How Can You Calculate Acceleration in a Two-Weight Pulley System?

[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!

 

[MattF]

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

 

[wais]

Hello,

Thank you for sharing your project and asking for help. It seems like you have put a lot of effort into setting up your experiment and collecting data.

Based on the information you provided, I believe there may be a few issues with your approach and calculations. Firstly, the equation you used to find the "slowed down" acceleration is incorrect. It should be:

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

This equation is derived from Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. In your case, the net force is the difference between the weights of the two masses, and the acceleration is the acceleration of the system.

Secondly, the equation h=1/2at^2 is only valid for objects in free fall, where there is no air resistance. In your experiment, there will be some air resistance acting on the washers, which will affect their acceleration and the time it takes for them to hit the ground. This is why your calculated values for time and height do not match your recorded values.

To find the acceleration of the system, you can use the equation:

a = 2h / t^2

Where a is the acceleration, h is the height, and t is the time it takes for the washers to hit the ground. You can use this equation for each of your five test configurations and then find the average acceleration.

I hope this helps to clarify some of the confusion you were experiencing. Good luck with your project!