# Pulley physics

Wells, elevators, construction sites, exercise machines and belt-driven generators are all applications that use pulleys as a basic function of the machinery. An elevator uses counter weights with pulleys to provide a lift system for heavy objects. Belt driven generators are used to provide backup power to modern-day applications such as a manufacturing factory.

Military bases use belt-driven generators to provide power to the station when there is a conflict. The military uses generators to provide power to military bases when there is no external power supply. The applications of belt-driven generators are enormous. Pulleys are also used to lift cumbersome objects in construction, such as a human being cleaning windows on a very tall building or even lifting very heavy objects used in construction.

The belt generators are powered by two different pulleys moving at two various revolutions per minute, which means how many rotations a pulley can complete in a minute. The reason why the pulleys rotate at two different RPMs is that it affects the period or the time it takes the pulleys to complete one rotation or cycle.

Period and frequency have an inverse relationship, meaning the period affects the frequency, and the frequency affects the period. Frequency is an essential concept to understand when powering specific applications, and frequency is measured in hertz. Alternators are also another form of a pulley-driven generator that is used to recharge the battery's in the vehicles that are driven today. Many types of generators use alternating current and some use direct current. The first direct current generator was built by Michael Faraday which showed that both electricity and magnetism are a unified force called the electromagnetic force. Pulley systems are used in mechanics problems in physics. The best way to solve pulley problems in mechanics is by utilizing Newton's second law of motion and understanding Newton's third and first laws of motion. Where, F is for the net force, which is the vector sum of all the forces acting on the object.

Acceleration gives Newton's second law its vector property. In the given examples of pulley system problems, familiarity with algebraic substitution will be required. The most simple pulley system to solve is a primary Atwood's machine using algebraic substitution. Pulley systems are usually constant acceleration systems. An Atwood's machine is a single pulley system with two weights attached with one weight on each side of the pulley.

The problems regarding an Atwood's machine consist of two weights of equal mass and two weights of uneven masses. If an Atwood's machine consists of one 50 kilogram weight to the left of the pulley and a kg weight to the right of the pulley, what is the system's acceleration?

If tension is pulling up in the positive direction therefore the tension is positive, clockwise going with with respect to a clockwise rotation. If the weight is pulling down in the negative direction therefore the weight is negative, counterclockwise opposing with respect to a clockwise rotation.

If the pulley system was released from rest with two unequal masses and was graphed on a velocity versus time graph, it would produce a linear model, meaning it would not form a parabolic curve but a diagonal straight line starting from the origin. The slope of this graph would produce acceleration. If the system were graphed on a position versus time graph, it would produce a parabolic curve starting from the origin if it was realized from rest.

The slope of the graph of this system would produce the velocity, meaning the velocity varies throughout the pulley system's motion. A pulley system with friction is a system that interacts with some surface that has resistance, slowing the pulley system down due to frictional forces.

In this cases the surface of the table is the form of resistance interacting with the pulley system, slowing the system down.

### Pulley – Simple machines – Physics

The following example problem is a pulley system with frictional forces acting on the system. The frictional force in this case is the surface of the table interacting with the block of wood.

A 50 kg block rests on a table with a coefficient of friction between the block and the table of 0. The second block is hanging on the right side of the pulley and has a mass of kg.Several interesting situations can be set up with pulleys to test students' understanding of Newton's second law of motion, the law of conservation of energy and the definition of work in physics.

One particularly instructive situation can be found from what is called a differential pulley, a common tool used in mechanic shops for heavy lifting. As with a lever, increasing the distance over which a force is applied, compared to the distance the load is lifted, increases the mechanical advantage, or leverage.

Suppose two blocks of pulleys are used. One attaches to a load; one attaches above to a support. If the load is to be lifted X units, then the bottom pulley block must also rise X units. The pulley block above does not move up or down. Therefore, the distance between the two pulley blocks must shorten X units. The lengths of line looped between the two pulley blocks must each shorten X units. If there are Y such lines, then the puller must pull XY units to lift the load X units.

The mechanical advantage is said to be Y This leveraging is a result of the law of conservation of energy. Recall that work is a form of energy. By work, we mean the physics definition: force applied to a load times distance over which the load is moved by the force. So if the load is Z Newtons, the energy that it takes to the lift it X units must equal the work done by the puller. In other words, ZX must equal force applied by puller XY.

An interesting equation arises when you make the line a continuous loop, and the block hanging from the support has two pulleys, one slightly smaller than the other. Suppose also that the two pulleys in the block are attached so that they rotate together.

