1. Foundations of Physical Science
Workshop: Ropes & Pulleys: Mechanical Advantage

2. Ropes & Pulleys: Mechanical Advantage
CPO Science

3. Key Questions
What are simple machines?
How do simple machines work?

4. Overview Build a simple machine using ropes and pulleys
Measure the input and output forces of different pulley arrangements needed to lift load
Compare the input force needed by different pulley arrangements to lift load

5. Simple Machines Include:
rope and pulley
wheel and axle systems
gears
ramps
levers
screws
Simple machines transform input forces into output forces. The concept of mechanical advantage is the measure of how much the forces are increased or possibly decreased.
When we use simple machines, we apply an input force to accomplish some task, and the machine converts it into an output force that makes the task easier, or provides us with a more convenient option to accomplish the task.
For instance, we can climb a ladder, or we can go up stairs( a kind of ramp ) to reach to top of a tower. Either way, we wind up the same height off the ground. However, the stairs allow us an easier option than the ladder to reach to the top.

6. Pulleys as Simple Machines
Simple machines can change the direction and/or magnitude of an Input Force
Mechanical systems and machines require an input force to achieve an output force.
Pulleys can have one supporting strand, like the simple diagram, or more than one, like the pulley system used to lift the elephant. That kind of pulley arrangement is called a block and tackle.

7. Pulley Investigation #1
Add a few weights (3 or 4) to the bottom block
The bottom block and the weights are the load to be lifted
Use the Force scale to measure the weight of the load - record it
In this investigation we need a load to lift, and naturally the bottom block is it. To really get a good tactile feel of the effect we are looking to investigate, we add some weights to the bottom block, making it much heavier than on its own. This way, we’ll be able FEEL the advantage of using the pulley system to accomplish a task. Use the force scale to measure the weight of the load like the diagram on the slide, and record your result.
What does the Force Scale Measure? The force scale measures how much gravity is pulling ( down) on the load ie: its weight. If we apply this exact same force in the opposite direction ( up) while we measure the weight of the load, the load will hang from the end of the scale and not move, the forces are balanced in the up and down direction. If we lift the scale up while we measure the load, we must be applying more force than gravity is applying, and therefore the load is moves in the upward direction. Try this and look at the scale while the load is lifted quickly, it should indicate greater force is applied at this time. The opposite is true when the block is allowed to drop, there must not be enough force being applied to the load, and therefore gravity wins the tug of war and the load moves downward.

8. Pulley Investigation #1
Why does the pulley have so many strings?
Red Strings support bottom pulley block only when hanging
Yellow String is the one we pull to lift the lower block, it then supports the block and transfers the lifting force to the block
The Red strings just keep the lower and upper block together when not in use and simply provides the support while hanging. Once the yellow string is pulled on, the red string no longer provides support, and you’ll see it just sag as the weight of the lower block becomes supported by the yellow string.
The yellow string supports the block while lifting, and can take different configurations as we experiment with different ways to loop it through the pulley system.

9. How Can We Lift the Block?
1. We can attach the yellow string to the bottom block and then thread it up and over the top set of pulleys and pull
OR….
2. We can attach the yellow string to the top block, thread it down through the bottom pulley set and then up and over the top set of pulleys and pull
We have two places we can attach the string, the bottom block or the top block. Both options lead to the string eventually going up and over the top pulley set so we have a string to pull on. But there really is a difference; When connected to the bottom block, there is a total of one string supporting the weight and providing the lifting force, just that one strand of yellow string. When connected to the top, and threaded down and then up and over, there is actually two strands of strings supporting the weight and providing the lifting force. Try these two set ups and see if you can feel a difference in the force required to lift the weight of the bottom block.

