lever Lab

After the Tile Lab, we discussed the lever lab.  We were asked, "Is there a relationship between the mass of the weight and the distance to the fulcrum." Keep in mind that my group did not do this lab, so I'm not sure exactly how the other groups did it.  According to the groups, they did say that their procedure was to balance a weight on a stick.  Depending on the mass of the weight, they would need to move the weight closer or farther to the fulcrum.  During our class discussion, we decided:

• Our clonclusion would be that for every gram of mass, the distance to the fulcrum would decrease by an exponent.
• The graph and data would never hit (0,0) because there would always be some weight on the stick. This would mean that the five percent rule wouldn't apply. 
• The relationship is indirect because when you increase one, the other decreases.
• The relationship is inversely proportional because as one doubles, the other halves.
• When choosing units, you should choose the one that makes the most sense and works the best for you.
• There is no y-intercept or x-intercept in this relationship.
• y and x go on infinitely. 
• The best type of graph for this relationship is a power graph.
• Distance= 1393x^-1
• Distance(inches)=1393(inches times grams)/mass(grams)
• inches times grams= unit of torque

The Pendulum Lab

The last lab we discussed was the pendulum lab.  For this lab, we were asked, "What is the relationship between the mass and the length of a period?" Again, my group and I did not do this lab, but I was told that the groups put a weight on a pendulum and timed how long it took to swing back and forth.  The groups would add mass to the weight and see if it would effect the time.  In the class discussion, we decided:

• For every 500 grams of mass added, the period stays relatively the same.
• The groups time depended on how long they decided a period was.  Some groups thought 10 swings was a period, while another thought 2 swings was.
• The more swings you measure the more accurate your data is?
• There was systematic error when the person clicked the timer to measure the time.
• Scientific notation: 7 E -5 and E= times 10, so 7 times 10^-5 is 0.00007.
• To be more accurate, we could use motion sensors or photo gates.
• The graph is a straight line, so the equation should be about y=17.
• Bowling Ball vs. Tennis Ball: The amount of time for a period wouldn't change.  Their periods would both be the same.
• Periods are the same no matter how big or heavy an object is.  This is because of the acceleration of gravity.  No matter what the object is or where you are one Earth, the pull of gravity is always the same, causing it to fall, swing, or whatever it is doing at the same rate as another object.
• There is no relationship.  If you do something to one, nothing will happen to the other.
• It has a slope of 0.

Converting Between Metric Units

We also talked somewhat about converting between metric units.  We came up with the basic idea of KHDUDCM or King Henry Drinks Unlimited Delicious Chocolate Milk.  However, we know that there are other units that we need to convert to, so there has to be another way.  I think we will talk about it next class.

Reflection

I think that this week I definitely improved in my participation skills.  Our teacher told us to get our ideas out there, and that is exactly what I am trying to do.  I am just trying to get better every week, and I hope that I will be a master of all this by the end of the year.  I still feel like I am understanding the information we have been discussing, and I am beginning to become more comfortable with my fellow students. Until next week!

The Next Week...

Discussion after discussion after discussion.  That's all we've done this entire week.  Now, I like discussing as much as the next guy, but sometimes it can become a little too much.

 For our discussion, we decided to talk about a packet we did last week for homework.  The title is Proportional Reasoning, and let me tell you I was a little skeptical of it.  I'm not the best at reasoning.  I can do it, but sometimes I write a little too much.  It just goes on and on unless I stop myself because I feel the need to make sure the reader of my work understands exactly what I'm saying.  I think this comes from the need to get a good grade, but I'm not exactly sure.  At least I'm working on it.

Anyway, the packet was about understanding proportions, converting to different units, and understanding different types of graphs.  From my standpoint, I was pretty okay with the proportions and conversions part. I had learned about both in math and science last year so I had them pretty down pat.  The thing that really tripped me up was the different types of graphs.  I knew I had learned it before but it was still hazy in my head.  It was probably the same for everyone, because my teacher decided to talk about that part the most.

I do remember talking about the answers of the packet with my group first to compare what we got.  There were some varying answers every few questions or so, but overall my group had pretty similar results.  This was mostly for the proportions and converting part.  However, when we came to the graphs, we were all stumped.  Some of us thought one thing while the rest of us thought another, and we didn't know what to do.

Later in the week, we did a Socratic Circle to talk about the graph questions.  For those of you who don't know what a Socratic Circle is, it's when the class is divided into two circles; the inner circle and the outer circle.  The inner circle actually talks about the topic at hand, while the outer circle observes the inner circle and comments on what the group did well and what they did not-so-well.  The circles then switch, and they discuss again.  This was our first one in physics, so it wasn't fantastic.  However, we did come up with some ideas.
For the equation y=a/(bx^2) :

• When a is doubled, keeping b and x constant, y also doubles.
• When b is doubled, keeping a and x constant, y halves.
• When x is doubled, keeping a and b constant, y quarters.
• Plugging in numbers works best.
• When the number doubling is in the numerator, y increases.
• When the number doubling is in the denominator, y decreases.
• You should plug in simple constants.

When x is halved...

• In the equation y=kx, y is halved.
• In the equation y=k/x, y us doubled.
• In the equation y=k/x^2, y is quartered.

The last time we met for class this week, we had a class discussion about different types of graphs in our packet.  Those different types were linear, direct, directly proportional, indirect, and inversely proportional. We discussed the meaning of these words, and drew graphs to see what they would look like.  We decided that:

• Linear- A straight line.
• Direct- When x goes up, y goes up or when x goes down, y goes down (they both have to do the same thing).
• Directly Proportional- x to y is the same ratio (Example: If you double x, you have to double y), the slope is always constant, and the line has to go through the origin.
• Indirect- Not direct. x and y do opposite things (Example: if x goes up, y goes down).  Also, anything not direct is indirect (Example: vertical and horizontal lines).
• Inversely Proportional- When x doubles, y halves (y is like the reciprocal of y).  Also, sometimes inverse can be indirect depending on the situation.
• Not all curved lines are exponential.
• Proportional lines cannot have y-intercepts.
• y=kx is direct, linear, and directly proportional.
• y=kx+b is linear and direct.
• y= -kx+b is linear and indirect.

Reflection

This week was a very interesting one with no labs.  Just continuous talking and reviewing topics.  I think I need to make sure that it is known when I have an idea or that I need to raise my hand more.  I have to say thanks to my teacher because he actually asked if I had an opinion on the topic multiple times.  I think he knew that I had something to say.  I also think that I am grasping the concept.  I don't find this too hard and I think that at the very least I understand it at the basic level.  I wonder what we will do next week.