Note that if the radii differ by only 2 percent, the mechanical advantage is a whopping to Such a pulley is called a differential pulley. It is a common fixture in car repair shops. It has the interesting property that the line that the puller pulls can hang loose while a load is held aloft, because there is always enough friction that the opposing forces on the two pulleys prevent it from turning. Suppose two blocks are connected, and one, call it M1, hangs off a pulley.

How fast will they accelerate? Acceleration is unknown. Keep in mind that M1 and M2 will be accelerated together. What if both blocks are hanging? Then the left-hand side of the equation has two addends instead of just one.

The lighter one will travel in the opposite direction of the resultant force, since the larger mass determines the direction of the two-mass system; therefore, the gravitational force on the smaller mass should be subtracted. Then the left-hand side above changes from Mg to Mg-Mg. Acceleration, a, is then trivially solved arithmetically. Paul Dohrman's academic background is in physics and economics.

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About the Author. Copyright Leaf Group Ltd.Both pulleys and levers have been utilized for centuries as a means of accomplishing heavy tasks. These simple machines utilize the laws of physics to efficiently move weight over a distance.

They allow a single person to move weights that a human would be incapable of lifting without the intervention of such tools. If you feed a rope over the top of a single pulley and lift a weight with it, you will be pulling the rope the same distance as the weight is lifted, and effectively lifting the same weight.

However, if you attach the rope to the bottom of the pulley's frame, run it through another pulley and back up through the first, you will then be pulling the rope twice the distance that the weight is lifted, but lifting only half of the weight.

The practical result of this is that you could lift, for example, a pound weight 10 feet by pulling a rope 20 feet with what feels like a weight of 50 pounds on it. This principle can be extended indefinitely by adding more pulleys. The ratio of weight to distance can also be modified by using pulleys with different diameters. This is essentially the same principle as the familiar operation of bicycle gears.

When you turn a gear with a large diameter that is attached by a chain to a gear with a small diameter, the smaller gear will rotate more rapidly. By attaching pulleys of different diameters to one another with ropes or chains, you can greatly extend your lifting power by simply pulling the rope or chain for a longer distance than the weight is lifted. A lever operates under the same principle as a pulley, but in a very different physical manner.

If you take a foot board and rest it on a fulcrum at its center, you can place a weight on one end and lift it by pressing down on the other end. The distance you lower one end will be identical to the distance that the other end lifts and will require the same amount of weight.

However, if you offset the fulcrum from the center of the board -- the lever -- you gain a mechanical advantage. If the fulcrum is one foot from one end and nine feet from the other end, you can lift a very heavy weight by simply lowering the long end nine times farther than the shorter end rises. Pulleys and levers and the physics that underlie them are the basis for many modern machines. Everything from water wheels to internal combustion engines utilize the principle of transforming weight into distance.

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About the Author. Photo Credits. Copyright Leaf Group Ltd.One of the most common topics covered in a high school physics class is simple machines. An I think the compound pulley is the coolest simple machine. Let's start with some basic physics. The compound pulley, like all simple machines, uses the work-energy principle. I will skip the explanation of energy it's very abstract and start with this:. Don't worry about the change in energy and just look at the definition of work.

In this form, work is done by a force F pushing over some distance s. OK, here's a quick example. Suppose I push a box across a floor with or without friction, it doesn't matter :.

That means the work will be 10 newtons multiplied by 5 meters for a value of 50 joules. Not too bad, right? Now for the key to simple machines. A simple machine doesn't provide more energy. Instead, it transforms the work. What if you want to do 50 joules of work and instead of pushing with 10 newtons, you just push with 1 newton? You would have to move the block 50 meters to get the same 50 Joules of work.

A simple machine increases the distance you push so the required force is less. It's that simple. Maybe that's why they call them simple machines. Actually, probably not. There is a box or something with a string going through the pulley. When you pull down on the right side, the box rises. You would pull down with a the same force required to raise the box. The distance the box rises is the same as the distance you pull down. This is a simple machine, and kind of boring.

To make it interesting, the force that pulls down must move a greater distance than the box rises up. Here is one way of accomplishing that with a compound pulley:. This setup uses two pulleys. By pulling down on the string on the right, the lower pulley rises. Now, here's the magic part—the force you pull down with is lower than the force that pulls up on the load. Of course you must "pay" for this by pulling a larger distance. If the pulley was perfectly frictionless with massless pulleys then the work done lifting the box would be the same as the work done pulling the string.

I can write this as:. For this configuration, the load should rise about half the distance that the string is pulled but with twice the force. Let's get right to it and see if this actually works.

