Car Crashes

This week's physics class, as far as I'm concerned, was the most fun yet.  Even my friend said that she now officially loves physics because of this class.  I mean, we did get to "blow things up."

My teacher said that this week, instead of having another discussion on motion before the Thanksgiving break (even though he does agree that we need more), he decided to let us "make" action movies. Apparently he loves them, so he came up with three different scenarios for us to chose from.

The Rules

My teacher decided on giving us a set of rules so that this wouldn't be too easy.  They are as follows:

1. You only get one shot at it, and if you screw up, "you'll never work in this town again!"
2. You cannot test it out beforehand.
3. You must follow your scenario exactly, meaning that, if it gives you measurements, you must use them.
4. Your two cars will be at different speeds.
5. You cannot run both cars at the same time.  Only one can run.  Otherwise, you will be disqualified.
6. If you make the two cars crash and you follow the scenario, you will "have your people call his people."

Our Scenario

My group and I decided to chose scenario number 1.  In this scenario, we had to have two cars come at each other from two different directions.  They MUST be 2 meters away from the crash point, but we get to decide at what time we should start each car.

Of course, one car was slower and one car was faster.  To make it a bit more comical, we decided to name the slower car Grandma and the faster car something about speed.  I can't remember the real name we came up for him, except for the fact that I called him Speedy McSpeedson.

Our Process

To find out how fast each of the cars went, we decided to measure how much time it took for each car to travel 1 meter.  We then doubled it to see how much time it took for 2 meters.  For each car, we actually recorded the time 5 different times to make it more accurate, and then we found the average.

• Grandma: 1 meter= 5.6 seconds, 2 meters= 11.2 seconds
• Speedy McSpeedson: 1 meters= 4.26 seconds, 2 meters= 8.52 seconds

From this data, you can obviously tell that Speedy was faster than Grandma.  However, we actually got stumped on what to do next. Eventually, we figured out that all you had to do was subtract the two times to find out when to release the second car.  We did 11.2- 8.52 and found that the answer was 2.7 seconds, meaning that we needed to release Speedy McSpeedson 2.7 seconds after we released Grandma.

In the End...

In the end, we ended up succeeding and causing the cars to crash.  It felt good to have gotten it right.  I'm very happy that I got to work with my group.  They all did a great job trying to figure out the answer, and everyone in the class, including myself, had a great time.  Personally, I would like to do another activity like this one again.

Another Worksheet... Darn

Hello everyone out there listening, or I guess reading, if you want to get technical.  This week, just like the last one, I had to miss class.  You can blame my orthodontist for this one, but of course, missing class meant missing another discussion, and I really don't like missing discussions.  I mean, those things contain some valuable information which now, because of my appointment, I will never know.  Really, all I took out of this week was a fairly easy fiesta (quiz) and a worksheet.

Fiesta

You all know how it is.  When you think something is easy, you usually end up doing horrible, especially in a class like math.  However, I seemed to understand the fiesta.  After all, it was on Position vs. Time graphs which are easier for me to comprehend anyway, so overall I think I did pretty good.  I've got my fingers crossed.

Worksheet

The worksheet was called Constant Velocity Model Worksheet 4: Velocity vs. Time Graphs and Displacement.  We were told to do the worksheet with our tables and discuss any questions we had. Again, like the fiesta, I didn't find this to be too hard, and I found it very helpful to work and discuss in a group.

Basically, the worksheet went through making motion maps, writing written descriptions of the motion of objects, making Position vs. Time graphs, making Velocity vs. Time graphs, writing mathematical expressions for motion, and determining displacement.  However, there were three other things which still kind of have me confused; the area under the curve, average velocity, and average speed.

The Area Under the Curve

The only reason I understood this part of the worksheet was because I had actually watched a video on my own about it.  The area under the curve is basically the area of the "squares," I guess, on a Velocity vs. Time graph.  You would basically do length times width or base times height or side times side (whichever you prefer) to get the area of each little rectangle, and then you would add them all together to find the total area under the curve.  Supposedly, this comes out to the displacement of the object, so this could actually be quite a handy way to find it.

