An elevator is a modern engineering use of a pulley system that performs much like the raising of a large stone for pyramid building. Without the use of pulleys, an elevator would require a large motor to pull the cable straight up. Instead of using a large motor, some elevators use a large weight that takes advantage of gravity to help raise the elevator car see Figure 3.
In this situation, the powering motor can be much smaller and only be used to determine the direction the elevator should go. Figure 3. Adding a counterweight and two pulleys with a motor in the middle makes an elevator easier to move.
But how can a wheel with string over it help us move the huge stones required to build a pyramid? Well, pulleys help us by changing the direction of the force we use to lift an object. Is it easier for you to pull up on a rope or pull down on a rope? By using a pulley, we do not have to pull up on a rope to lift a heavy object attached to it, but instead we can pull down on it.
Think of a flagpole as an example. When you pull down on the rope of a flagpole, the flag goes up the pole to wave in the air. That's because a flagpole has a pulley on it. By using pulleys to redirect force , a stone could be lifted off the ground, allowing more people to grab on to the rope, and adding weight so workers have to pull less. To simplify this effort even more, workers using a pulley could move a large stone up a ramp by pulling on a rope while walking down the ramp, using gravity to their advantage.
The real mechanical advantage of a pulley is in using many pulleys at once. Using multiple pulleys decreases the amount of force necessary to move an object by increasing the amount of rope used to raise the object.
The mechanical advantage MA of a pulley system is equal to the number of ropes supporting the movable load. That means, do not count ropes that are only used for redirecting, see Figures 6 and 7.
We know from other lessons on simple machines that to gain a greater mechanical advantage, there is a trade-off. With a pulley, the trade-off is distance. So, if two pulleys are used together, the amount of force required is cut in half, but twice the amount of rope is needed to be pulled to raise the object to the same desired height. Illustrate this concept to students by conducting the following classroom demonstration; see Figure 4. Figure 4. Tie the rope to one of the brooms broom 1 and wrap the rope around the other broom broom 2.
Have two students stand about a meter apart each holding one broom, and try to keep the brooms separated while the third student pulls on the free end of the rope; it should be a difficult task to pull the broom sticks together. Next, wrap the rope around each of the brooms again. This is an example showing the power of mechanical advantage.
Refer to the associated activity Pulley'ing Your Own Weight to further students involvement in understanding pulley systems by illustrating how a pulley can be used to easily change the direction of a force, making the moving of large objects easier. Pulleys can be much more complicated.
Engineers combine many pulleys into a pulley system that significantly reduces the amount of force required to lift an object. They often use pulley systems to move extremely heavy objects. A block and tackle is an example of a pulley system that can be attached to anything. It may take a lot of cable or rope, but a human using enough pulleys could lift several tons. Engineers use the block and tackle along with motors and electronics to create modern devices that operate with very low power requirements, such as cranes and elevators.
At Disneyland, engineers even use a pulley system to move Tinkerbell across the sky. We are unsure if the Egyptians used pulleys, and have yet to find any evidence that they did, but we do know, that if they had used them, life would have been easier than if they did not. Now, since we understand pulleys and have modern materials, we can build the pyramids much easier.
Today we are going to look at engineering a pulley system and see if we can design a way to get our heaviest stones to the top of our pyramid with the help of this simple machine. Use the Pulleys and the Pyramids PowerPoint presentation as a helpful classroom tool. Show the PowerPoint presentation, or print out the slides to use with an overhead projector.
The presentation is animated to promote an inquiry-based style; each click reveals a new point about each machine; have students suggest characteristics and examples before you reveal them. The pulley, a simple machine, helps to perform work by changing the direction of forces and making easier the moving of large objects. When thinking of pulleys, most people think of the type of pulley that allows a person to redirect the direction of a force.
With this type of pulley — called a fixed pulley — pulling down on a rope makes an object rise off the ground.
There are also movable pulleys and pulley systems. Thousands of years ago, early engineers used pulleys to help with construction and many useful everyday tasks.
Many obelisks were erected using pulleys and wells have pulleys to help retrieve water. Figure 5. A fixed pulley with no mechanical advantage. The most commonly understood concept of a pulley is that it is a simple machine that redirects force.
This means that by looping rope around a pulley and attaching the rope to an object, one pulls down on the rope to raise the object, instead of having to lift the object see Figure 5; imagine raising a flag. Although this is a helpful and convenient use for pulleys, it has a major limitation: the force you must apply to lift the object is the same amount as if you were just lifting the object without the pulley which is acceptable for raising a flag, but not helpful enough if trying to raise a pyramid stone.
This means that a fixed pulley does not give any mechanical advantage. A fixed pulley configuration is useful for raising an object to a level above your head. Using this type of pulley also enables you to take advantage of gravity. And, by attaching weights to the end of the rope that you pull, you can lessen the amount of force you must apply.
This type of pulley can also be used to balance an object, by attaching objects of equal weight to both sides of the rope, neither object moves. Once a force is applied to either side, the system continues moving in that direction. This kind of pulley system is used in some elevators. The elevator has cable attached to it that goes up, around a pulley, then comes down and attaches to a counterweight.
The motor that moves the elevator car uses much less power since the counterweight keeps the elevator balanced. Figure 6. A movable pulley with a mechanical advantage of two. Another type of pulley is a movable pulley. In a movable pulley system, the rope is attached to a fixed non-moving point, the pulley is attached to the object that you want to move and the other end of the rope is left free see Figure 6.
By pulling on the rope, the pulley moves and the object raises. This type of system is good if you are trying to raise an object located below you to your level. In a variation, if both sides of a movable pulley system are fixed and the rope is taut between the fixed points, the system becomes like a wheel and axle because the object can ride along the rope if a force is applied to it for example, a zip line.
Figure 7. This is generally a common consideration for pulley tension problems. The acceleration a of each subject is indicated. The cart accelerates to the right when the cylinder accelerates downward. Coordinate systems with X-axis and Y axis were used to make calculations easy.
The tight rope ensures that the acceleration of both the cylinder and the cart has the same magnitude. This choice of coordinates means that the acceleration of both objects is along a positive x-axis to the right for the cart; downward for the cylinder.
The acceleration of the cart along x must equal the acceleration of the cylinder, so we have used the same symbol a for both. The cart has no acceleration in the y-direction. As per this setup of the pulley in physics, there is no movement of the cart along the Y-axis positive and negative of Y-axis , and the cart only moves along the positive x-axis.
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