Today, groups either cleaned up notions about projectiles or jumped into relative motion. Unfortunately, a meeting pulled me out of class for C and E blocks, but we'll have plenty of time to pick up relative velocity tomorrow as we review for Friday's exam. B Block conducted their Projectile Motion lab and got to put into practice the concepts and calculations we discussed in class. As we look towards Friday, here are some videos to help you with working problems dealing with projectiles:
9/27/11
And More Projectiles...
Although B Block did start their discussion of relative motion today, the first portion of their period and the other blocks of the day continued on with projectiles. C Block conducted their Projectile Motion lab, investigating the properties of and practicing calculations with horizontally-launched projectiles. E and F Blocks had more practice time working with projectiles launched at angle, which we will go over tomorrow. Remember - the exam is on Friday, so Thursday is going to be some review time for people. I'd start looking over things now and be ready with questions...
9/26/11
Projectiles!
Today was projectiles launched at an angle day for all blocks - some getting their first bite at the information, others getting some review and more practice. Horizontally-launched projectile are a little easier to work with since we have only 1/2 of a parabola to work with and we know that vi,y will be 0 m/s. That goes out the window for many projectiles, such as balls thrown through the air or missiles launched at a target. Some of the initial velocity is in the x-direction and some is in the y-direction, and you need to find those values and use them appropriately in your analyses. Most often, the x-component of the initial velocity will be found through the cosine function and the y-component through the sine function. So, for a problem where a projectile was launched at 20 m/s at an angle of 30°, you would see me write on the board:
vx = 20 m/s(cos 30°)
vi,y = 20 m/s(sin 30°)
right off the bat. Then, just make sure to use the proper velocity component when you work in the x- or y-directions. Another helpful trick is to break the parabola in two. This can make solving for time in the air simple. Solve for time for one-half of the parabola and then multiply times two to get full time in the air. Then, with that time, finding horizontal range is super simple (vx = Δx/t). Different groups have different problems that they are working on tonight, and we will check over them tomorrow before moving forward. If more practice is needed, we'll take the time to do that. C Block will be doing a lab on horizontally-launched projectiles and some groups may dip toes in relative motion, depending on quickly we move through our projectiles review. Test on Friday and the Chapter 3 review sheet is up on Edline. Then - Forces!
vx = 20 m/s(cos 30°)
vi,y = 20 m/s(sin 30°)
right off the bat. Then, just make sure to use the proper velocity component when you work in the x- or y-directions. Another helpful trick is to break the parabola in two. This can make solving for time in the air simple. Solve for time for one-half of the parabola and then multiply times two to get full time in the air. Then, with that time, finding horizontal range is super simple (vx = Δx/t). Different groups have different problems that they are working on tonight, and we will check over them tomorrow before moving forward. If more practice is needed, we'll take the time to do that. C Block will be doing a lab on horizontally-launched projectiles and some groups may dip toes in relative motion, depending on quickly we move through our projectiles review. Test on Friday and the Chapter 3 review sheet is up on Edline. Then - Forces!
9/24/11
9/23/11
Projectile Motion
All blocks today worked with projectile motion - some blocks working with horizontal projectiles and others with projectiles launched at angle. B and C blocks worked with projectiles launched at an angle, building on the techniques they practiced with horizontally-launched projectiles. We lose the ability to set the initial velocity in the y-direction to 0 m/s, which complicates matters, but if you work thoughtfully and in a stepwise fashion, the problems are manageable. Break the initial velocity into it's x-and y-components, remember that vx is constant and the y-velocity at the top of the rise is 0 m/s and that if you launch and land at the same point, you have a symmetrical parabola. That last piece can be of great help, since sometimes it is easy to work with one half of the parabola, rather than the whole thing, and just multiply your values by two. Solve for time to top of rise and multiply by two to get the entire time in the air, for instance. On Monday, we will look over these some more and get more practice, if necessary.
E Block worked on the Projectile Motion lab, which verified the assumptions and calculations we worked on with our practice problems. As long as you know height, you can calculate how long it takes the projectile to hit the ground. With time and and a known, constant horizontal velocity, predicting horizontal displacement is quick and easy. We'll go over this lab on Monday and then start on projectiles launched at an angle.