I made a quick pulley system and used spring scales to measure the forces. Take a look:. It's difficult to get measurements from a gif, so let me do it for you.Pulleys are simple machines that have been used to help humans construct large buildings and structures for thousands of years. Pulleys are an example of how engineering and physics work together to make a job easier. Kids can learn more about engineering and physics by playing with pulleys. Try this fun pulley physics activity and let your kids make their very own DIY pulley system.

Related post: Engineering Projects For Kids. A pulley is a simple machine. Pulleys were invented thousands of years ago by early humans and have been in use since around BC. The Mesopotamians are credited with inventing the pulley, although it may have been in use in other places before that time. Pulleys were used to move heavy rocks to construct buildings and even the pyramids. A pulley uses a string wrapped around a wheel or other anchor point.

One end of the string is attached to an object, while the other end is pulled to lift the object. The more anchor points on a pulley, the easier it is to lift something. This works with the principles of force. The more anchor points you have in a pulley system, the bigger the mechanical advantage of the pulley.

Each anchor point reduces the mechanical load by half. However, the more anchor points you have, the longer the string must be to lift the object. Before starting the construction of a pulley, discuss the invention of pulleys, their science, and how they work.

Show the kids how lifting a container of heavy rocks is difficult if you try to pull straight up. This activity will let the kids experiment with command hooks to create their own pulley system. They will learn how adding additional anchor points makes lifting with a pulley even easier. However, a small load should be just fine. You can always attach the command hooks directly to a wall that you are ok possibly damaging. Start with just one hook and keep adding additional hooks. Try looping your string around the command hooks in different patterns.

Compare how easy it is to lift the rocks depending on the arrangement of the hooks and the number of hooks. Let your kids really experiment with this and see who can create the best pulley system using your given materials. Salt Pendulum Science Activity.

Making Water Defy Gravity Experiment. Static Electricity Ghosts. Simple Radiation And Conduction Experiments. Wrecking Ball Physics Experiment. Sound Experiments. Convection Current Experiment. Make An Electroscope. Your email address will not be published. This site uses Akismet to reduce spam. Learn how your comment data is processed. Please enter your name. Please enter a valid email address.A bucket with mass m 2 and a block with mass m 1 are hung on a pulley system.

Find the magnitude of the acceleration with which the bucket and the block are moving and the magnitude of the tension force T by which the rope is stressed. Ignore the masses of the pulley system and the rope.

## Pulley in Physics – pulley tension problems with solution

The bucket moves up and the block moves down. Figure out which forces affect the bucket and the block. Draw a picture. Write down the force equations for the bucket and the block. Choose a suitable coordinate system and rewrite the force equations to scalar form. Decide what relations will hold for the magnitude of the tension forces TT' and T''. We choose the y- axis the way it is marked on the picture. We rewrite equations 1 and 2 to scalar form:. The following holds for the magnitude of the tension forces:.

Decide what the magnitude of the acceleration a 1 will be in relation to a 2. Imagine that the bucket goes up a distance s what distance does the block go down? Relation between the magnitudes of acceleration a 1 and a 2 :. We have two equations 8 and 9 in two variables T and a 1.

Solve these equations and from equation 7 determine the magnitude of the acceleration a 2. From them we can determine the magnitude of the acceleration a 1 and the force T. We multiply equation 8 by 2 and add both equations up:. Draw all the forces which affect the bucket and the block in the picture. Write the force equations for them. Task list filter? Choose required ranks and required tasks. The table of contents will list only tasks having one of the required ranks in corresponding rankings and at least one of the required tags overall.

If you wish to filter only according to some rankings or tags, leave the other groups empty. Task tags General Qualitative task Graphical task Task with unusual solution Complex task Task with theory Task requires extra constants.But pulleys are so important that people give them their own category. A pulley is a wheel with two raised edges. The raised edges are so that a rope or a string will run along the wheel without coming off.

We also call a pulley a block and tackle. So maybe not. Anyway somebody invented pulleys around that time. You can use a pulley to make it easier to pull a rope, or to change the direction of a force. Or a pulley can get you more mechanical advantage to lift something heavier than you can lift by yourself. With a fixed pulleyyou attach a pulley to a hook or a wall. For instance, you can pull down in order to lift something up, or you can pull the upper clothesline toward you in order to move the lower clothesline away from you. With a movable pulleyyou do have a mechanical advantage.

You can pull with less force for a longer distance to get the same work done. This lets you lift things that would be too heavy for you without a pulley.

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Kinetic Energy, Gravitational & Elastic Potential Energy, Work, Power, Physics - Basic Introduction

Learn how your comment data is processed. Pulley — Simple machines — Physics. Clothesline pulley. Cite this page: Carr, K. April 14, About the Author: Karen Carr. Related Posts. Why is the sky blue?

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