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Mechanical Comprehension Study Guide 1 for McGraw-Hill's ASVAB (page 2)

By — McGraw-Hill Professional
Updated on Jun 26, 2011

Principles of Mechanical Devices

Machines are devices that multiply force or motion. Some machines are simple devices that involve only a single force. A lever is an example. Other machines involve combinations of devices working together. A bicycle is an example. The essential thing about all machines is that in order to make them multiply your force, you must exert that force over a longer distance. You'll see how this works in the following section, which describes the main simple machines one by one. First, however, you need to learn how to calculate how much a machine multiplies your force.

Mechanical Advantage

The amount your force is multiplied by a machine is called the mechanical advantage, or MA. There are two ways to calculate MA.

  1. Divide the output force (called the load or sometimes the resistance) by the input force (called the effort): Load/effort = MA.
  2. Example

    With a lever, you use a 50-lb force (the effort) to lift a 200-lb weight (the load). What is the mechanical advantage of the lever? 200/50 = 4. MA = 4.

  3. Divide the length of the effort (called the effort distance) by how far the load moves (called the load distance): Effort distance/load distance = MA.
  4. Example

    With a pulley, you use 5 feet of rope (the effort distance) to lift a load 1 foot (the load distance). What is the mechanical advantage of the pulley? 5/1 = 5. MA = 5

Simple Machines

The simple machines are a group of very common, basic devices that have all been in use for a very long time. They are called simple because each one is used to multiply just one single force. The simple machines include the lever, the pulley, the inclined plane, the gear, the wedge, the wheel and axle, and the screw. You can count on the ASVAB to test your knowledge of simple machines.

Levers   The first kind of simple machine is the lever, a device that helps you apply force to lift a heavy object. To understand levers, you'll need to know the following terms:

  • Fulcrum: The stationary element that holds the lever but still allows it to rotate.
  • Load: The object to be lifted or squeezed.
  • Load arm (load distance): The part of the lever from load to fulcrum.
  • Effort: The force applied to lift or squeeze.
  • Effort arm (effort distance): The part of the lever from force to fulcrum.

There are three classes of levers. Let's examine them one at a time and see how to calculate MA for each.

Class 1 Lever In a class 1 lever, the fulcrum is between the load and the effort. If the fulcrum is closer to the load than to the effort (as it usually is), the lever has a mechanical advantage.

Mechanical advantage = effort distance/load distance = load/effort

Example

The figure shows a class 1 lever. What force (effort) is needed to lift the load? Since you know that MA = 3, use this formula to find the effort.

    MA = load/effort
    3 = 150 lb/effort
    3 × effort = 150 lb
    effort = 50 lb

Class 2 Lever In a class 2 lever, the load is between the effort and the fulcrum. The effort arm is as long as the whole lever, but the load arm is shorter. So a class 2 lever always has a mechanical advantage.

Example

The wheelbarrow shown is a class 2 lever. What is its mechanical advantage?

    MA = effort distance/load distance = 3/1.5 = 2

Class 3 Lever In a class 3 lever, the effort is between the load and the fulcrum. Tweezers and tongs are good examples of class 3 levers. The length of the effort arm and the load arm are calculated from the fulcrum, as with the class 2 lever.

Example

The figure shows a class 3 lever. What is the mechanical advantage?

    MA = load/effort = 1/2 = 0.5

In other words, 2 pounds of effort would produce 1 pound of "squeeze" on the orange. We could call this a fractional mechanical advantage, or a mechanical disadvantage. But in return for reducing the squeezing force, each inch of effort movement produces 2 inches of load movement.

Balancing a Lever Some ASVAB problems may show you a diagram of a lever with various parts marked and ask you what force or weight is needed to balance the lever. To answer this kind of question, keep in mind that the moments of force (effort or load = distance) on either side of the fulcrum must be equal. Here is an example.

Example

What is the force F, in kilograms, needed to balance the lever? Add up the moments of force on either side of the fulcrum:

    (2 kg × 8 ft) + (4 kg × 6 ft) = (8 ft × F)
    16 + 24 = 8F
    40 = 8F
    F = 5 kg

Pulleys   Another kind of simple machine that helps you lift a heavy object is the pulley, also called a block and tackle. In pulleys, the mechanical advantage is found in either of the following two ways:

  • MA = effort distance/load distance.
  • MA = number of supporting strands. Supporting strands of rope or cable get shorter when you hoist the load. We'll return to this, but don't just count strands—some do not shorten as you hoist.

Example

The figure shows a pulley attached to a beam that is used to hoist a heavy crate. Each foot of pull on the rope lifts the crate 1 foot. Effort distance = load distance, so MA = 1. Although this pulley allows you to pull down instead of up, it gives no mechanical advantage.