The graph above is actually the Velocity vs. Time graph from the worksheet.  If you notice, there are three rectangles, and if you were to find the area of those and add them, then you would find the total displacement.

If you were wondering what you do for the "non-rectangle" parts, you basically do nothing. Technically, you would find the area of them too, but since it isn't a rectangle, it only has one dimension, so its area is technically 0.  Basically, there is no need to find it because it is always 0.

Average Velocity

For this one, I must thank my group for helping me figure it out.  To find average velocity, you first need to know what velocity is.

Velocity is basically speed with direction included.  This hints that velocity can be negative.  If you used the graph above, and you were asked to find the average velocity form t=4 to t=8, you could do so easily.

All you do is take the firs velocity at t=4, which happens to be 3 meters/second, and add the velocity at t=8 which is -5 meters/second. So, 3+(-5)= -2 meters/second.

You would then divide by the amount of time passing to get the average.  This comes out to be 4 seconds, so you would do -2/4 which is equal to-1/2 meters/second.

Average Speed

Again, I must thank my group for helping me figure this out.  However, we still aren't 100% positive on this one, so I may be wrong in what I am saying.  To find average speed, you need to know what speed is.

Speed is distance divided by time.  There is no mention of direction in the definition, so we know that speed cannot be negative. 

If you were asked to find the average speed from t=4 to t=8, you would take the two velocities mentioned before and make them positive.  You would get 3+5=8 meters/second, and you would then divide by 4 to get 2 meters/second.

Reflection

Again, I am not positive on the average speed portion of this worksheet, but I am fairly certain about the other parts.  Truthfully, I wish that I hadn't missed two days of class.  It really makes me feel behind, but I guess I have to embrace the confusion like they always say.  I hope that I can get back on track next class. Although, I know for sure that all I can do is try my best.

Lists of Motion Info

This week, sadly, I was only able to get one class worth of information.  Today in fact, was supposed to be my second day for physics this week, but of course I had to be absent.  I really hope that I didn't miss too much, and that our fiesta (test, quiz thing) wasn't too hard.

Anyway, this week, we continued to focus on motion.  However, we definitely got more in-depth on different parts, especially this new term called displacement.

Displacement is the change in position, but it is NOT I repeat NOT distance, however close the two words may sound.  I mean really, why start them both with the letter D?  That just makes things more confusing for everyone.  To explain, I should probably review the words that could possibly confuse me more and show how they are different.

The Differences

1. Distance

• Distance is the total amount traveled.  For example, if you walk 9 steps to the right, 3 steps back, and 1 step left, your distance is equal to 13 steps.
• Distance compares two (or more) locations.  For example, if you travel from point A to point B, your distance is the length between the two.

2. Position

• Position is the point you are at at one point in time.
• To find your position, you use your reference point.
• There is only one way you can get to the position that someone else is in right now.
• Position deals with direction.
• Position can be negative or positive depending on the direction relative to the reference point.
• Position is a single point, like Point A. 
• To sum it up, position is the distance from a reference point (with direction) at one point in time.

3. Displacement

• Displacement is the change in position.
• Displacement has direction associated with it.
• It can be negative or positive.
• Displacement is where you end up relative to your starting point.  For example, if you go on a long journey, the only thing that matters for displacement is where you end up and how far that end point is from where you started.
• In another sense, if you start from point A, then walk to point B, then walk to point C, displacement is only how far you are from point A to point C.
• Displacement uses the starting point, not the reference point.
• To sum it up, displacement is the change in position relative to the starting point, not the reference point.

Putting Things Together

So now that you know that these three terms are obviously different, let's relate them to something else... like... Speed and Velocity!

As a class, we deduced that displacement seems to go more with velocity, while distance goes with speed.

