1. Efficiency and Simple Machines

2. Ideal Mechanical Advantage
Ideal mechanical advantage (IMA) is calculated by dividing a machine’s output force by the amount of force put into it.
For example, if you used a lever to open a can of paint, you push down with 50N of force and the lid is pushed of wit]h 250N of force. This means the Ideal Mechanical Advantage (IMA) is 250/50 or 5.
IMA=Foutput/FInput

3. Actual Mechanical Advantage (AMA)
AMA=dinput/doutput
Actual Mechanical Advantage (AMA), on the other hand, use the DISTANCES supplied to and provided from the machine.
As in the previous example, the lever would be much longer on the end I was holding vs. the end that was stuck under the paint can lid. The end I would hold is the input distance, and the other end is the distance the machine moves.
So, If I used a 1st class lever and the arm length I held was 6m and the length opposite the fulcrum was 2, then the AMA would be 3.

4. Efficiency Any machine can be rated by its efficiency.
Energy put into the machine is not all converted to useful work. The energy in gasoline is not entirely used to power your car. Some of the energy is lost as heat in the car’s engine because of Friction.
Efficiency=(Work machine does / Work put into machine)*100
E=(woutput/winput)*100

5. Entropy
Because of the energy lost in a machine’s moving parts, no machine can have 100% efficiency.
If a machine had 100% efficiency, it could run forever without having more energy put into it. This is known as a perpetual motion machine.
If you solve for efficiency and get an efficiency of 100% of more, you did something wrong.

6. Mechanical Advantages in Selected Machines
Inclined Plan

7. Continued…
Fixed and moveable pulleys have an IMA and AMA of 1. Pulley system’s IMA and AMA are determined by counting the rope segments.

8. Sample Problems
1) What is the IMA for an inclined plane who’s ‘ramp’ portion is 50m and who’s height reaches to only the first story off the ground? (2m)
2) An inclined plane has a mechanical advantage of 4. If the length of this plane is 4m, then how tall is it? What if the length of the plane was 20m?
3) What’s the efficiency of a pulley system that lifts an object of weight 40N a distance of 10m if the person pulling the pulley has to pull with a force of 5N for a distance of 100m? What is the mechanical advantage of this pulley system? How many rope segments does it have?

9. Individual Practice
What is the mechanical advantage of an inclined plane that is 12m high and has a length of 24m? If I pushed an object up this ramp with a force of 20N, then what force would be required just to simply lift the object off the ground?
What’s the actual mechanical advantage of a pulley system that requires you to pull down with 500N of force for a distance of 100m only to lift an object of mass 4000N a distance of 10m? What is the ideal mechanical advantage of this pulley system? What is the efficiency of this pulley system?
A car uses 50,000J of energy from gasoline. However, the car only moves a distance of 100m with a force of 25N. What is this car’s efficiency?

10. Test Your test on Tuesday will consist of:
1) Work and Power problems. Be able to tell whether or not work is being done, which objects have more or less power, and whether or not work is being done.
2) Simple machines. Be able to name simple machines based on descriptions. Also be able to calculate mechanical advantage and efficiency of simple or compound machines.