# Work, Energy, and Simple Machines

## Simple Machines


### Section Key Terms


### Simple Machines

Simple machines make work easier, but they do not decrease the amount of work you have to do. Why can’t simple machines change the amount of work that you do? Recall that in closed systems the total amount of energy is conserved. A machine cannot increase the amount of energy you put into it. So, why is a simple machine useful? Although it cannot change the amount of work you do, a simple machine can change the amount of force you must apply to an object, and the distance over which you apply the force. In most cases, a simple machine is used to reduce the amount of force you must exert to do work. The down side is that you must exert the force over a greater distance, because the product of force and distance, fd, (which equals work) does not change.
Let’s examine how this works in practice. In (a), the worker uses a type of lever to exert a small force over a large distance, while the pry bar pulls up on the nail with a large force over a small distance. (b) shows the how a lever works mathematically. The effort force, applied at F, lifts the load (the resistance force) which is pushing down at F. The triangular pivot is called the fulcrum; the part of the lever between the fulcrum and F is the effort arm, L; and the part to the left is the resistance arm, L. The mechanical advantage is a number that tells us how many times a simple machine multiplies the effort force. The ideal mechanical advantage, IMA, is the mechanical advantage of a perfect machine with no loss of useful work caused by friction between moving parts. The equation for IMA is shown in (b).
In general, the IMA = the resistance force, F, divided by the effort force, F. IMA also equals the distance over which the effort is applied, d, divided by the distance the load travels, d.
Getting back to conservation of energy, for any simple machine, the work put into the machine, W, equals the work the machine puts out, W. Combining this with the information in the paragraphs above, we can write 
The equations show how a simple machine can output the same amount of work while reducing the amount of effort force by increasing the distance over which the effort force is applied.
Some levers exert a large force to a short effort arm. This results in a smaller force acting over a greater distance at the end of the resistance arm. Examples of this type of lever are baseball bats, hammers, and golf clubs. In another type of lever, the fulcrum is at the end of the lever and the load is in the middle, as in the design of a wheelbarrow.
The simple machine shown in  is called a wheel and axle. It is actually a form of lever. The difference is that the effort arm can rotate in a complete circle around the fulcrum, which is the center of the axle. Force applied to the outside of the wheel causes a greater force to be applied to the rope that is wrapped around the axle. As shown in the figure, the ideal mechanical advantage is calculated by dividing the radius of the wheel by the radius of the axle. Any crank-operated device is an example of a wheel and axle.
An inclined plane and a wedge are two forms of the same simple machine. A wedge is simply two inclined planes back to back.  shows the simple formulas for calculating the IMAs of these machines. All sloping, paved surfaces for walking or driving are inclined planes. Knives and axe heads are examples of wedges.
The screw shown in  is actually a lever attached to a circular inclined plane. Wood screws (of course) are also examples of screws. The lever part of these screws is a screw driver. In the formula for IMA, the distance between screw threads is called pitch and has the symbol P. 
 shows three different pulley systems. Of all simple machines, mechanical advantage is easiest to calculate for pulleys. Simply count the number of ropes supporting the load. That is the IMA. Once again we have to exert force over a longer distance to multiply force. To raise a load 1 meter with a pulley system you have to pull N meters of rope. Pulley systems are often used to raise flags and window blinds and are part of the mechanism of construction cranes.
A complex machine is a combination of two or more simple machines. The wire cutters in  combine two levers and two wedges. Bicycles include wheel and axles, levers, screws, and pulleys. Cars and other vehicles are combinations of many machines.

### Calculating Mechanical Advantage and Efficiency of Simple Machines

In general, the IMA = the resistance force, Fr, divided by the effort force, Fe. IMA also equals the distance over which the effort is applied, d, divided by the distance the load travels, d.
Refer back to the discussions of each simple machine for the specific equations for the IMA for each type of machine.
No simple or complex machines have the actual mechanical advantages calculated by the IMA equations. In real life, some of the applied work always ends up as wasted heat due to friction between moving parts. Both the input work (W) and output work (W) are the result of a force, F, acting over a distance, d.
The efficiency output of a machine is simply the output work divided by the input work, and is usually multiplied by 100 so that it is expressed as a percent.
Look back at the pictures of the simple machines and think about which would have the highest efficiency. Efficiency is related to friction, and friction depends on the smoothness of surfaces and on the area of the surfaces in contact. How would lubrication affect the efficiency of a simple machine?

### Practice Problems


### Check Your Understanding


### Section Summary

1. The six types of simple machines make work easier by changing the fd term so that force is reduced at the expense of increased distance. 
2. The ratio of output force to input force is a machine’s mechanical advantage.
3. Combinations of two or more simple machines are called complex machines.
4. The ratio of output work to input work is a machine’s efficiency.

### Key Equations


### Concept Items


### Critical Thinking


### Problems


### Performance Task


### Test Prep Multiple Choice


### Test Prep Short Answer


### Test Prep Extended Response
