Archive for November 2008
When we discuss normal forces, I drum into the students’ heads that the force is perpendicular to the surface. They get that eventually. Where they get into trouble is on an incline when the angled component of the weight of an object F(i)=mg*cos(Θ). I called this force F(i) meaning the force exerted on the incline (and the (i) is really a subscript, but I can’t make that work in this blog).
This is sometimes the normal force, but not always. If there are any other forces, like F(x), in the angled Y-axis, then the normal force is not the same as F(i).
Here is what I tell them: imagine there is a scale under the object in question, what would it read? If it is only the object and no other forces, then F(n) is F(i). From the drawing above, it’s fairly clear that there are two forces down that combine to create our normal force up. The scale under the block would read the value of F(i) + F(x), so that is our F(n).
My 12th grade Physical Science class has been restructured. Basically, about half of my students had Physical Science in 9th grade at other schools and they all had Chemistry last year. While it’s still Physical Science, we are spending a great deal of time on astronomy and the basic physics they need to understand the universe. The kids are very excited about their astronomy course, as am I. I am thinking about showing them the entire series of “From the Earth to the Moon.” It’s long, real long. There are 12, one-hour episodes. I also plan on showing them Apollo 13. I’m just not sure I want to show twelve days of shows, but I don’t think there are any episodes I would leave out. Showing one, or even two a week will take too long, we’ll be done astronomy before I finish. So I’m looking for the opinions of other teachers. What do you think? What would you do?
Students get a Nerf gun, a meter stick, a level, and a long metric tape measure. They launch several darts horizontally from 1 meter in height and mark where the darts first hit the ground. They measure this distance and average them together. Then using this distance and the time it takes for an object to fall 1 meter, they can calculate the muzzle velocity of their Nerf gun. (My Nerf gun in the picture has a muzzle velocity of around 12 m/s.)
Part two, they are to use what we did in class to calculate how far the dart will go if they are launched from the ground at 10º, 15º, and 20º. (Any higher angle and they hit the ceiling.)
Part three, they go back to the range and using a large cardboard protractor that I made, they launch the darts from the ground at those three angle and see how they did. The lab is attached below along with another one I do at the same time. Enjoy.
For some reason, I find the books totally inadequate on this section. I also don’t like their method of teaching it. Our book has one small section and a few problems, but not enough for the kids to see the pattern and understand what’s happening. I break projectiles into three main parts.
Part 1 – Horizontally Launched Projectiles
The idea here is that a ball is kicked out horizontally with no vertical velocity up or down. An important concept here is that a ball dropped off a cliff or kicked out horizontally, it will take the same time to fall. I break these problems into three variations:
- I give the students the Vx and the height of the cliff and ask them to find the distance horizontally that the ball hits the ground.
- I give the students the Vx and the distance and ask the students to find the height of the cliff.
- I give the students the height of the cliff and the distance horizontally that the ball hits the ground and ask them to find the initial velocity.
One the second day we play “Survivor Physics.” We pick a vocal member of the class and vote him off the airplane. I draw a picture of him falling and hitting the ground below. I usually give them the height of the airplane and the speed of the airplane, they have to tell me how long it takes him to fall and how far horizontally he travels before hitting the ground. Actually I say, “How long does he scream before he goes splat?” (Problem 1 all over again.)
Next problem, I name a student who drops a water balloon off a building and on to another student. They get the height of the building and the distance the other student is standing from the bottom of the building. They need to calculate the horizontal launch velocity. (Problem 3)
Last, I draw a watch tower and tell them that a student pushes another student off the tower with a certain horizontal velocity. He has to push him onto a waiting cactus below that is a certain number of meters out. They need to determine the height of the tower.
Now before you get up in arms over student abuse, understand they are all asking for it to be them that is pushed and thrown and dropped on. It is all in good fun and they hopefully see a connection to the work. Hopefully.
Part 2 – Upwardly Launched Projectiles
I teach my students to break these launched projectile problems into two halves; the up half and the down half. We can solve every problem this way. The steps are basically the same for every problem.
- Get Vx and Vy from the velocity and angle.
- Get the time_up using Vy/g
- Get the height of the projectile using using 0.5gt^2.
- Get the total_time by doubling time_up if the projectile lands at the same height it was launched from.
- Get the distance using d=(Vx)*total_time
Using this method, they can also move the cannon or whatever we launch with up on a hill. They can then calculate the up time and the down time and see they are different for a different height. They can also do problems where they determine the height some distance down range by finding out how far an object falls after reaching the maximum height. These are some of the more tedious projectile problems, but I don’t ease up, they work through them until they get them right.
Part 3 – Unknown Velocity
I was worried my kids wouldn’t be able to solve these problems because you end up with two unknowns and two different equations. But because the problems are done exactly the same each time, they figured them out fairly quickly. To solve these, you get the total time like above, just keep a variable for velocity. Then solve for total time horizontally using Vx and the distance traveled. Setting them equal to each other lets you get the launch velocity of the projectile.
I know this was a lot of words. I spend almost two weeks on these problems. Along the way I take out specifications on military weapons and use those to find the distance they travel. We use the specs from the Barrett .50 caliber sniper rifle for the horizontal only and upward launch. The numbers are mind blowing, I find it really gets their interest, especially if any of them are hunters.
The test will be attached below, I need to scan it.
Perhaps I expect too much. I think I am going to create a new lab that is just about measuring stuff correctly and accurately. I had my own tools from when I was big enough to walk, so I take for granted that everybody knows how to read a tape measure or meter stick. Apparently this and analog clocks are skills our children no longer have to master. Despite three months of using nothing but meters in class and lab, I still have students who use the inches and feet when I lower my guard.
Moms and Dads, please teach your kids to use a ruler. Not everything in life is a teacher’s job. Sorry for the rant.
This is an interactive applet that allows the student or teacher to change the velocity and acceleration of a car. There is a graphical representation of the car and the velocity vector as it moves across the top of the screen. On the bottom are three graphs that show the distance v time, the velocity v time, and the acceleration v time. I wish I had found this a month ago, it would have been helpful explaining these principles.
I found this teacher’s site because one of my students plagarized it for his lab report. Not only was it clearly not his writing, but he just did a cut and paste and didn’t notice that some of it didn’t even pertain to our lab. So, yeah, he got caught.
The site is hosted by the Physics department of Glenbrook South High School. I counted 10 physics teachers on the faculty page. There is a lot here, but if you plan on using it, please read their usage page. They have apparently licensed and paid for the use of some of the material. Do not just download their work, please follow their policies and contact them if you have questions.