F Block had their horizontal projectile lecture, which helped to clarify and explain observations made in yesterday's lab. Yes, the velocity in the x-direction is constant. Yes, the acceleration in the y-direction is the standard velocity for gravity. Yes, you can analyze each component of the motion separately, for they are independent. Use the skills you practice in lab and the example problem we worked on the board to tackle the homework problems this weekend. On Monday, we'll go over them and then start with projectiles launched at an angle.
Have a good weekend!
E Block worked on the Projectile Motion lab, which verified the assumptions and calculations we worked on with our practice problems. As long as you know height, you can calculate how long it takes the projectile to hit the ground. With time and and a known, constant horizontal velocity, predicting horizontal displacement is quick and easy. We'll go over this lab on Monday and then start on projectiles launched at an angle.
F Block had their horizontal projectile lecture, which helped to clarify and explain observations made in yesterday's lab. Yes, the velocity in the x-direction is constant. Yes, the acceleration in the y-direction is the standard velocity for gravity. Yes, you can analyze each component of the motion separately, for they are independent. Use the skills you practice in lab and the example problem we worked on the board to tackle the homework problems this weekend. On Monday, we'll go over them and then start with projectiles launched at an angle.
Have a good weekend!
9/22/11
Bombing the Enemy
F Block conducted a lab investigation on horizontally-launched projectiles. The mission was simple - use photogates to determine the velocity of a ball-bearing, take the height of the launch platform and determine where to place the target for the bearing to hit. The thing was, the bearing was only allowed to hit the ground once - when groups were ready to make their bombing run for me (and the rest of the class to see). This lab required careful measurements of horizontal velocity and height and careful calculation of the bearing's horizontal displacement. Groups did an excellent job - the targets were either nailed on the first go or with a little lateral adjustment of the target. The range calculations were fine, but the launch ramp and target were a little off right-left. Tomorrow, E Block sees if they can make as good a showing...
B and C Blocks reviewed the idea of projectiles launched horizontally and had class time to work practice problems for this type of motion. Remember that time is y-dependent and the most commonly used formula to find time for these problems is Δy = vot + 1/2at2. Since the initial velocity in the y-direction is 0 m/s, the formula simplifies to: Δy = 1/2at2. Once you have time, solving for horizontal aspects of the motion is simple. You've got one formula to use: vx = Δx/t. You're generally asked for either horizontal displacement (and they give you vx) or for launch velocity (and they give you Δx). Just use the time you found for the y-component of the motion and you're good as gold. We'll look over these tomorrow and then start to discuss projectiles launched at an angle. They take a bit more work, but it builds on what we've already done, so it won't be exhausting.
E Block had their full horizontally-launched projectiles chat today and also has a set of problems to work. We'll be going over those on Monday, since tomorrow is your lab block. I'd get them out of the way tonight for two reasons:
For everyone, the test is looking like it will be next Friday. That's a little later than I had planned but we're losing a couple of periods next week for various things, so c'est la vie...
B and C Blocks reviewed the idea of projectiles launched horizontally and had class time to work practice problems for this type of motion. Remember that time is y-dependent and the most commonly used formula to find time for these problems is Δy = vot + 1/2at2. Since the initial velocity in the y-direction is 0 m/s, the formula simplifies to: Δy = 1/2at2. Once you have time, solving for horizontal aspects of the motion is simple. You've got one formula to use: vx = Δx/t. You're generally asked for either horizontal displacement (and they give you vx) or for launch velocity (and they give you Δx). Just use the time you found for the y-component of the motion and you're good as gold. We'll look over these tomorrow and then start to discuss projectiles launched at an angle. They take a bit more work, but it builds on what we've already done, so it won't be exhausting.
E Block had their full horizontally-launched projectiles chat today and also has a set of problems to work. We'll be going over those on Monday, since tomorrow is your lab block. I'd get them out of the way tonight for two reasons:
- They will help you with you lab calculations tomorrow.
- You'll have the lab write-up to do over the weekend, so don't give yourself double homework.
For everyone, the test is looking like it will be next Friday. That's a little later than I had planned but we're losing a couple of periods next week for various things, so c'est la vie...