Speed= Distance/time

Velocity= speed with direction= Distance/time with direction= Displacement/time

Reflection

I realize that this blog is kind of a mess, but that's a little like how I feel right now.  Missing today definitely didn't help, but it couldn't be helped.  I'm still pretty confused, although a little less so, and I hope that my understanding will increase next week.  However, I will have to take my fiesta next week, and I am a little worried.  I guess all I can do is try.

All Parts of Motion

Position vs. Time graphs, Velocity vs. Time graphs, and Motion Maps.  Anyone know what those are? Anyone?  Well I'm not sure I know either.

This week, we learned about the three things mentioned above, but of course, my mind jumped from certainty to confusion and back again, as I tried to figure out how they worked.  I felt so dumb, especially because I had gone through all of this last year, with the exception of motion maps.  I started off only remembering the names.  Then, there was a flash of light and I instantly remembered what they were, but then I forgot how to draw them.  Then, there was yet another flash of light as I remembered, but now I'm not positive I'm right.

My class seems to be very confused, and that is not boosting my confidence.  Usually, I have a pretty good grasp on what's going on, and I still kinda do.  It's just that we haven't really figured out exactly what they are, and of course our teacher won't tell us.  We have to learn it for ourselves, and I guess that does make sense to some degree.

My First Understandings

This week, we did a lab that dealt with Position vs. Time graphs and Velocity vs. Time graphs.  We were given one of them, and we had to figure out the other.  To do so, we were given a motion sensor and a computer.  We had to try to mimic the graph given, and then draw the other, so if we were given a Position vs. Time graph, we had to do a "walk" in front of the sensor to try to make that graph.  At the same time, the computer would make the other graph, in this case a Velocity vs. Time graph, and we would draw it on our packet.  Then, we would put our "walk" into words, and then draw a Motion Map.

Off of this lab, my understandings were:

• I have no idea how to do a motion map.
• Position vs. Time graphs are easier to do than Velocity vs. Time graphs.
• Your motion sensor is the reference point. (definition in my other post http://ittakesphysics.blogspot.com/2013/10/movin-around.html )
• When you walk towards the motion sensor (reference point), your Position vs. Time graph goes down towards the x-axis, and when you walk away, your Position vs. Time graph goes away from the x-axis.
• If you go at a constant speed, your slope for your Position vs. Time graph is constant.
• If the line is flat on a Position vs. Time graph, your position is constant.
• I seem to only understand Position vs. Time graphs.
• I think I did the lab wrong...

Worksheet Understandings

Then my teacher decided to give us a worksheet called Constant Velocity Particle Model Worksheet 2: Motion Maps and Velocity vs. Time Graphs. Yep, it's a mouthful, but it helped me out greatly.

Off this worksheet, I found out that:

• When an object moves in a negative direction, the velocity is shown as a negative velocity on a Velocity vs. Time graph and when moving in a positive direction, it's the opposite.
• When an object isn't moving, the velocity is 0.
• When an object moves at a steady speed, the velocity is a constant, straight line.
• If the object starts off in one direction at a constant speed and then changes its direction, but still goes at the same constant speed, the graph would look like this:
  
  
• If the object is going the same speed, but in a different direction, the line needs to be at the same number, but negative.
• If the object changes speed, you draw a line straight down because it is changing its velocity instantly.
• This website helped: http://www.physicsclassroom.com/class/1dkin/u1l4b.cfm

Motion Map Understanding

Our teacher then emailed us a reading on motion maps to help us do them on the worksheet. It's http://daisleyphysics.com/worksheets/mmap.pdf 

I learned that:

• Motion maps look like this:

• If an object moves at a constant speed, the arrows have to be the same length.
• To draw one, you must put a point for each time marked.
• The slower the speed, the shorter the arrow, and the faster the speed, the longer the arrow.
• If an object doesn't move, or stays in the same position, you use dots for each amount of time, and since the object doesn't move, the dots stack.
• From the picture above, each notch on the line is a meter.  For the first arrow, it starts at 0 meters.
• If an object turns around, the arrows do too, and they can go over each other because they head back to 0 meters.
• If an object moves in a positive direction, the arrows go to the right, and if the object moves in a negative direction, the arrows go to the left.
• I am still a little confused.

