Here are some sample graphs of Fuc vs Vtan and Fuc vs. Angular Velocity
And here's the analysis for the Fuc v. Angular Velocity graph. The trend follows y=ax^2, "y" is the Fuc in Newtons, and x is the angular velocity in rad/s. When you're doing dimensional analysis, 'rad' doesn't really count as a unit, so the unit for angular velocity is basically 1/s. That angular velocity is squared in the equation means that the unit for x^2 is 1/s^2. The units on the left-side of the equation are Newtons, or kg*m/s^2 which means that the units on the constant "a" in the equation have to combine with the units on x^2 to give the same units. So what the heck is kg*m, well, it suggests that you have things that you held constant in the data collection that had units of kg and meters. Your stopper mass didn't change, so that's the kg, and your radius didn't change, that's the meters. When this group multiplies those two things together, they get something darn close to 0.0083. So the general form of their equation would be
Fuc=radius*mass (of thing going in a circle)*angular velocity^2
For the Vtan version of the lab, x^2 in the equation has the units (m/s)^2 because you're squaring the Vtan, so what are the units on that constant? What would you multiply times the m^2/s^2 (that we get from x^2) in order to get kg*m/s^2, it needs to bring kg into the equation, and get rid of the "squared" on the meters. So kg/m it is then. That makes the general form of that equation
So now, get some practice with those two equations by attacking the worksheet you picked up on the way in today!
...sorry gang, I know this is less than ideal. Fever was worse on Wednesday, so I didn't get in to verify where you left off the day before. Hopefully I'll be back on Friday so we can tie up the loose ends before break. I'd like to quiz on Friday, but let's just worry about quizzing once we're back from spring break (and not until a couple of days into the week.) Anyway, the videos from the other day dealt with objects that both initially start from rest. Here's some follow up to go along with that and give you some practice at analyzing explosions. Don't get too excited, this is a public school, our budget doesn't allow for videos of real explosions, you just get these videos of kids pooshing off of each other. Craft IF Chartz for each of these situations, use the info on the video to determine things like velocity, and pmomentum. Fit all that onto a whiteboard (are there any blank ones left? group some shorties together if you must!) and share it out near the end of the hour (it's ok if all groups aren't all the way done, least done group explains there answers for the first part, and you can just follow along from there.) You don't need to put these in Logger Pro, you can just get the info that you need directly from the videos (hopefully.)
Anyway, grab a laptop (or use your own if it's fancy) and some whiteboards and have at these videos.
If you have completed presenting whiteboards for the problems 3-9 on the IF Chartz packet, go ahead and move on to the problems on this new worksheet, Momentum Problems 2. You'll need to use the Impulse (product of UnBalanced Force and Time Interval) and Change in Pmomentum (product of mass and change in velocity) equation to solve some of these problems. Recognize that "Impulse" would be found on a graph of Fu vs. t by finding the area between the graph and the x-axis.
As you view these videos, think about how the masses compare, and how the velocities compare (direction matters!) After they 'interact' with each other, think about what the velocity-mass bar graph, aka IF Chart, would look like, and reconcile that with what the IF Chart would look like before the 'splosion,
Find a pattern for projectiles launched at angles as you vary the launch angle between 70 degrees and 20 degrees above the horizontal.
As a result of working with the sim, be able to report back with...
1. Something you thought you knew that was confirmed
2. Something you did not know that you now know
3. Something that you want to know
I'm a little under the weather, so enjoy this video introduction on problem solving with the projectile motion particle model. This should be enough to help you get started on the projectile problem worksheet I had waiting for you on the cart this morning. You only need to watch two segments, time 0:00 to 3:00 and time 7:00 to 12:40. Then you can work on the sheets together/alone with your groupmates.
The angled launch stuff picks up around the 12:30 part of the first video, and then carries into this second video.
Use Logger Pro Video Analysis to Create Position v. Time and Velocity
v. Time graphs for the horizontal and vertical motion of these
projectiles.The meterstick for scaling is a 2 (TWO!) meter stick, so use
that information accordingly.... You will need to find the slopes for any linear graphs (don't pretend to be taking the slope of a curve). The motion is interesting once it leaves the hand of the thrower until just before it reaches the target/catcher. Use the frame advance button to skip forward to the interesting part of the motion.
in case you've forgotten, here's the how to video for Logger Pro video
analysis (for a different model, so your analysis will be different
because you need X and Y position graphs and X and Y velocity graphs)...
In the first part of class on Friday, we established Cameron/Huff's Law, "The Fu and acceleration point in the same direction.
In the elevator activity, we drew velocity v. time graphs that made it look like the acceleration would be upwards during part #2 and downwards during part #4.
We then took a closer look at what the FBD and FAD would need to look like for part #2, and settled on either C or D because their FADS had Fu's that point upwards (A and B had FADs that showed balanced forces).
We can analyze the motion of the elevator based on the amount of UnBalanced Force the guy is experiencing. Given that C and D are the only options with UnBalanced Forces, and they both show an UnBalanced force of 55 lb directed up, they'll both result in the same acceleration for the guy. We need to use conversion factors to make this problem manageable. First, since the scale reads 157 pounds when he first steps on it, we can use the knowledge that 1 kg weighs 2.25 lbs to determine that his mass is around 71 kg. Then, we can use the understanding that 1 lb is roughly 4.5 Newtons in order to determine that the Fu of 55 lb would be 245 Newtons. Using a=Fu/m we can then find the acceleration by taking the 245 N divided by 71 kg of mass. The guy is accelerating at 3.45 m/s/s at that point in time. Use this process as you work through the problems on the worksheet. Good luck!