9/21/11
Horizontal Projectiles
Here's a decent video discussing the basics of projectile motion, using a horizontally-launched projectile as an example:
Straddling a Line
Two blocks today dove into projectile motion and two blocks delved deeper into vector operations and non-perpendicular vectors. B and C Blocks began their discussion of projectile motion and we started with basic characteristics of this type of motion and spent time focusing on projectiles launched horizontally. Projectiles can be thought of objects in free fall that are given a little bonus - a horizontal velocity. Remember that whatever happens in the horizontal direction is independent of the party going on in the vertical plane and vice versa. So, the components of the motion can be analyzed independently using our familiar kinematics formulas. For motion in the x-direction, the velocity (in the absence of air resistance) remains constant, because there is no net external force acting in that direction to accelerate the object. Motion in the y-direction is accelerated by gravity. Everything we talked about and practiced for an object being dropped or tossed straight up into the air applies to the vertical motion of a projectile. Also, remember that the initial velocity in the vertical direction for a horizontal projectile is 0 m/s. Tomorrow, we'll finish up that chat and work problems with this type of projectile before adding another twist - what do you do with a projectile launched at an angle?
E and F Blocks reviewed vector resolution and working with non-perpendicular vectors. The most attention was given to those non-perpendicular beasts, because they are a handful to work with. Read the problem closely and carefully draw your vector diagram. Don't be afraid to draw the first vector, then draw a nice coordinate plane at the tip of this guy. Then, draw the second right at the tip of the first vector, right at the origin of the grid exactly as if the first vector wasn't there at all. Do that for every vector in the problem. Break down each vector into it's x- and y-components and pay attention to what trig function is used to determine each. Then, make you list of Σx and Σy, making sure the signs of each vector you add to the lists have the proper sign. Now, it's a matter of adding everybody up and making that final, blessed right triangle and getting the magnitude and direction of the resultant. Tomorrow, E Block will start discussing projectile motion and F Block will conduct a lab investigation focusing on horizontally-launched projectiles.
E and F Blocks reviewed vector resolution and working with non-perpendicular vectors. The most attention was given to those non-perpendicular beasts, because they are a handful to work with. Read the problem closely and carefully draw your vector diagram. Don't be afraid to draw the first vector, then draw a nice coordinate plane at the tip of this guy. Then, draw the second right at the tip of the first vector, right at the origin of the grid exactly as if the first vector wasn't there at all. Do that for every vector in the problem. Break down each vector into it's x- and y-components and pay attention to what trig function is used to determine each. Then, make you list of Σx and Σy, making sure the signs of each vector you add to the lists have the proper sign. Now, it's a matter of adding everybody up and making that final, blessed right triangle and getting the magnitude and direction of the resultant. Tomorrow, E Block will start discussing projectile motion and F Block will conduct a lab investigation focusing on horizontally-launched projectiles.
9/20/11
More Vectors!
Today, various discussions were launched for vector resolution and working with non-perpendicular vectors. Both vector combination and vector resolution are going to be used this year as we work with things like force and momentum, so make sure that you are very confident in your vector operation skills. Non-perpendicular vectors are the test - if you can successfully work problems with non-perpendicular vectors, then you can wear the vector crown with pride...
Tomorrow, we'll review these ideas and apply them to the concept of horizontally-launched projectiles. When motion occurs in two dimensions, as it does with projectiles, we have to be able to break a launch velocity into it's horizontal and vertical components to analyze the motion. The lab we'll do for this section will let folks work with horizontally-launched projectiles and give groups a chance to mathematically predict where a ball will fall. Yes... there will be prizes involved...
Tomorrow, we'll review these ideas and apply them to the concept of horizontally-launched projectiles. When motion occurs in two dimensions, as it does with projectiles, we have to be able to break a launch velocity into it's horizontal and vertical components to analyze the motion. The lab we'll do for this section will let folks work with horizontally-launched projectiles and give groups a chance to mathematically predict where a ball will fall. Yes... there will be prizes involved...
9/19/11
Go Go Gamers Go
I have never hidden that I'm a gamer from way back (yeah, had the original Pong that I played on a rickety black and white TV I inherited from my grandparents) and although multiplayer jerks can give gamers a bad name, sometimes we get a bit of good press:
Gamers solve problem in 3 weeks scientists couldn't in 10 years
Gamers solve problem in 3 weeks scientists couldn't in 10 years
Stop that Celebrating
I'll be in tomorrow. Just fighting off a cold and since I hate losing a fight, this cold will be tapping the mat in no time. Everyone is working on vectors today, so I hope that folks are helping each other out. C, E and F Blocks are working vector resolution problems, sort of the flip flop of the vector combination work you did on Friday. Using the same trig relationships, take a look at your vector diagram, decide which side of your triangle is the opposite to the angle and which is the adjacent. Write out your relationship and plug in the information you know. For vector resolution, that part is easy. It's probably going to boil down to either sin Θ • hypotenuse = opposite side or cos Θ • hypotenuse = adjacent side. Now, don't always think that the adjacent side will be the x-axis and the opposite will be the y-axis. Look closely at your diagram to determine the proper relationship to use for each component of your triangle.
