Introduction to Machines
Part Two
This website was created by a Kirkwood High School student as part of an Honors Physics program. It is designed to educate you about simple machines and the physics concepts that they operate on. The following pages are designed to introduce you to this website.
Conservation of Energy:
Here is one of the most important equations that you can ever learn about machines:
The conservation of energy!
The formula you see pictured above is a very important formula whereas machines are concerned. In mathematical language it states that no machine can create or destroy energy. It is a common misconception that machines can create energy, when in fact they can only change it. This law is known as the conservation of energy.
So what exactly CAN machines do if they can't change their energy. Although they cannot change the resulting energy itself a machine can change the factors of energy, force and distance. For example does 2x3 = 3x2? You bet it does! Although each value was changed the end result was still 6. In much the same way a machine can "trade in" less input force for more input distance. The resulting energy remains the same, but it is easier to move objects that way. As you get into the machines section you will realize the conservation of energy makes sense.
In a perfect world all things are equal. However the world is perfect and things are not equal. The same is true for the conservation of energy. You do not get out of a machine exactly what you put into it. Whenever you conduct an experiment with a machine you will find that there is some energy loss. Why do you think this is? The conservation of energy says energy cannot be destroyed, so where did it go? Into a black hole or something? I think not.
I think I have found your missing energy: it has been transformed. When you rub your hands together on a cold day to keep warm your hands are giving off energy in the form of heat, from the friction that your hands encounter. Every machine must move air out of the way, or perhaps slide along the floor. Whenever a machine does that it gives off energy in the form of heat and sometimes sound. If you were able to measure the energy given off this way you will find that it is equal to your "missing" energy.
Mechanical Advantage and Efficiency:
Exactly how much does a machine alter it's force and distance? The mechanical advantage tells you just that. Mechanical advantage shows just how much a certain machine helps you. The greater the mechanical advantage the more distance you have to move the machine but the less force you require. There are two ways to calculate the mechanical advantage. Here is the first way:
Ideal Mechanical Advantage (IMA)
Equation Analysis:
- I.M.A: Ideal Mechanical Advantage (unitless number)
- Distance (in): The distance that you move the machine in meters
- Distance (out): The resulting distance that the object moves in meters.
The above equation calculates the ideal mechanical advantage. Ideal mechanical advantage is how much advantage a machine should have. It is based on how far you move the machine over how far the object moves. For example, if you move a machine 8 cm and the object only moves 2 cm then the resulting mechanical advantage is 4. Mechanical advantage does not have any units.
In a perfect world the Ideal Mechanical Advantage would be exact, but the world is not perfect. Here is the second way to calculate mechanical advantage:
Actual Mechanical Advantage (AMA)
Equation Analysis:
- A.M.A: Actual Mechanical Advantage (unitless number)
- Force (out): The force that the machine outputs in Newtons.
- Force (in): The force you exert on the machine in Newtons.
This equation calculates the real mechanical advantage, or the actual mechanical advantage. The actual mechanical advantage is the real advantage based on the results of an experiment. The A.M.A. takes into account energy loss due to friction and sound.
Efficiency is a term used to express how much energy loss a machine has. In a perfect world a machine would be 100% efficient but that is not how the world works. Since there will always be friction there will always be an efficiency of less that 100%. Always. To calculate efficiency we use the following equation:
The Efficiency of any machine
Equation Analysis:
- Efficiency: How efficient the machine is, expressed in a decimal number.
- A.M.A: The actual mechanical advantage (see above).
- I.M.A: The ideal mechanical advantage (see above).
You can change the result of this equation to a percent if it makes it easier for you to understand by moving the decimal place to the right two places and adding a percent (%) sign. This percent is how efficient the machine is. As with mechanical advantage the efficiency of a machine does not have any units associated with it.
Congratulations, you have reviewed all of the necessary physics concepts and can now proceed to the machines section of this website.
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