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| Force applied over a specific distance. |
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| Energy in a moving object. |
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| Energy that can be released under certain conditions. For Example, potential energy is stored in objects when they are lifted off the ground. It is released when the object falls. |
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| Energy stored in chemicals, such as in a flashlight battery. Chemical energy is potential until it is released in a chemical reaction. |
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| Energy in moving electrons in a electric current. |
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| Push or Pull. A force has a magnitude (strength) that you can measure, and it has a direction. |
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| Attractive force between objects. |
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| Force that results from the interaction between two surfaces that are touching each other. Friction acts as a resistance to the movement of an object. |
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| What is the formula to measure force? |
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| Force = Mass × Acceleration |
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| Force that pushes materials together. |
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| Force that pulls materials apart. |
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| Mechanical Advantage (MA) |
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Definition
Load/Effort
Effort Distance/Load Distance |
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| Stationary element that holds the lever but still allows it to rotate. |
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| Object to be lifted or squeezed. |
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| The part of the lever from load to fulcrum. |
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| Forced applied to lift or squeeze. |
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| Effort arm (effort distance) |
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| Part of the lever from force to fulcrum. |
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| In a class 1 lever, the fulcrum is between the load and the effort. If the fulcrums is closer to the load than to the effort (as it usually is), the lever has a mechanical advantage. |
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| 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. |
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| In a class 3 lever, the effort is between the load and the fulcrum. |
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(2 kg × 8 ft) + (4 kg × 6 ft) = (8 ft × F)
16 + 24 = 8F
40 = 8F
F = 5 kg
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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 me- chanical advantage.
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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.
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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
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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.
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| Example of Sheave System. |
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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.
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The figure shows an inclined plane. What is the mechanical advantage? If the load weighs 400 lb, how much force is needed to push it up the ramp?
[image] |
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Definition
MA = 12/3 = 4
MA = load/effort
4 = 400/effort
4 × effort = 400
Effort = 100 lb
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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.
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The figure shows a wedge. What is the MA?
[image] |
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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.
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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
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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 ∏ ×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.
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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. For wheel- and-axle machines, mechanical advantage is calculated as follows:
MA = effort distance (radius of the wheel)/load distance (radius of the axle)
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The figure shows a brace and bit, a kind of heavyduty screwdriver that is an example of a wheel and axle as a simple machine. What is the MA?
[image] |
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Definition
Effort distance/load distance = MA
6 in./0.25 in. = 24
MA = 24
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A compound machine is one in which two or more simple machines work together. For example, a screwdriver (wheel and axle) driving a screw is a compound machine. To find the mechanical advantage of a compound machine, multiply the MA of the simple machines together.
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When a load of any kind is supported by two support beams, posts, or people, the load is perfectly balanced if it is exactly centered. In that case, each beam, post, or person is bearing exactly half the load. However, if the load is not centered, then the beam, post, or person nearer to the load is bearing the greater part of the weight.
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Which of these four shelves can bear the most weight?
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Choice D can bear the most weight. Of the four shelves, it is the strongest because it has the largest brackets, and because it has the most brackets.
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Which bridge is the strongest?
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In the diagram, bridge C is the strongest because its framework is made of many triangles.
A structure in which the support beams form rectangular shapes is not as strong as one in which the beams form triangular shapes. The reason is that while rectangular supports can easily bend out of shape, a triangle keeps its shape unless it falls apart entirely. That’s why triangular shapes are used in support structures such as shelf brackets. That is also why you often see triangular shapes in the support structures of bridges, towers, and other buildings.
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| What is the formula to calculate the speed of a particular pulley in a system of pulleys? |
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Definition
Speed1 × Diameter1= Speed2 × Diameter2
(Note that pulley speed is measured in revolutions
per minute, or rpm.)
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Pulley 1 measures 9 in. in diameter. Pulley 2 meas- ures 3 in. in diameter. If pulley 1 rotates at 1,200 rpm, how fast will pulley 2 rotate? |
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Speed1 × Diameter1 = Speed2 × Diameter2
1,200 × 9 = 10,800 = Speed2 × 3
Speed2 = 10,800/3 = 3600
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!
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When pulley A runs at 400 rpm, what will be the speeds of pulleys B, C, and D?
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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:
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● Diameter of pulley A/diameter of pulley B = 4/8, so pulley B will run 1/2 as fast as pulley A.
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400/2 = 200 rpm
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● You already know that pulley C runs at the same speed as pulley B.
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● Diameter of pulley C/diameter of pulley D = 4/16 = 1/4, so pulley D will run 1/4 as fast as pulley C.
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200/4 = 50 rpm
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The gears in a system typ- ically 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 driving gear) turns, it turns the other gear (the driven gear). 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.
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Gear A and gear B make up a system of gears. If gear A makes 6 revolutions, how many revolutions will gear B make?
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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.
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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 idler gear.
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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.
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In this pin and slot arrangement, each time the driv- ing 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?
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Definition
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Which point will travel farthest as the wheel makes 10 rotations?
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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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Cams are lobes attached to rotating shafts to push separate pieces, called cam followers. Cams are often found in engines, where they push intake and exhaust valves open when the engine turns. For every complete rotation of the camshaft, the cam follower will move away from and then back to its original position. A spring pushes the follower tight to the cam.
[image]
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Cranks are used to change motion in a straight line to motion in a circle. You’ll find cranks connected to pedals on a bike, and to pistons in a car engine. When a crank makes one complete revolution, the piston must go up and down and return to its original position.