Example

The figure shows two pulleys. When you hoist, two strands of the rope must be shortened. So for every 2 feet of pull (effort distance), you get 1 foot of lift (load distance).

    MA = effort distance/load distance = 2/1
    MA = 2

The simplest way to find the pulley MA is to count the strands of rope on the movable pulley (in this case, the one attached to the load). MA = number of supporting strands.

Until now, we have ignored friction and the weight of the movable pulley and extra rope. As MA increases, these factors also increase, so there is a practical limit to the mechanical advantage of pulleys.

Gears   Gears are a simple machine used to multiply rotating forces. Finding the MA of a gear is simplicity itself. Identify the driving gear (the one that supplies the force) and count the teeth. Count the teeth on the driven gear. Then use this formula:

Number of teeth on driven gear/number of teeth on driving gear = MA

Example

The figure shows a driving gear with 9 teeth and a driven gear with 36 teeth.

    36/9 = 4
    MA = 4

You will learn more about systems of driving and driven gears later in this chapter.

Sheaves   Sheaves (often also called pulleys) and belts are a simple machine closely related to gears. To calculate the MA of a sheave system, divide the diameter of the driven sheave by the diameter of the drive sheave:

    MA = driven diameter/drive diameter

Whenever the driven sheave is larger than the drive sheave, you get a mechanical advantage.

Example

The figure shows a sheave system. What is the MA?

    9/3 = 3

You will learn more about systems of sheaves (pulleys) later in this chapter.

Inclined Plane   Inclined plane is a fancy term for "ramp." An inclined plane is another simple machine that is used to lift heavy objects. The formula for finding the mechanical advantage of an inclined plane is as follows:

    MA = length of the slope/vertical rise

To find the mechanical advantage, measure vertically and diagonally along the ramp.

Example

The figure shows an inclined plane. What is the mechanical advantage?

    MA = 12/3 = 4

If the load weighs 400 lb, how much force is needed to push it up the ramp?

    MA = load/effort
    4 = 400/effort
    4 × effort = 400
    Effort = 100 lb

In real life, friction can play a huge role in ramps if the load is not on wheels. Most ASVAB problems will allow you to ignore friction in dealing with all simple machines.

Wedge   The wedge is a type of inclined plane. It is one of the rarer simple machines. As always, MA = effort distance/load distance. The wedge is essentially two inclined planes, and the MA calculation also requires you to measure perpendicular to the long axis of the wedge.

Example

The figure shows a wedge. What is the MA?

Every time the wedge moves 5 inches, the load will move 2 inches. MA = 5/2 = 2.5. In reality, friction plays a major role in wedges.

Screw   Screws are some of the handiest simple machines, although we usually think of a screw as a fastener rather than as a way to multiply force. Finding mechanical advantage can be complicated because it comes from two sources: the threads and the wrench you use to tighten the screw. But if you consider effort distance and load distance, the calculation is simple.

    MA = effort distance/load distance

Example

The figure shows an 8-inch wrench turning a screw with 8 threads per inch. This screw has a pitch (movement per turn of the screw) of 1/8 inch. The effort distance is π × diameter = 3.14 × 16 inches = about 50 inches. The load distance per turn of the wrench is 1/8 inch, so MA = 50/1/8 = 400. In reality, the MA is much less, because of friction and because you don't push on the absolute end of the wrench. But this still demonstrates the power of screws as simple machines!

Most ASVAB questions will not require this much calculation, but it never hurts to be prepared!

Wheel and Axle   Wheels are a common and essential part of daily life, but most of these wheels are not simple machines. Instead, they are a way to reduce friction by the use of bearings. A wheel and axle is a simple machine only when the wheel and axle are fixed and rotate together.

A typical wheel-and-axle simple machine is the screwdriver. The screwdriver's handle is the wheel, and the screwdriver's blade is the axle. For wheel-and-axle machines, mechanical advantage is calculated as follows:

    MA = effort distance (radius of the wheel)/load distance (radius of the axle)

So for a screwdriver, MA = radius of the handle/ radius of the blade.

Example

The figure shows a brace and bit, a kind of heavy-duty screwdriver that is an example of a wheel and axle as a simple machine. What is the MA?

    Effort distance/load distance = MA
    6 in./0.25 in. = 24
    MA = 24

A wheel and axle can also give a mechanical disadvantage. In a car or a bicycle, where the axle drives the wheel instead of the wheel driving the axle, a small motion at the axle creates a large motion at the circumference of the rim. In these cases, you need a larger force, but you get more motion in return.

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