Math Experiment

Today I did an experiment in math. My dad and I ran rope through a pulley, which was attached to a beam on a ladder.  Once we ran the rope through the pulley we tied it to a bucket that had a 25 pound weight in it. We measured the distance from the knot on the bucket to the bottom of the pulley. This was the maximum amount the bucket could go up before running into the pulley.  This distance was 26 inches.  With the weight and the distance moved, we calculated the work to move the weighted bucket from the floor to its highest point.

For our second experiment, we added another pulley, which is called a block and tackle. This time, I had to pull the rope 56 inches to get the bucket to move the same 26 inches off the floor. When there were three pulleys, I had to move the rope 93 inches to get the bucket to move 26 inches. When there were 4 pulleys, I had to move the rope 116 inches.

My dad asked me to figure out how much I would need to pull the rope if there were five pulleys.  To start, I calculated the work with one pulley.Work equals force times distance or w=fd. So for the first equation of work is 650 lbs in = (25 lbs)(26in). The bucket weighed the same in each experiment and it moved the same in each experiment, so the work done in each experiment was the same. However the amount of force I had to use to pull the bucket seemed to decrease the more pulleys we added. This makes sense because the work done to the bucket has to be equal to the work I did.   Since I moved more each time a pulley was added, it makes sense that it would be with less force.  It is like a trade, you are trading distance for force. Next, I made a line graph to the show how a decrease in force relates to an increase in distance. `Last, I calculated a ratio between distance I had to pull the rope and number of pulleys.  I figured out this was about 29.  With this ratio I was able to predict that I would have to move 145 inches.  I used that value in the work equation to predict that I would only need 4.4 lbs of force to lift 25 lbs if I had 5 pulleys.

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