Mechanical Comprehension Study Guide 2 for McGraw-Hill's ASVAB (page 2)
Practice problems for this study guide can be found at:
Many Mechanical Comprehension questions have to do with things that move or rotate: gears, pulleys, and other mechanisms.
Systems of Pulleys
You have already learned about pulleys as simple machines used to hoist heavy objects. Pulleys are also used as drive mechanisms. That is, systems of interconnected pulleys are used to transfer power, and often rotational speed, from one shaft to another. Two pulleys (sheaves) that are connected by a belt will run at the same speed if they are the same size. When the sheaves are of different sizes, the smaller one will run faster than the larger one because the smaller one must make more turns to move the belt the same distance.
In most cases on the ASVAB, you will simply be asked which of two or more interconnected pulleys runs fastest or slowest, and you can easily solve these problems by identifying the smallest or largest pulley. However, if you are asked to calculate the speed of a particular pulley in a system of pulleys, you can easily do so by using the following formula:
Speed1 × diameter1 = speed2 × diameter2
(Note that pulley speed is measured in revolutions per minute, or rpm.)
Pulley 1 measures 9 in. in diameter. Pulley 2 measures 3 in. in diameter. If pulley 1 rotates at 1,200 rpm, how fast will pulley 2 rotate?
Another way to calculate the speed of pulley 2 is to look at the ratio between the two diameters. A ratio of 9:3, or 3:1, will multiply speed × 3. So 1,200 rpm × 3 = 3,600 rpm. Remember that the pulley with the smaller diameter is always the one that rotates faster!
Using these methods, you can calculate the speed of any pulley system as long as you know the diameters of both pulleys and the speed of either pulley.
When pulley A runs at 400 rpm, what will be the speeds of pulleys B, C, and D?
In this system, assume that the linked pulleys (B and C in the example) run at the same rpm, since they are attached to the same shaft. Break the problem down into parts, and calculate them in order:
- Diameter of pulley A/diameter of pulley B = 4/8, so pulley B will run 1/2 as fast as pulley A. 400/2 = 200 rpm
- You already know that pulley C runs at the same speed as pulley B.
- Diameter of pulley C/diameter of pulley D = 4/16 = 1/4, so pulley D will run 1/4 as fast as pulley C.
200/4 = 50 rpm
Systems of Gears
Another way to transfer power between shafts is through systems of gears. The gears in a system typically have different diameters and different numbers of teeth per gear. The teeth of one gear mesh with the teeth of another, and as one gear (the drivinggear) turns, it turns the other gear (the drivengear). When interlocking gears have different numbers of teeth, the gear with fewer teeth will rotate more times in a given period than the gear with more teeth. To see how this works, look at the following example.
Gear A and gear B make up a system of gears. If gear A makes 6 revolutions, how many revolutions will gear B make?
To solve this problem, use the picture and your common sense. Count the teeth on each gear. Gear A has 9 teeth. Gear B has 27 teeth. The ratio of the teeth on the two gears is 9:27 or 1:3. Common sense should tell you that gear A must rotate 3 times to make gear B rotate once. So if gear A rotates 6 times, gear B will rotate twice. Always keep in mind that in this kind of system, the gear with more teeth makes fewer rotations in the same period than the gear with fewer teeth.
Notice, too, that gears change the rotation direction, while pulleys usually do not. To rotate a gear in the same direction as the driving gear, you need a third gear, called an idlergear.
In this system, gear A (the driving gear) is rotating clockwise. Gear B is the idler gear. Gear A makes gear B rotate counterclockwise. Gear B then makes gear C rotate clockwise, the same direction as gear A.
Rotating Wheels and Disks
Another way to drive shafts is to use what is called a pin and slot arrangement. In this arrangement, a pin is attached to a driving shaft, and a slotted disk is attached to a driven shaft. When the driving shaft rotates, the pin enters a slot on the disk and turns the driven shaft.
In this pin and slot arrangement, each time the driving shaft turns one full revolution, the disk on the driven shaft will make 1/4 revolution. How far will the disk rotate when the pin turns three complete revolutions?
3 × 1/4 = 3/4 turn.
You may also be asked simple questions about what happens to points on a wheel when the wheel turns.
How many rotations will point A make when point C makes 5 rotations? Point A will make 5 rotations because Point A and Point C are both fixed on the same wheel.
Which point will travel farthest as the wheel makes 10 rotations? Point B will travel farthest because it is farthest from the center. The distance it travels in each rotation is greater than the distance traveled by the other points.
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