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Air pressure is measured in pounds per square inch. Atmospheric pressure at sea level is 14.7 lb/in2, which is actually quite a bit of pressure. Since it’s present all around us, we don’t notice it. However, if you create a vacuum inside a weak container, the container will be crushed by all that pressure.
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Systems that use compressed air to do work are called pneumatic systems. Air is easily compressed, and the calculations are more complicated than they are with liquids, which usually can’t be compressed. The larger the driven cylinder, the more air pressure it is exposed to, and the greater the force it can exert.
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The “gas laws” apply to air as it is compressed and expanded.
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● When a gas is compressed, it gains thermal energy—it warms up. The gas also gains potential energy, which is why compressed air can be used to drive nail guns and pneumatic hammers.
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● When a given amount of gas expands, its pressure drops and the gas cools.
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● When a gas cools without a change in outside pressure, it loses volume.
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What happens when you increase the air pressure outside a balloon? The balloon shrinks until the pressure inside becomes great enough to balance the pressure outside.
Air pressure is also what keeps airplanes aloft. The bulge on the top of an airplane wing increases the speed of air passing over the wing, and that causes a reduction in pressure. Because air pressure does not change below the wing, the result is an unbalanced upward force. This force lifts the airplane.
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A compressor compresses a fluid, called a refrigerant. The refrigerant warms up, as predicted by the gas laws. Then the refrigerant loses heat (but not pressure) in the condenser. The refrigerant is piped into an evaporator, where it goes through a small hole and evaporates under reduced pressure. Expansion causes the temperature to drop, and the cold refrigerant can pick up heat from the surroundings. This is why the evaporator is placed in the area to be cooled. The condenser is placed where it’s easy to get rid of excess heat—in the backyard for an air conditioner, or in back for a refrigerator.
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| Water Pressure Principles |
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Definition
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Total flow through a pipe system must be the same everywhere because water cannot be com- pressed.
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When liquid speeds up, pressure falls.
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When liquid slows down, pressure rises.
In the diagram, the same amount of water isflowing everywhere in the pipe system. For this to be true, water must be flowing faster at point B than at point A. That means that pressure is lower at point B.
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Water in a container also exerts pressure on the bottom of the container. The deeper the water, the greater the pressure. To find the amount of water pressure in a tank, calculate the total weight of the water and divide by the area of the base of the tank.
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| A tank with a base that measures 2 feet × 4 feet holds 1,600 pounds of water. What is the water pressure at the base of the tank? |
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Definition
2 ft × 4 ft = 8 ft2
1,600 Ib/8ft2 = 200 lb/ft2
Remember too that 1 ft2 = 144 in2. To convert pressure between pounds per square inch and pounds per square foot, divide or multiply by 144.
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Water is being piped into a tank at the rate of 2 gal- lons per second. At the same time, it is being piped out of the tank at the rate of 60 gallons per minute. How many gallons will be added in 5 minutes?
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Definition
Convert the inflow rate so that you are working only with gallons per minute.
gal/sec × 60 = gal/min
2 gal/sec × 60 = 120 gal/min
Subtract:
120 gal/min inflow − 60 gal/min outflow
= 60 gal/min net gain
The net gain in 5 minutes is 5 × 60 = 300 gallons.
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| A 100-gallon tank contains 10 gallons of water. Water is added through one pipe at the rate of 3 gallons per minute. It is drained away through another pipe at the rate of 2 gallons per minute. How long will it take to fill the tank? |
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Definition
Find the net gain of water per minute:
3 gal/min – 2 gal/min = 1 gal/min
It will take 100 − 10 = 90 gallons to fill the tank.
At the rate of 1 gal/min, it will take 90 minutes to fill the tank.
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Chemical Energy: Energy stored in chemicals or released in a chemical
reaction
Compression: A force that pushes materials together
Compound Machine: A machine made up of two or more simple machines working together
Effort: In a lever, the point where you apply force
Effort Arm: In a lever, the distance from the force to the fulcrum
Electrical Energy: Energy in moving electrons
Flexibility: The ability of a material to bend without breaking
Friction: The force that resists the relative motion of two surfaces in contact
Fulcrum: The stationary element that holds a lever but also allows it to rotate
Gravity: An attractive force between objects
Kinetic Energy: Energy in a moving object
Load: In a lever, the part where output force lifts or squeezes
Load arm: In a lever, the distance from the load to the fulcrum
Mechanical Advantage: The amount by which a machine multiplies the force applied to it
Potential Energy: Energy that can be released under certain conditions
Tension: A force that pulls materials apart
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| Laws and Formulas to Know |
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Definition
How to calculate mechanical advantage (MA):
- Lever: MA = load/effort = effort distance/load distance
- Pulley: MA = load/effort = number of supporting strands
- Gears: MA = number of teeth on driven gear/ number of teeth on driving gear
- Sheaves: MA = driven diameter/drive diameter
- Inclined plane: MA = horizontal length/vertical rise
- Wheel and axle: MA = radius of wheel/radius of axle
Speed of pulleys in a system:
Speed1× Diameter1 = Speed2 × Diameter2
The gas laws:
- When a gas is compressed, it heats up.
- When a given amount of gas expands, its pressure drops and the gas cools.
- When a gas cools without a change in outside pressure, it loses volume.
Water pressure:
- Total flow through a pipe system is the same everywhere.
- When liquid speeds up, pressure falls.
- When liquid slows down, pressure rises.
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