Reflection

This week, I was more confused than I have ever been so far in the year.  However, we still need to have a real, in-depth discussion on it, and I think that will help.  I am doing good in my groups as well, and I am still participating and helping out.  I also feel like I only talk when I need to, at least that's what I try to do.  I am trying not to talk too much, and I am trying not to talk too little.  I guess it's all about making sure I understand, and that is why I have decided to ask questions to clarify certain things that we talk about.

Motion Detectors, Cyclists, and Motion Maps

Hey everyone!  Don't worry, I'm still here, but this week, I've come to the realization that my blogs are long... VERY long.  I've realized that you guys probably don't want to read all that lengthy garble, so I'm going to try to cut it down, just for you.  You had better feel special...

Anyway, this week in class, we discussed motion... again.

I have this odd feeling that the motion section is going to last for a long while, seeing as how confused the class is, as well as myself at certain points in time.

For most of the week, we had a class discussion on this worksheet we did called "Unit 2 Worksheet 1".  I know guys, I love the name just as much as you do.

Question 1 

Anyway, for this worksheet, we were asked multiple questions about this graph for question 1:

If you didn't read the little blip above the graph, this graph is specifically a position vs. time graph and it has to do with 2 cyclists, Cyclist A and Cyclist B.  Position is the y-axis (in meters) and time is the x-axis (in seconds).  In our class discussion, we found:

• The cyclists do not start at the same point.  Cyclist B starts before cyclist A because it is farther up the y-axis.
• The reference point is the origin which is where Cyclist A started.
• When the time is 7 seconds, Cyclist A is ahead because it is above Cyclist B, so it is in a position which is farther away.
• When the time is 3 seconds, cyclist A is travelling faster because its slope is steeper.  Although, this is what I believe.  There is some controversy in my class on whether or not the slope is the speed.
• Their velocities aren't equal at any time.  Again, this is what I believe because it is still being debated.  To me, their slopes are never the same, so their velocities aren't.
• At the intersection of the two lines, they are at the same position at the same time.  However, they are not at the same speed or velocity.
• The biker's speeds are constant because it is a straight line.  My belief again.
• My theory: Velocity=Distance/Time and since position is measured in distance (y-axis) and time is the x-axis, it only makes sense that the slope is velocity.
• You don't travel a position, you travel a distance, so a certain point is a position, while the line is made up of tons of different positions.
• Position= Speed times Time + Starting Position or P=Speed times t + Po

Question 2

For question 2, we used the original graph and another:

We were asked basically the same questions as in question 1.  As a class, we found:

• Compared to the old Cyclist A, the new Cyclist A is going in the opposite direction.  It is going towards the x-axis or the starting point, instead of heading away from it.
• Compared to the old Cyclist B, the new Cyclist B is going the exact same speed.
• Cyclist A has the greater speed due to steeper slope.  Again, very controversial.
• At the intersection, they are at the same position at the same time.
• During the first 5 seconds, neither cyclist traveled farther.  At exactly 5 seconds, both cyclists end up at the same position.  The speed at which they got there doesn't make a difference.  They still ended up in the same place.

New Lab

We also started a new lab with motion sensors and motion maps.  However, since we haven't finished it yet, I will save it for  my next blog.  Also, does anyone know what a motion map is?

Reflection

This week, I have decided that my new goal is to speak only when I am absolutely necessary, and when I have a question of course.  If there is ever a lag in the conversation, I will try to come up with something to say or ask to keep the conversation going, as well as to benefit others.  Also, as mentioned before, my blogs are very long and "thorough" as my teacher would say.  I did try to cut it down, but I'm not sure it worked.  I just have so much to say.

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.

