# Homework Help: Pulley system acceleration

1. Nov 6, 2004

### MattF

Hi, I'm working on a project involving a two-weight pulley system. The idea is to take two washers of slightly different masses and devise a method of determining a numerical value for the acceleration of gravity using the pulley. Basically the pulley slows down the effect of gravity, and I need to find that new acceleration.

mass one = 13.92 g = 0.01392 kg
mass two = 16.31 g = 0.01631 kg

I set up five test configurations at different heights, so I have five heights total. Then I released the washers and recorded the time it took to hit the floor with a friend (so three sets of two values). Then I averaged them. So, at this point I have five different hieghts, each with an average time it took to hit the floor. Here are three of them:

height one = 1.02 m
time = 1.78 s

height two = 1.115 m
time = 1.728 s

height three = 12.22 m
time = 1.843

Now, here is where I'm starting to have doubts. This is an equation I used to find the "slowed down" acceleration.

gravity * (mass one - mass two) = (mass one + mass two) * acceleration

This equation doesn't need the time, and I'm REALLY starting to wonder. Using this equation I get an acceleration value of 0.7756 m/s^2. To verify this, I take the first height of 1.02 m and use this derived equation:

t^2 = (2*height)/acceleration (from h= 1/2at^2)

Take the square root and you get a value of 1.62 seconds. Height two, I get 1.70 seconds, height three 1.78 seconds. What's wrong here??? Those are NOT the recorded values I have!!

Another verification is h=1/2at^2

For the first time (my recorded value and a=0.7756), h = 1.23 m. What is wrong HERE too???

Basically I am VERY confused. Can someone PLEASE help me out? I need the acceleration of the system using my recorded times and heights. Any help is very much appreciated!

2. Nov 6, 2004

### MattF

Just to add a comment here, the pulley system is the two weights on your basic pulley, friction and string weight negligible. Thanks!