There aren't 70 candles, bc we didn't have that many, but I know it was somewhere in the forties. haha! =)
sMiLeS,
Saturday, November 26, 2011
My Dad's 70th Birthday
There aren't 70 candles, bc we didn't have that many, but I know it was somewhere in the forties. haha! =)
sMiLeS,
Tuesday, November 15, 2011
Apologia General Science, Module 4, Science, Applied Science, and Technology
►Videos and resources for this module
This module was not quite as fun for the kids because there was MATH!!! =)
We already knew about the simple machines - lever, inclined plane, etc, but mainly we were learning what the advantage was for using these machines.
This advantage can be measured, and is called a Mechanical Advantage, or MA.
Mechanical advantage makes a job easier.
If the slope of two inclined planes are different, the Mechanical Advantage for each slope will be different.
This is easy to imagine, for if a wheelchair ramp is longer and less steep, it is easier to push the chair up the ramp. This has a greater MA than a ramp that is shorter and more steep.
But with each advantage comes a "pay." The pay for having a less steep slope is that you have to push farther. Now this may seem like a no-brainer, and if one ramp had a height of 1.5 feet, and was only 3 feet long, and another ramp with a height of 1.5 feet was 10 feet long, you'd definitely say you'd rather have a longer ramp.
But suppose a ramp was 1.5 feet high, and was 40 feet long. More MA is not always desirable if the advantage is not great enough to make the job significantly easier, or if the job wasn't hard to begin with.
Mechanical Advantage is measurable in numbers.
The formula for finding the MA for an inclined plane is MA = (length of the slope) ÷ (height).
So for a ramp that is 1.5 feet height and 10 feet long, you find the MA by dividing 10 ÷ 1.5 = 6.666...
The MA is 6.666...
The shorter ramp of 3 foot in length has a much smaller mechanical advantage. 3 ÷ 1.5 = 2. Two is a very small mechanical advantage!
Since a wedge is 2 inclined planes placed back to back, it uses the same formula as an inclined plane.
We learned the formula for each of the six simple machines. the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.
A screw is a type of inclined plane -- it is just wound around. To illustrate this, the kids took a piece of paper shaped like a right triangle, and highlighted the slope. They wound it around a pencil to show that a screw is an inclined plane.
It would be hard to measure the length of the slope on a screw though, so there are extra steps involved in finding the MA of a screw, involving finding the circumference of the screwdriver or device that is turning the screw, then dividing that by the pitch (distance between threads).
The formula for pulleys was the easiest. To find the MA for pulleys.... simply count the pulleys! =)
(Unless you use only 1 pulley -- if you use only one pulley, you have no MA because you are simply reversing the direction of your pull.)
The more pulleys, the greater MA.
This means that using 6 pulleys is 3 times easier than using 2 pulleys!
To simulate how more pulleys can make things easier, we used a broom, a mop handle, and some rope. Each time the rope wrapped around a handle, that simulated a pulley. The kids first pulled with the rope wrapped around once, then three times.
They said it was much easier with more "pulleys."
The formula for the lever was the most complicated because there are three classes of levers.
MA = (distance from fulcrum to effort) ÷ (distance from fulcrum to resistance/load)
We used the term "fe-fr" to help us remember the order.
If you look at this image of the three classes of levers, you will see it can take a bit of brain work to think how to apply this formula to each of these different levers.
In a first class lever where the fulcrum is in the middle, we learned that the more distance between the fulcrum and the effort (where we placed on book), the easier it was to lift the load (resistance). We illustrated this by placing a book on each end of a board, and using my pencil sharpener for the fulcrum (lol). As we increased the number of books on the load end, we also increased the distance from the fulcrum to the effort (one book). We illustrated that even though there were more and more books on the load end, the effort of one book was able to lift them all because of the increasing mechanical advantage by lengthening the distance between the fulcrum and the effort. In other words, a longer lever. =)
I had nothing ready to illustrate a wheel and axle, but I wish I had! Something like bar weights on one end of the bar would have worked great.
I needed to impress upon the kids that turning the axle to make the wheel turn takes greater effort, but once it gets going, the wheel can turn fast.
►If you are turning the axle, the speed of the wheel is magnified. You didn't turn the axle that fast, but it is magnified so that the wheel is turning faster.