10. Measure the Input Force
Attach the Spring Scale to the pulling end of the yellow string
Pull on the string and lift the load - read the value from the scale as this happens
Lower the load with the string - again read the scale as this happens
Average the two values from the scale - this is the value of your Input Force
This is Investigation 4.1 and you can follow along with your handout/Investigation Manual. When there is just one supporting string, that one string is supporting all the weight of the load. Lifting the load by pulling the string means that the output force of the string has exceeded the weight force of the load, so it moves up. Lowering the load means that the output force is less than the weight, and it moves downward. The average of these two values applied to the string will be the value we use for the input force. With only one supporting string, we’ll see that input force = output force. The force required to lift the load will be equal to its weight.

11. Measure the Input Force for Two Supporting Strands
Unclip the yellow string from the bottom block
Thread the string through the lower set of pulleys
Attach the yellow string to the top block
Repeat the Input Force measurement process for TWO supporting strings
When there is just one supporting string, that one string is supporting all the weight of the load. Lifting the load by pulling the string means that the output force of the string has exceeded the weight force of the load, so it moves up. Lowering the load means that the output force is less than the weight, and it moves downward. The average of these two values applied to the string will be the value we use for the input force. With only one supporting string, we’ll see that input force = output force. The force required to lift the load will be equal to its weight.

12. Looping the String Around the Pulleys
With either set up, the # of supporting strings can be increased. This is done by unclipping the string and threading it up and over or under and up both pulley sets. Doing this can allow for up to 6 strings to be used to support the load. It turns out there can be either odd, or even #s of supporting strings depending on whether the top or bottom block is the attachment site. You can see that unclipping the string on the one supporting string set up, threading it under the bottom pulley set, and then up and clipping it to the top block will create a two string support set up. From here, we can unclip the string, go up and over and clip it to the bottom block and we’d have three supporting strands. By continuing this process we can work our way all the way up to 6 supporting strings. At each set up the input force to hold the block up should be measured, and recorded in the data table provided.
Interesting Aside: Some of the more creative people may discover that the string can continue to be looped around and around. We’ve gone up to 12 supporting strings, and it really makes a difference. However, since so many sets of strings are rubbing against one another when they are double-looped, friction begins to add up and offset the additional mechanical advantage gained. This happens when;
Total Frict. of strings rubbing+Total Frict. of pulleys=Weight of load/# of sup. strings
Supporting strings #: 1, 3, 5
Supporting strings #: 2, 4, 6

13. Forces Involved
The Weight of the load does not change, it is the same for each trial
The Output Force will be the force required to hold the load still– it does not change since the weight remains the same
As more strings are added, the Input Force required to achieve the same Output Force decreases
Each new strand of supporting string that is added to the total # of supports provides lift. When there is one string, the force is the weight of the load. When there is two strings, the force is half the weight of the load. When there are three strings, the force is one-third the weight of the load. This pattern continues throughout the Investigation. The total weight is split up evenly between each supporting string, and that is the force required to hold the load in place. Any extra force applied to the string by pulling will result in more lift up than the downward pull of gravity and the load will move up. Anything less than this and the load will move down. Just the right amount, and the load will stay put, because the net force acting on it is zero.

14. Mechanical Advantage Ratio of Output Force to Input Force
The Mechanical Advantage is calculated by dividing the Output Force by the Input Force. This is used for ANY simple machine. After the trials for 1-6 strings have been completed it is time to look at the results obtained. It becomes clear that the more strings used to support the load, the force needed to lift the load decreases. We call this an Inverse Relationship. The relationship between the mechanical advantage and the # of strings supporting the load may become much clearer at this point.
Ratio of Output Force to Input Force
Follows simple pattern with Ropes and Pulley system

15. What is the Mathematical Rule?
We found that the input force required to lift the load decreased as the # of supporting strings increased
What is the relationship?
# of strings x Input Force = Weight of load
# of strings = Mechanical Advantage
The mechanical advantage of a pulley system is equal to the number of strings. Each string helps to share the load, and thus reduces the amount of force required to lift it. However, we find we have to pull much more string through the pulley as we add supporting strings. We don’t get something for nothing; Less force required means more string needs to be pulled. It may take longer, and it may take lots of string, but with pulleys, really heavy loads can be lifted without a lot of force.