B Block got a heavy dose of vector work - don't be upset if you have some problems with the non-perpendicular vector piece. They take very careful attention to diagram-drawing and organization of information. Take each individual vector and resolve it into it's components, paying close attention to the signs of each component. Add up all the x-components of the vectors and all the y-components and use them to make a single right triangle, the hypotenuses of which is the resultant for the overall problem. Think of it as a puzzle or game and don't let yourself get frustrated if you''re having trouble. Put the problems aside, take a few minutes break and come back with a fresh head. We'll start going over this tomorrow and more practice is needed, that's ok.
Well, off to open a fresh box of tissues...
B Block got a heavy dose of vector work - don't be upset if you have some problems with the non-perpendicular vector piece. They take very careful attention to diagram-drawing and organization of information. Take each individual vector and resolve it into it's components, paying close attention to the signs of each component. Add up all the x-components of the vectors and all the y-components and use them to make a single right triangle, the hypotenuses of which is the resultant for the overall problem. Think of it as a puzzle or game and don't let yourself get frustrated if you''re having trouble. Put the problems aside, take a few minutes break and come back with a fresh head. We'll start going over this tomorrow and more practice is needed, that's ok.
Well, off to open a fresh box of tissues...
9/16/11
Vectors
Before we move into 2-dimensional motion, we have to tackle the wonderful world of vectors. The ability to combine and resolve vectors will be critical in this course and we have to make sure that the necessary skills are hammered out now. B, E and F Blocks discussed the properties of vectors today and a method for constructing vector diagrams. We'll use the tail-to-tip method in this class, but if you already know the parallelogram method, go ahead and use it. But, definitely take the time to draw a vector diagram before tackling a problem; you will be surprised how much easier setting up your problem will be and how much better you can visualize the situation with a good diagram staring you in the face. We also took time to demonstrate using the Pythagorean theorem and the tangent function to calculate the magnitude and direction of a resultant vector and will add on the sine and cosine functions when we discuss vector resolution on Monday.
C Block had an overview of vector operations and then worked through a computer simulation that allowed them to work with vectors both graphically and mathematically. You got to combine vectors, resolve vectors and work with situations were there were many vectors involved in a problem. As long as you can get them sorted into vectors along the x-axis and vectors along the y-axis, you can make a nice right triangle to find your resultant. We'll go over that activity on Monday and then put a little more flesh on the vector bone.
Blocks B, E and F may want to practice with the simulation that C Block worked on today, so here it is for your enjoyment (along with the LAB SHEET)
C Block had an overview of vector operations and then worked through a computer simulation that allowed them to work with vectors both graphically and mathematically. You got to combine vectors, resolve vectors and work with situations were there were many vectors involved in a problem. As long as you can get them sorted into vectors along the x-axis and vectors along the y-axis, you can make a nice right triangle to find your resultant. We'll go over that activity on Monday and then put a little more flesh on the vector bone.
Blocks B, E and F may want to practice with the simulation that C Block worked on today, so here it is for your enjoyment (along with the LAB SHEET)
9/15/11
Test Day!
Test day is over!
Well, you've gotten a look at what a typical test looks like and it's not really going to change. Same format each time, so no surprises. If you find you run short of time, it's ok to come back and finish, but always make sure to do it in a very timely fashion. Same goes if you're absent and miss a test. Make it up quickly, since I can't return and discuss the other folks' exams until yours is taken.
Tomorrow, we start with vectors. Some of you have worked with them, others of you haven't. Some of you have worked with basic trig functions (sine, cosine, tangent), others haven't. Not a problem. We'll get everyone up to speed with some good hard grunt work and there will be no complaining! We'll need these skills to be sharp and shiny as we move into 2-dimensional motion and then into our study of every other vector topic we hit this year. C Block has long block tomorrow and we'll start with some basic discussion of vectors, then you will work with a computer simulation to walk you through adding vectors. The rest of you guys will get a more in-depth discussion of vectors and how we can use vectors to explore aspects of physics. Trust me, it won't be too painful...
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