This is like a 3rd class lever since a 3rd class lever is like a catapult.
►When turning the wheel to make the axle move, the effort is magnified. You didn't put forth that much effort, but it is magnified. The axle turns easily.
This is similar to the first- and second-class levers.
sMiLeS,
This module was not quite as fun for the kids because there was MATH!!! =)
We already knew about the simple machines - lever, inclined plane, etc, but mainly we were learning what the advantage was for using these machines.
This advantage can be measured, and is called a Mechanical Advantage, or MA.
Mechanical advantage makes a job easier.
If the slope of two inclined planes are different, the Mechanical Advantage for each slope will be different.
This is easy to imagine, for if a wheelchair ramp is longer and less steep, it is easier to push the chair up the ramp. This has a greater MA than a ramp that is shorter and more steep.
But with each advantage comes a "pay." The pay for having a less steep slope is that you have to push farther. Now this may seem like a no-brainer, and if one ramp had a height of 1.5 feet, and was only 3 feet long, and another ramp with a height of 1.5 feet was 10 feet long, you'd definitely say you'd rather have a longer ramp.
But suppose a ramp was 1.5 feet high, and was 40 feet long. More MA is not always desirable if the advantage is not great enough to make the job significantly easier, or if the job wasn't hard to begin with.
Mechanical Advantage is measurable in numbers.
The formula for finding the MA for an inclined plane is MA = (length of the slope) ÷ (height).
So for a ramp that is 1.5 feet height and 10 feet long, you find the MA by dividing 10 ÷ 1.5 = 6.666...
The MA is 6.666...
The shorter ramp of 3 foot in length has a much smaller mechanical advantage. 3 ÷ 1.5 = 2. Two is a very small mechanical advantage!
Since a wedge is 2 inclined planes placed back to back, it uses the same formula as an inclined plane.
We learned the formula for each of the six simple machines. the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.
A screw is a type of inclined plane -- it is just wound around. To illustrate this, the kids took a piece of paper shaped like a right triangle, and highlighted the slope. They wound it around a pencil to show that a screw is an inclined plane. It would be hard to measure the length of the slope on a screw though, so there are extra steps involved in finding the MA of a screw, involving finding the circumference of the screwdriver or device that is turning the screw, then dividing that by the pitch (distance between threads).
(Unless you use only 1 pulley -- if you use only one pulley, you have no MA because you are simply reversing the direction of your pull.)
The more pulleys, the greater MA.
This means that using 6 pulleys is 3 times easier than using 2 pulleys!
To simulate how more pulleys can make things easier, we used a broom, a mop handle, and some rope. Each time the rope wrapped around a handle, that simulated a pulley. The kids first pulled with the rope wrapped around once, then three times.
They said it was much easier with more "pulleys."
The formula for the lever was the most complicated because there are three classes of levers.
MA = (distance from fulcrum to effort) ÷ (distance from fulcrum to resistance/load)
We used the term "fe-fr" to help us remember the order.
If you look at this image of the three classes of levers, you will see it can take a bit of brain work to think how to apply this formula to each of these different levers.
In a first class lever where the fulcrum is in the middle, we learned that the more distance between the fulcrum and the effort (where we placed on book), the easier it was to lift the load (resistance). We illustrated this by placing a book on each end of a board, and using my pencil sharpener for the fulcrum (lol). As we increased the number of books on the load end, we also increased the distance from the fulcrum to the effort (one book). We illustrated that even though there were more and more books on the load end, the effort of one book was able to lift them all because of the increasing mechanical advantage by lengthening the distance between the fulcrum and the effort. In other words, a longer lever. =)
I had nothing ready to illustrate a wheel and axle, but I wish I had! Something like bar weights on one end of the bar would have worked great.
I needed to impress upon the kids that turning the axle to make the wheel turn takes greater effort, but once it gets going, the wheel can turn fast.
►If you are turning the axle, the speed of the wheel is magnified. You didn't turn the axle that fast, but it is magnified so that the wheel is turning faster.This is like a 3rd class lever since a 3rd class lever is like a catapult.
►When turning the wheel to make the axle move, the effort is magnified. You didn't put forth that much effort, but it is magnified. The axle turns easily.
This is similar to the first- and second-class levers.
sMiLeS,
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