The Beginning Labs

Hello and welcome to my physics blog!  I'm Lisette LeMerise and this is my first blog entry of many to come. I hope that it all sounds okay.  During the first few weeks of school, my physics class has done multiple experiments.  In fact, my group has done exactly six. However, we have only discussed three of them together as a class.  The ones we discussed include the Hex Nut Lab, the Rod Lab, and Circle Lab #1 in that order.

Hex Nut Lab

For our starting lab, we did the Hex Nut Lab. We were asked, "What is the relationship between the number of hex nuts and the mass of the system?" and we were given multiple Petri dishes with different numbers of hex nuts inside.  However, we had one rule: Don't open the Petri dishes. With that one rule in mind, we started.  First, my group and I drew a predictive graph. We all agreed on a constant linear graph going in the upward direction, along with the prediction, "If the amount of hex nuts in the Petri dish increases, then the mass of the whole system will increase."

We decided to use a balance to measure the mass of the Petri dish with the hex nuts and count the number of hex nuts in each.  After it was all said and done, we recorded our data.  It is shown below left.

With this data, we soon graphed it (above right) and went into a class discussion.  We put all of our information on whiteboards and quickly started talking about the lab.


From our class discussion, my group concluded, "For every hex nut added to the dish, the overall mass increases by 7 grams."  As a class, we also realized that the slope of our graph was equal to the mass of an individual hex nut and that, if the hex nuts would have had more or less mass, the slope would have become more steep.  Along with that, we found a ratio between the number of nuts and the mass, giving it a direct linear relationship, and that the y-intercept of the graph (about 15 grams) was the mass of the Petri dish and the tape alone.

Rod Lab

For our second lab, we did the rod lab. For this investigation, we were given different size rods and we were asked, "Is there a relationship between the length of the rod and it's mass?"  We decided on having another linear graph as our predictive graph.  Then, we started our work.  To find the mass of the rod, we used a triple-beam balance.  Then, we traced the rods on their sides using graph paper and counted the number of cubes to find its length. Our data and graph is as follows:

Soon after, we had another class discussion.  This time, my group's conclusion came out as, "For every cube the length of the rod increases, the mass also goes up at a constant rate of 0.7 cubes.  It is also a direct, proportional, positive, and linear/constant relationship. " This time, we also learned the 5% rule from our teacher to see how good our data was. You take the y-intercept of your graph and divide by your largest y (in this case your largest mass) and then multiply by 100.  If it is under five percent, it's safe to assume you did a pretty good job. This time, our result was 3.9%.  We also learned that our points graph a ray, not a line because it can't be negative, and that the slope is how much the mass increases.

Circle Lab #1

For our last discussed lab, we did Circle Lab #1.  We were asked, "How does the diameter of a circle affect its circumference." and we were given different size circles.  To find the diameter, our group traced the circles on your average graph paper and counted the number of cubes across the middle.  To find the circumference, we put a string around the traced circles and measured, on graph paper, how much of the string was used. This way, we kept both of the units in cubes so they would be the same.  Our data and graph came out as follows:

Later, we had yet another class discussion.  For this lab, our group came up with the conclusion, "For every cube the diameter increases, the circumference goes up by 3.3314 cubes.  It goes up at a constant rate, causing a linear-style pattern."  We also did another 5% rule check, and our check came out to 0.07% which was even better than last time.  This time, as a class, we decided that the circumference of the circle should increase by pi for every cube of diameter added.  We also came to the conclusion that it would be useful to add the point (0,0) to our data because it logically makes sense in this situation and maybe others, and that logic does play a part in choosing our line of best fit.  Lastly, we concluded that if the y-intercept is off, it is usually systematic error, not human error.

Reflections

From these first couple of weeks, I have noticed that I talk at a moderate amount in class discussions.  That being said, I guess I could talk a little more, but only when I am really needed.  I also am doing what I think to be a fairly decent job in class.  I seem to be able to understand everything that's going on so far, although I'm still a little confused on how this class works.  This is mostly due to the fact that I have never learned in this style of science class before.  I even took a physics class last year, but it was nothing like this one.  I think that my group and I are doing pretty well, and I hope to learn more as the year goes on.